Spin-boson dynamics A unified approach from weak to strong coupling

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Annu.Rev.Phys.Chem.2000.51:129–52Copyright c2000by Annual Reviews.All rights reserved G ENERALIZED B ORN M ODELS OFM ACROMOLECULAR S OLVATION E FFECTSDonald Bashford and David A.CaseDepartment of Molecular Biology,The Scripps Research Institute,La Jolla,California 92037;e-mail:bashford@,case@Key Words solvation energy,continuum dielectricss Abstract It would often be useful in computer simulations to use a simple de-scription of solvation effects,instead of explicitly representing the individual solvent molecules.Continuum dielectric models often work well in describing the thermo-dynamic aspects of aqueous solvation,and approximations to such models that avoid the need to solve the Poisson equation are attractive because of their computational efﬁciency.Here we give an overview of one such approximation,the generalized Born model,which is simple and fast enough to be used for molecular dynamics simulations of proteins and nucleic acids.We discuss its strengths and weaknesses,both for its ﬁdelity to the underlying continuum model and for its ability to replace explicit con-sideration of solvent molecules in macromolecular simulations.We focus particularly on versions of the generalized Born model that have a pair-wise analytical form,and therefore ﬁt most naturally into conventional molecular mechanics calculations.INTRODUCTIONThere are many circumstances in molecular modeling studies where a simpliﬁed description of solvent effects has advantages over the explicit modeling of each solvent molecule.One of the most popular models,especially for water,treats the solvent as a high-dielectric continuum,interacting with charges that are em-bedded in solute molecules of lower dielectric.The solute charge distribution,and its response to the reaction ﬁeld of the solvent dielectric,can be modeled either by quantum mechanics or by partial atomic charges in a molecular me-chanics description.In spite of the severity of the approximation,this model often gives a good account of equilibrium solvation energetics,and it is widely used to estimate pKs,redox potentials,and the electrostatic contributions to molec-ular solvation energies (for recent reviews,see 1–6).For molecules of arbitrary shape,the Poisson-Boltzmann (PB)equations that describe electrostatic interac-tions in a multiple-dielectric environment are typically solved by ﬁnite-difference or boundary-element numerical methods (1,7–12).These can be efﬁciently solved0066-426X/00/1001-0129$14.00129A n n u . 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F o r p e r s o n a l u s e o n l y .130BASHFORD¥CASEfor small molecules but may become quite expensive for proteins or nucleic acids.For example,the DelphiII program,which is a popular program that computes a ﬁnite-difference solution,takes about 25min on a 195-Mhz SGI processor to solve problems on a 1853grid with 600atoms.Obtaining derivatives with respect to atomic positions adds to the time and complexity of the calculation (13).Even though progress continues to be made in numerical solutions,and other approaches may be signiﬁcantly faster,there is a clear interest in exploring more efﬁcient,if approximate,approaches to this problem.One such simpliﬁcation that has received considerable recent attention is the generalized Born (GB)approach (14,15).In this model,which is derived below,the electrostatic contribution to the free energy of solvation isG pol =−12 1−1w i ,j q i q jf GB , 1.where q i and q j are partial charges,εw is the solvent dielectric constant,andf GB is a function that interpolates between an “effective Born radius”R i ,when the distance r i j between atoms is short,and r i j itself at large distances (15).In the original model,values for R i were determined by a numerical integration proce-dure,but it has recently been shown that “pair-wise”approximations,in which R i is estimated from a sum over atom pairs,can be nearly as accurate and provide a simpliﬁed approach to energies and their derivatives (16–21).In the following sections,we present one derivation of this model and compare it to the underlying continuum dielectric model on which it is based.This is followed by a review of pair-wise parameterizations and of practical applications of GB and closely related approximations.Our emphasis is almost exclusively on the use of this approach to describe aqueous solvation of macromolecules.A comprehensive review of other applications of the GB model has recently appeared (6).GENERALIZED BORN AND RELATED APPROXIMATIONSThe underlying physical picture on which the GB approximation is based is the two-dielectric model described above.To obtain the electrostatic potential φin such a model,one should ideally solve the Poisson equation,∇[ε(r )∇φ(r )]=−4πρ(r ),2.where ρis the charge distribution,and the dielectric constant εtakes on the solute molecular dielectric constant εin in the solute interior and the exterior dielectric constant εex elsewhere.For gas phase conditions,εex =1,whereas in solvent conditions,εex =εw ,the dielectric constant of the solvent (here,water);solving Equation 2under these two conditions leads to potentials that can be denoted φsol and φvac ,respectively.The difference between these potentials is the reaction ﬁeld,φreac =φsol −φvac ,and the electrostatic component of the solvation free energy isG pol =12φreac (r )ρ(r )dV , 3.A n n u . 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F o r p e r s o n a l u s e o n l y .GENERALIZED BORN MODELS 131or if the molecular charge distribution is approximated by a set of partial atomic point charges q i ,G pol =12i q i φreac (r i ). 4.In the case of a simple ion of radius a and charge q ,the potentials can be found analytically and the result is the well-known Born formula (22),G Born =−q 22a 1−1εw. 5.If we imagine a “molecule”consisting of charges q 1···q N embedded in spheres of radii a 1···a N ,and if the separation r i j between any two spheres is sufﬁciently large in comparison to the radii,then the solvation free energy can be given by a sum of individual Born terms,and pair-wise Coulombic terms:G pol =N i q 2i 2a i 1w −1 +12N i N j =i q i q j r i j 1w −1 , 6.where the factor (1/εw −1)appears in the pair-wise terms because the Coulombicinteractions are rescaled by the change of dielectric constant on going from vacuum to solvent.The goal of GB theory can be thought of as an effort to ﬁnd a relatively simple analytical formula,resembling Equation 6,which for real molecular geometries will capture,as much as possible,the physics of the Poisson equation.The linearity of the Poisson equation (or the linearized PB equation)assures that G pol will indeed be quadratic in the charges,as both Equations 1and 6assume.However,in calculations of G pol based on direct solution of the Poisson equation,the effect of the dielectric constant is not generally restricted to the form of a prefactor,(1/εw −1),nor is it a general result that the interior dielectric constant,εin ,has no effect.With these caveats in mind,we seek a function f GB ,to be used in Equation 1,such that in the self (i =j )terms,f GB acts as an “effective Born radius,”whereas in the pair-wise terms,f GB becomes an effective interaction distance.The most common form chosen (15)isf GB (r i j )= r 2i j +R i R j exp −r 2i j /4R i R j 12,7.in which the R i are the effective Born radii of the atoms,which generally dependnot only on a i ,the intrinsic atomic radii,but also on the radii and relative positions of all other atoms.Ideally,R i should be chosen so that if one were to solve the Poisson equation for a single charge q i placed at the position of atom i ,and a dielectric boundary determined by all of the molecule’s atoms and their radii,then the self-energy of charge i in its reaction ﬁeld,q i φreac (r i )/2,would be equal to −(q 2/2R i )(1−1/εw ).Obviously,this procedure per se would have no practical advantage over a direct calculation of G pol using a numerical solution of the Poisson equation.To ﬁnd a more rapidly calculable approximation for the effective Born radii,we turn to a formulation of electrostatics in terms of integration over energy density.A n n u . 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F o r p e r s o n a l u s e o n l y .132BASHFORD¥CASEDerivation in Terms of Energy DensitiesIn the classical electrostatics of a linearly polarizable media (23),the work required to assemble a charge distribution can be formulated either in terms of a product of the charge distribution with the electric potential,as above,or in terms of the scalar product of the electric ﬁeld E and the electric displacement D :W =12 ρ(r )φ(r )dV 8.=18π E ·D dV .9.We now introduce the essential approximation used in most forms of GB theory:that the electric displacement is Coulombic in form,and remains so even as the ex-terior dielectric is altered from 1to εw in the solvation process.In other words,the displacement due to the charge of atom i (which for convenience is here presumed to lie on the origin)isD i ≈q i r r3.10.This is called the Coulomb ﬁeld approximation.In the spherically symmetric case (as in the Born formula),it is exact,but in more complex geometries,there may be substantial deviations,a point to which we turn presently.The work of placing a charge q i at the origin within a molecule whose interior dielectric constant is εin ,surrounded by a medium of dielectric constant εex and in which no other charges have yet been placed,is thenW i =18π (D /ε)·D dV ≈18π in q 2i r 4εin dV +18πex q 2i r 4εex dV .11.The electrostatic component of the solvation energy is found by taking the differ-ence in W i when εex is changed from 1.0to εw ,G pol i =−18π 1−1w ex q ir dV ,12.where the contribution due to the interior region has canceled in the subtraction.1Comparing Equation 12to the Born Formula 5or to Equations 1or 6,we conclude that the effective Born radius should beR −1i =14π ex 1r 4dV .13.1Itmay be noticed that the interior integral contained a singularity at r →0.This a con-sequence of representing the charge distribution as a set of point charges,and similar singularities appear in treatments based on the electrostatic potential.The validity of can-celing out such singularities can be demonstrated by replacement of these point charges by small charged spheres and consideration of the limit as the sphere radii shrink to zero.A n n u . 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F o r p e r s o n a l u s e o n l y .GENERALIZED BORN MODELS 133It is often convenient to rewrite this in terms of an integration over the interior region,excluding a radius a i around the origin,R −1i =a −1i −14π in ,r >a i 1r 4dV ,14.where we have used the fact that the integration of r −4over all space outside radius a is simply 4πa −1.Note that in the case of a monatomic ion,where the molecular boundary is simply the sphere of radius a i ,this equation becomes R i =a i and the Born formula is recovered exactly.The integrals in Equation 13or 14can be calculated numerically by constructing a set of concentric spherical shells around atom i and calculating the fractional area of these shells lying inside or outside the van der Waals volume of the other atoms,j =i (15),or by using a cubic integration lattice (24).Ghosh et al (25)have proposed an alternative approach,in which the Coulomb ﬁeld is still used in place of the correct ﬁeld,and Green’s theorem is used to convert the volume integral in Equation 14to a surface integral.At this level,the S-GB (surface-GB)model is formally identical to the model outlined above.(There are potential computational advantages in the surface integral approach,especially for large systems and for evaluating gradients,but these have not yet been exploited.)In practice,empirical short-range and long-range corrections (discussed below)are added to improve agreement with numerical Poisson theory.Solute Dielectrics Other than UnityStrictly speaking,the Coulomb ﬁeld approximation assures that the internal dielec-tric constant,εin ,does not appear in GB theory;the only dielectric constants that matter are those of the solvent and the vacuum.(See the passage from Equation 11to Equation 12.)However,εin can reappear in an indirect and somewhat deceptive way,in GB-based expressions for energy as a function of solute conformation or intermolecular interaction energies.In such cases,one would like to have a poten-tial of mean force described on the hypersurface of the solute degrees of freedom.Its electrostatic component would bePMF elec =E elec ,ref + G pol (ref →sol ),15.where E elec ,ref is the electrostatic energy of the solute in some reference environ-ment that is chosen so that the calculation can be done simply,and G pol (ref →sol )is the energy of transferring the system from this reference environment to solvent.If the solute is presumed to have an internal dielectric of 1,the obvious choice of reference medium is the vacuum,where E elec ,ref can be calculated by Coulomb’s law,and the usual GB expressions for G pol can be used unchanged for G pol (ref →sol ).However,if the internal dielectric has a value εin that is different from 1,a more convenient choice is a reference medium of dielectric constant εin ,so that Coulomb’s law can again be used.In this case,all occurrencesA n n u . 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F o r p e r s o n a l u s e o n l y .134BASHFORD¥CASEof (1−1/εw )in the GB theory expressions are replaced by (1/εin −1/εw ).The resulting expression for the electrostatic potential of mean force isPMF elec =12 i =j q i q j in r i j −12 i ,j 1in −1wq i q jf GB i j 16.(compare with Equation 1).At long distances,where f GB goes to r i j ,the εin de-pendence disappears.It should be emphasized that εin appears in these formulaenot so much because it is the internal dielectric constant as because it is the ex-ternal dielectric constant of the reference environment.In particular,GB theory,because of its Coulomb ﬁeld approximation,and in contrast to Poisson-equation theory,cannot capture the tendency of solvation to increase the dipole moment of a dipolar solute,thus enhancing its solubility,through the use of an internal dielectric constant.Of course,such effects can be captured by methods that ex-plicitly couple some other theory of solute polarizability to GB theory,e.g.though quantum mechanical descriptions of the solute (6).Incorporation of Salt EffectsGB models have not traditionally considered salt effects,but the model can be extended to low salt concentrations at the Debye-Huckel level by the following arguments (21).The basic idea of the GB approach can be viewed as an inter-polation formula between analytical solutions for a single sphere and for widely separated spheres.For the latter,the solvation contribution in the Poisson model becomesG pol =− 1−e −κr i j wq i q jr i j ,17.where κis the Debye-H¨u ckel screening parameter.The ﬁrst term removes the gas-phase interaction energy,and the second term replaces it with a screened Coulombpotential.For a single spherical ion,the result is (26,27)G pol =−12 1−1εwq 2a −q 2κ2εw (1+κb ),18.where a is the radius of the sphere and b is the radial distance to which salt ionsare excluded,so that b −a is the ion-exclusion radius.To a close extent,these two limits can be obtained by the simple substitution1−1w → 1−e −κf GBw19.in Equation 1.This reduces directly to Equation 17for large distances,and thesalt-dependent terms become,as r i j goes to zero,−q 2i κ2εw 1+12κR i 20.A n n u . 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F o r p e r s o n a l u s e o n l y .GENERALIZED BORN MODELS 135through terms in κ2.To terms linear in κ,Equations 20and 18agree,but the quadratic terms differ by the replacement of b with 1/2(R i ).In practice,Equation 19gives salt effects that are slightly larger than those predicted by ﬁnite-difference linearized PB calculations,but which are strongly correlated with them.One likely reason is that the GB model outlined here does not have the concept of an ion-exclusion radius and,hence,tends to overestimate salt effects (compared with the usual PB model)by allowing counterions to approach more closely to the solute than they should.A simple ad hoc modiﬁcation that leads to acceptable results can be obtained by a simple scaling of κby 0.73in Equation 19(21).Figure 1compares linearized PB and GB estimates of the effect of monovalent added salt on the solvation energy of a 10-bp DNA duplex.The GB model is clearly capturing most of the behavior of linearized PB,especially at low salt concentrations.It is worth emphasizing that the linearized PB model itself is an imperfect model for salt effects (28),so that Equation 20should only be viewed as a rough approximation;it does,nonetheless,introduce the exponential screening of long-range Coulomb interactions,which is one of the hallmarks of salt effects.Limitations and Variations of the GB ModelThe crux of the GB approximation for the self-energy terms and effective radii is the Coulomb ﬁeld approximation,Equation 10,and this is also the main source of its deviation from solvation energies calculated using solutions of thePoissonFigure 1Difference in the solvation energy at ﬁnite and zero added salt for a 10-bp DNA duplex,calculated by numerical solutions to the linearized PB model,and from Equation 38.(Data from Reference 21.)A n n u . 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F o r p e r s o n a l u s e o n l y .136BASHFORD¥CASEequation.In general,the electric displacement generated by a charge q i located at a position r i within the low dielectric cavity of the solute will consist of a Coulomb ﬁeld and a reaction ﬁeld component D reac ,the latter being a consequence of the nonuniformity of the dielectric environment.The reaction ﬁeld contains no Coulombic singularities within the molecular interior and is usually fairly smoothly varying within this region.If the dielectric boundary between solvent and solute is sharp,which is the usual assumption,then D reac can be thought of as arising from an induced surface charge density on the dielectric boundary.In spherically symmetric cases,such as the case analyzed in the original Born theory,D is given exactly by the Coulomb ﬁeld (D reac is zero),and GB solvation goes over into Poisson-equation solvation.Schaefer &Froemmel (29)have an-alyzed deviations from the Coulomb-ﬁeld approximation for the case of charges at arbitrary positions within a spherical dielectric boundary,a case for which an-alytical solutions of the Poisson equation are available (26).They found that the Coulomb ﬁeld approximation leads to signiﬁcant errors in both self-energies and in the screening of charge-charge interactions,and they proposed an image-charge approximation for D reac that is very successful in recovering the energetic behavior of the exact Poisson model.Some additional quantitative sense of the limitations of the Coulomb ﬁeld ap-proximation can be gained by considering the case of a charge near a planar dielectric boundary (Figure 2).This can be thought of as the inﬁnite-radius limit of the situation where a charge is a distance d below the surface of a spherical macromolecule with a large radius (R d )and a dielectric constant εin ,and the macromolecule is transferred from an external medium of dielectric constant εin to a medium of dielectric constant εw .The electrostatic potential can be found exactly by the method of images (23).φz >0=q εin r 1+q εin r 2φz <0=q ex r 1,21.whereq =−qεex −εin ex in q =q 2εexex in .22.The reaction ﬁeld in the z >0region corresponding to a change of εex from εin to εw isφreac =q εin r 2=−q εw −εin εw +εin1εin r 2,23.A n n u . 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F o r p e r s o n a l u s e o n l y .GENERALIZED BORN MODELS137Figure 2A point charge q near a dielectric interface at z =0.The dielectric constant is εin or εex in the positive or negative z regions,respectively.The potential on the +z side is a sum of the Coulomb potential of the real charge q at z =d ,and an image charge q at z =−d .The potential on the −z side is the Coulomb potential of an image charge q at z =d .The distances of an arbitrary point r from the z =d and z =−d charge locations are denoted as r 1and r 2,respectively.where the r 1term has canceled in the subtraction of the potential in the εex =εin case from the potential in the εex =εw case.The electrostatic solvation energy can be found using Equation 4,G pol (exact )=−q 24d εw −εin εin (εw +εin )=−q 24d 1εin −1εw11+εin /εw .24.The corresponding formula for the solvation energy according to the Coulomb-ﬁeld approximation and an integration of the energy density difference over the“exterior”(z <0)region can be obtained using Equation 12:G pol (Coulomb )= 1in −1w 18πz <0q 2r 2=−q 28d 1in −1w .25.Note that in the usual case where εw εin ,the magnitude of G pol is underesti-mated by a factor of almost 2compared with the exact expression,Equation 24,although the form of the dielectric-constant dependence,a factor of (1/εin −1/εw ),is approximately correct.This suggests that for charges buried somewhat below the surface of large macromolecules,the |W i |of Equation 11may be underestimated,and thus the effective Born radii overestimated because of the Coulomb-ﬁeld ap-proximation.Of course the methods of approximating density integrals (such asA n n u . 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F o r p e r s o n a l u s e o n l y .138BASHFORD¥CASEthe pair-wise descreening approximation decribed below)will also affect the re-sults.On the other hand,most of the solvation energy of a macromolecule will be due to charged or highly polar groups that protrude into solvent,and for these groups,GB theory may be expected to work nearly as well as for analogous groups in small molecules.Luo et al (30)have also examined errors arising from replacing the true ﬁeld with a Coulomb approximation.Essentially,they assume that E ≈E vac /d F ,where E vac is the vacuum Coulomb ﬁeld and d F is a screening parameter having different values in the interior region or exterior regions.In the centrosymmetric case,d F is identical to the dielectric constant,but for more general shapes,it is a parameter to be optimized to provide realistic solvation energies.This leads toG pol =−18πεw −1d Fex E 2vac dV .26.Noting that in the Coulomb ﬁeld approximation D =E vac ,this expression is similarto Equation 12with (1−1/εw )replaced by (εw −1)/d F .Its other difference from GB theory is that this expression is used for the entire solvation energy,implicitly including charge-charge interactions terms rather than using a formula such as Equation 7.On a number of test cases,it was found to give good agreement with Poisson calculations,but the numerical integration required had roughly the same computational cost as solving the Poisson equation numerically.The limitations of both the density integration methods and the Coulomb ﬁeld approximation are also addressed in the electrostatic component of the SEED method for docking small molecular fragments to a macromolecular receptor (31).The desolvation of the receptor by the low dielectric of the ligand is taken to be the integral of D 2/(8π)over the ligand volume,and D is assumed not to change on ligand binding,as in conventional GB theory.The integration is done numerically using a cubic lattice,and the user can choose whether to estimate D by the Coulomb ﬁeld approximation,as in GB theory,or to calculate it by a ﬁnite difference solution of the Poisson equation for the ligand-free receptor.In its use of a D obtained by solving the Poisson equation,this method is similar in spirit to the SEDO approximation described below,except that the latter is based on solvation energy density rather than D 2.Solvation Energy DensityIn Equation 12,the solvation energy is expressed as the volume integral of an energy density that is zero within the solute volume,so that the integral need only run over the solvent volume.This could be thought of as a solvation energy density,but it is only by virtue of the Coulomb ﬁeld approximation that it falls to zero in the solute region.It is possible to give a more rigorous deﬁnition of solvation energy density that does not depend on approximations (32).In classical continuum electrostatics,an important problem is to ﬁnd the energy change caused by placing a dielectricA n n u . 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F o r p e r s o n a l u s e o n l y .object within some volume,in the electric ﬁeld of a ﬁxed set of charges outside that volume.This is essentially the same as the present solvation problem:We seek the change of energy associated with changing the dielectric constant of the region outside the molecule V ex ,from εvac to εw ,in the presence of the atomic partial charges,which remain ﬁxed in the molecular interior.Denoting the electric ﬁeld and displacement before the dielectric alteration as E vac and D vac ,and after the alteration as E sol and D sol ,respectively,the energy change isG pol =18π (E sol ·D sol −E vac ·D vac )dV ,27.where the volume integration runs over all space.It can be shown (23)that Equation 27can be transformed intoG pol =18π (E sol ·D vac −D sol ·E vac )dV ing D =εE ,it can be seen that the integrand falls to zero in the molecular interior because the dielectric constant there does not change (i.e.E sol ·εin E vac −εin E sol ·E vac =0).One can then writeG pol =exS (r )dV ,29.where the integral runs only over the exterior region,and S is the solvation energydensity,deﬁned byS =18π(E sol ·D vac −D sol ·E vac ).30.No approximations have been introduced up until this point,and Equations 29and 30are fully equivalent to Equation 3.Of course,if one introduces the Coulomb ﬁeld approximation,Equation 10,into the expression for S ,the GB theory expression for self energies is obtained.A different approximation based on S and oriented toward estimating desol-vation effects in intermolecular interactions has recently been proposed by Arora &Bashford (32).Suppose one would like to calculate the effect of the approach of a second molecule on the solvation energy of the ﬁrst molecule.The effect of the low dielectric of the second molecule on the solvation energy density S of the ﬁrst is twofold.First,S will go to zero in the interior of the second molecule,in other words a portion of S will be occluded.Second,in the solvent region near the second molecule,there will be some rearrangement of S .The approximation is to include the ﬁrst effect but neglect the second.This means that one can precalculate S by solving the Poisson equation and differentiating the potential to obtain the ﬁeld and displacement in both vacuum and solvent,for the ﬁrst molecule alone.Then the desolvation effect of a second molecule can be obtained byG desol =−mol 2S mol 1dV .31.A n n u . R e v . P h y s . C h e m . 2000.51:129-152. D o w n l o a d e d f r o m w w w .a n n u a l r e v i e w s .o r g A c c e s s p r o v i d e d b y N e w Y o r k U n i v e r s i t y - B o b s t L i b r a r y o n 09/24/15. F o r p e r s o n a l u s e o n l y .。

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5 Full domain nano-magnetic modeling 5.1 5.2 5.3 5.4 Excitations of incoherent spin waves Excitations of coherent spin waves Impact of contact point spin current injection on the magnetization dynamics MRAM - State of the art
Faculteit Wetenschappen Departement Fysica
Gilbert damping and noise in magnetic GMR multilayers
Proefschrift voorgelegd tot het behalen van de graad van Master of Nanophysics aan de Universiteit Antwerpen door
CONTENTS
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8 Conclusion 8.1 Most important realizations during this thesis 9 Dutch Summary 9.1 Inleiding tot de spintronica 9.2 Gilbert demping en ruis in magnetisch gelaagde GMR strukturen 10 Support CD References
43 43 47 47 49
6 Spin pumping and enhanced Gilbert damping 6.1 Precession-inducedheory of spin transfer torques in symmetric and asymmetric spin valves. 57 7.1 7.2 7.3 Symmetric spin valves Asymmetric spin valves Asymmetric versus symmetric spin valves 57 58 59

表面等离子共振技术特点

表面等离子共振技术特点
表面等离子共振技术（SurfacePlasmonResonance，SPR）是一种用于研究生物分子相互作用的强大技术。

该技术基于表面等离子体共振现象，利用特殊的传感器芯片和检测系统，可以实现实时监测生物分子相互作用的动态过程，如蛋白质-蛋白质、蛋白质-核酸、受体-配体等分子相互作用。

SPR技术具有以下特点：
1. 实时性：SPR技术可以实时监测生物分子相互作用的动态过程，无需标记，避免了标记分子对样品的影响。

2. 灵敏度：SPR技术具有极高的灵敏度，可以检测到非常低浓度的样品，一般可达到10-9mol/L级别。

3. 选择性：SPR技术可以实现对生物分子特异性的检测，可以区分不同的生物分子，并且可以实现对多个生物分子的同时检测。

4. 高通量：SPR技术可以实现高通量的样品检测，同时检测多个生物分子，提高实验效率。

5. 简便易用：SPR技术操作简便，不需要复杂的样品制备和处理步骤，适用于不同的生物样品。

由于SPR技术具有以上特点，已经广泛应用于药物筛选、生物分子互作机制研究、生物传感器等领域，成为生物分子研究和开发的重要手段。

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Spin-Boson and Spin-Fermion Topological Model of C

J. Chem. Chem. Eng. 11 (2017) 55-59doi: 10.17265/1934-7375/2017.02.003Spin-Boson and Spin-Fermion Topological Model of ConsciousnessAibassov Yerkin1, Yemelyanova Valentina1, Nakisbekov Narymzhan1, Alzhan Bakhytzhan1 and Savizky Ruben21. Research Institute of New Chemical Technologies and Materials, Kazakh National University Al-Farabi, Almaty 005012, Kazakhstan2. Columbia University, 3000 Broadway, New York, NY, 10027, USAAbstract: The authors propose a new approach to the theory of spin-boson and spin-fermion topological model of consciousness. The authors will offer a common mechanism of spin-boson and spin-fermion topological model of consciousness.Key words: Spin-boson, spin-fermion, topology, model of consciousness, magnetic field.1. IntroductionRecently, much attention is removed study of theory of consciousness [1-5]. All processes in the human brain occur in the form of electromagnetic processes. Therefore, it was interesting to see consciousness in terms of spin-boson and spin-fermion topological model.The aim is to study the spin-boson and spin-fermion topological model of consciousness.The novelty of the work lies in the fact that the authors have proposed a new mechanism of spin-boson and spin-fermion topological model of work of consciousness.2. TheoryNeuronal membrane saturated carrier spin nuclei such as 1H, 13C and 31P [1, 2]. Neuronal membrane are the matrix of the brain electrical activity and play a vital role in the normal functions of the brain and conscious of their basic molecular components are phospholipids, proteins and cholesterol. Each phospholipid contains 1% 31P, 1.8% 13C and over 60% 1H lipid chain. Neuronal membrane proteins such as ion channels and receptors neural transmittersCorresponding author: Aibassov Yerkin, professor, research field: metal organic chemistry of uranium and thorium, As, Sb and Bi. also contain large clusters spin-containing nuclei. Therefore, they are firmly convinced that the nature of the spin quantum used in the construction of the conscious mind. They suggested within neurobiology that perturbation anesthetics oxygen nerve pathwaysin both membrane proteins and may play a general anesthesia. Each O2 comprises two unpaired valence electrons strongly paramagnetic and at the same time as the chemically reactive bi-radical. It is able to produce large pulsed magnetic field along its path of diffusing. Paramagnetic O2 are the only breed can be found in large quantities in the brain to the same enzyme producing nitric oxide (NO). O2 is one of the main components for energy production in the central nervous system.NO is unstable free radical with an unpaired electron and one recently discovered a small neural transmitter, well known in the chemistry of spin-field concentrated on the study of free radical-mediated chemical reactions in which very small magnetic energy conversion can change the non-equilibrium spin process. Thus, O2 and NO can serve as catalysts in a spin-consciousness associated with neuronal biochemical reactions such as the double paths reaction initiated by free radicals.3. Results and DiscussionThey present the following Postulates: (a)All Rights Reserved.Spin-Boson and Spin-Fermion Topological Model of Consciousness 56Consciousness is intrinsically connected to quantum spin; (b) The mind-pixels of the brain are comprised of the nuclear spins distributed in the neural membranes and proteins, the pixel-activating agents are comprised of biologically available paramagnetic species such as O2 and NO, and the neural memories are comprised of all possible entangled quantum states of the mind-pixels; (c) Action potential modulations of nuclear spin interactions input information to the mind pixels and spin chemistry is the output circuit to classical neural activities; and (d) Consciousness emerges from the collapses of those entangled quantum states which are able to survive decoherence, said collapses are contextual, irreversible and non-computable and the unity of consciousness is achieved through quantum entanglement of the mind-pixels.In Postulate (a), the relationships between quantum spin and consciousness are defined based on the fact that spin is the origin of quantum effects in both Bohm and Hestenes quantum formulism and a fundamental quantum process associated with the structure of space-time.In Postulate (b), they specify that the nuclear spins in both neural membranes and neural proteins serve as the mind-pixels and propose that biologically available paramagnetic species such as O2 and NO are the mind-pixel activating agents. The authors also propose that neural memories are comprised of all possible entangled quantum states of mind-pixels.In Postulate (c), they propose the input and output circuits for the mind-pixels. As shown in a separate paper, the strength and anisotropies of nuclear spin interactions through J-couplings and dipolar couplings are modulated by action potentials. Thus, the neural spike trains can directly input information into the mind-pixels made of neural membrane nuclear spins. Further, spin chemistry can serve as the bridge to the classical neural activity since biochemical reactions mediated by free radicals are very sensitive to small changes of magnetic energies.In Postulate (d), they propose how conscious experience emerges. Thus, they adopt a quantum state collapsing scheme from which conscious experience emerges as a set of collapses of the decoherence-resistant entangled quantum states. They further theorize that the unity of consciousness is achieved through quantum entanglements of these mind-pixels.3.1 Spin-Boson and Spin-Fermion Model of ConsciousnessBosons, unlike fermions obey Bose-Einstein, who admits to a single quantum state could be an unlimited number of identical particles. Systems of many bosons described symmetric with respect to permutations of the particle wave functions.Bosons differ from fermions, which obey Fermi-Dirac statistics. Two or more identical fermions cannot occupy the same quantum state (Pauli exclusion principle).Since bosons with the same energy can occupy the same place in space, bosons are often force carrier particles. Fermions are usually associated with matter. Fermions, unlike bosons, obey Fermi-Dirac statistics:in the same quantum state can be no more than one particle (Pauli exclusion principle).3.2 Topological Model of ConsciousnessIt is known that the topological phase transition Kosterlitz-Thouless-phase transition in a two-dimensional XY-model. This transition is from the bound pairs of vortex-antivortex at low temperatures ina state with vortices and unpaired antivortices at a certain critical temperature.XY-model—a two-dimensional vector spin model which has symmetry U (1). For this system is not expected to have a normal phase transition of the second order. This is because the system is waiting forthe ordered phase that is destroyed by transverse vibrations, i.e. the Goldstone modes (see. Goldstone boson) associated with the breach of the continuousAll Rights Reserved.Spin-Boson and Spin-Fermion Topological Model of Consciousness 57Fig. 1 Symmetric wavefunction for a (bosonic) 2-particle state in an infinite square well potential.All Rights Reserved.Fig. 2 Antisymmetric wavefunction for a (fermionic) 2-particle state in an infinite square well potential.Spin-Boson and Spin-Fermion Topological Model of Consciousness58(a) (b)Fig. 3 Schematic image of a vortex (a) and antivortex (b) in the example of a planar magnetic material (arrows-vectors of the spin magnetic moments).symmetry, which logarithmically diverge with increasing system size. This is a special case of Theorem Mermin- Wagner for spin systems.Fig. 3 shows a schematic image of a vortex (a) and antivortex (b) in the example of a planar magnetic material (arrows - vectors of the spin magnetic moments).Thus, the topology does not depend on the measurement of distances, it is so powerful. The same theorems are applicable to any complex symptom, regardless of its length or belonging to a particular species.4. ConclusionsIn conclusion, the authors have presented an alternative model of consciousness in which the unpaired electron spins are playing a central role as the mind pixels and unity of mind is achieved interweaving these mental pixels.The authors hypothesized that these entangled electron spin states can be formed by the action potential modulated exchange and dipolar interactions, plus O2 and NO drive activations and survive rapid decoherence by quantum Zeno effects or decoherence-free spaces. Further, the authors have assumed that the collective electron spin dynamics associated with these collapses can have effects through the spin on the classic chemistry of neural activity, thereby affecting the neural networks of the brain. Our proposals involve the expansion of the associative neural coding of memories dynamic structures of neuronal membranes and proteins. Therefore, in our electron spin based on the model of the neural substrates of consciousness consists of the following functions: (a) electronic spin networks embedded in neuronal membranes and proteins, which serve as “crazy” screen with unpaired electron spins as pixels, (b) the nerve membrane and the proteins themselves, which serve as templates for the mind and nervous screen memories; and (c) free O2 and NO, which serve as agents pixel activating.Thus, the novelty of our work is that we were the first to propose that the electromagnetic field and free radicals have a great influence on the mind.Thus, the authors have proposed a possible mechanism of the free radical O2 and N2O in the consciousness.References[1]Hu, H. P., and Wu, M. X. 2006. “Nonlocal Effects ofChemical Substances on the Brain Produced ThroughQuantum Entanglement.” Progress in Physics 3: 20-6. [2]Hu, H. P., and Wu, M. X. 2006 “Photon InducedNon-local Effects of General Anaesthetics on the Brain.”Neuro Quantology 4 (1): 17-31. All Rights Reserved.Spin-Boson and Spin-Fermion Topological Model of Consciousness 59[3]Likhtenshtein, G. I. 1974. Spin labeling methods inmolecular biology. John Wiley and Sons; London, New York, Sydney, Toronto.[4]Likhtenshtein, G. I., Yamauchi, J., Nakatsuji, S., Smirnov,A., and Tamura, R. 2008. Nitroxides: Applications inChemistry, Biomedicine, and Materials Science. Cinii: Wiley.[5]Aibassov, Y., Yemelyanova, V., and Savizky, R. 2016.“Magnetic Effects in Brain Chemistry.” Journal of Chemistry and Chemical Engineering 10: 103-8.All Rights Reserved.。

Spin-coating method, determination method for spin

专利名称：Spin-coating method, determination methodfor spin-coating condition and mask blank发明人：Hideo Kobayashi,Takao Higuchi申请号：US10405505申请日：20030403公开号：US07195845B2公开日：20070327专利内容由知识产权出版社提供专利附图：摘要：A spin-coating method according to the present invention includes a uniforming step of rotating a substrate at a predetermined main rotation speed for a predetermined main rotation time so as to primarily make a resist film thickness uniform, and asubsequent drying step of rotating the substrate at a predetermined drying rotation speed for a predetermined drying rotation time so as to primarily dry the uniform resist film. In the present invention, a contour map, for example, of film thickness uniformity within an effective region (critical area) shown in FIG. A is determined (generated), and resist-coating is performed by selecting a condition within the optimum region in this contour map in which the film thickness uniformity (within an effective region) can be the maximum, or within the region in which the film thickness uniformity (within an effective region) can be high enough for a desirably specified.申请人：Hideo Kobayashi,Takao Higuchi地址：Tokyo JP,Tokyo JP国籍：JP,JP代理机构：Sughrue Mion, PLLC更多信息请下载全文后查看。

langevin dynamics

Espoo Feb2004'$BEYOND MOLECULAR DYNAMICSHerman J.C.BerendsenBiophysical Chemistry,University of Groningen,the NetherlandsGroningen Institute for Biosciences and Biotechnology(GBB)CSC,EspooLecture nr4,Thursday,5Februari,2004Molecular dynamics with atomic details is limited to time scales in the order of100ns.Events that are in micro-or millisecond range and beyond,as well as systemsizes beyond100,000particles,call for methods to simplify the system.The key is to reduce the number of degrees of freedom.Theﬁrst task is to deﬁne important degrees of freedom.The’unimportant’degrees of freedom must be averaged-out in such a way that the thermodynamic and long time-scale propertiesare preserved.The reduction of degrees of freedom depends on the problem one wishes to solve.One approach is the use of superatoms,lumping several atoms into one interactionunit.The interactions change into potentials of mean force,and the omitted de-grees of freedom are replaced by noise and friction.On an even coarser scale onemay lump many particles together and describe the behavior in terms of densitiesrather than positions.On a mesoscopic(i.e.,nanometer to micrometer)scale,theﬂuctuations are still important,but on a macroscopic scale they become negligibleand the Navier-Stokes equations of continuumﬂuid dynamics emerge.A modern development is to handle the continuum equations with particles(DPD:dissipative particle dynamics).'$ Espoo Feb2004 REDUCED SYSTEM DYNAMICSSeparate relevant d.o.f.rand irrelevant d.o.f.rForce on r :part correlated with positions rpart correlated with velocities˙rrest is’noise’,not correlated with positions or velocities of primed par-ticles.F i(t)=−∂V mf∂r i+F frictioni+F i(t)noiseF frictioni(t)is a function of v j(t−τ).F i(t)noise=R i(t)withR i(t) =0v j(t)R i(t+τ) =0(τ>0)R(t)is characterized by stochastic properties:•probability distribution w(R i)dR i•correlation function R i(t)R j(t+τ)Projection operator technique(Kubo and Mori;Zwanzig)give ele-gant framework to describe relation between friction and noise[Van Kampen in Stochastic Processes in Physics and Chemistry(1981):“This equation is exact but misses the point.The distribution cannot be determined without solving the original equation...”)]'$ Espoo Feb2004 POTENTIAL OF MEAN FORCE-1Requirement:Preserve thermodynamics!Helmholtz free energy A:A=−k B T ln QQ=ce−βV(r)d rDeﬁne a reaction coordinateξ(may be more than one dimension).Sep-arate integration over the reaction coordinate from the integral in Q:Q=cdξd r e−βV(r)δ(ξ(r)−ξ)Deﬁne potential of mean force V mf(ξ)asV mf(ξ)=−k B T lncd r e−βV(r)δ(ξ(r)−ξ),so thatQ=e−βV mf(ξ)dξandA=−k B T lne−βV mf(ξ)dξNote that the potential of mean force is an integral over multidimensional hyperspace.It is generally not possible to evaluate such integrals from simulations.As we shall see,it will be possible to evaluate derivatives of V mf from ensemble averages.Therefore we shall be able to compute V mf by integration over multiple simulation results,up to an unknown additive constant.'$ Espoo Feb 2004 POTENTIAL OF MEAN FORCE-2To simplify,look at cartesian coordinates.ξ=r .So r are the impor-tant coordinates,and r are the unimportant coordinates.How can we determine the PMF from simulations?Let us perform a simulation in which r is constrained,while r is freeto move.V mf(r )=−k B T lnce−βV(r ,r )d r∂V mf(r )∂r i =∂V(r ,r )∂r ie−βV(r ,r )d re−βV(r r )d r=∂V(r ,r )∂r i= F c i .Derivative of potential of mean force is the ensemble-averaged constraint force(cartesian).The constraint force follows from the coordinate resetting in constraint dynamics.(This is still true in more complex’reaction coordinates’,but there are small metric tensor corrections)'$ Espoo Feb2004DIFFUSION COEFFICIENTHow to determine the diﬀusion constant from constrained simulations? Determineﬂuctuation of constraint force∆F c(t)=F c(t)− F c . Fluctuation-dissipation theorem:∆F c(0)∆F c(t) =k B Tζ(t)ζ= ∞ζ(t)dtD=k B T ζHenceD=(k B T)2∞∆F c(0)∆F c(t) dt'$ Espoo Feb 2004LANGEVIN DYNAMICS-1General form of friction force:approximated by linear response in time,linear in velocities:F fr i(t)=m ij tγij(τ)v j(t−τ)dτThis gives(in cartesian coordinates)the generalized Langevin equation:m i d v idt=−∂V mf∂r i−m ijtγij(τ)v j(t−τ)dτ+R i(t)If a constrained dynamics is carried out with r constant(hence v =0), then the’measured’force on i approximates a representation of R i(t). So one can determine an approximation to the noise correlation functionC R ij(τ)= R i(t)R j(t+τ).(assumption:motion of r that determines R(t)is fast compared to the motion of r )There is a relation between friction and noise.Espoo Feb2004'$ LANGEVIN DYNAMICS-2Relation between friction and noiseAverage total energy should be conserved(averaged over time scale large compared to noise correlation time)•Systematic force is conservative(change in kinetic energy cancelschange in V mf)•Frictional force is dissipative:decreases kinetic energy•Stochastic force has inﬁrst order no eﬀect since v j(t)R i(t+τ) =0.In second order it increases the kinetic energy.The cooling by friction should cancel the heating by noise(ﬂuctuation-dissipation theorem).This leads toR(0)R(t) =k B T mγ(t)'$ Espoo Feb 2004LANGEVIN APPROXIMATIONS(write m iγij=ζij)Generalized Langevinm i˙v i(t)=−∂V mf∂x i−jtζij(τ)v j(t−τ)dτ+R i(t)withR i(0)R j(t) =k B Tζji(t) includes coupling(space)and memory(time). Simple Langevin with hydrodynamic couplingm i˙v i(t)=−∂V mf∂x i−jζij v j(t)+R i(t)withR i(0)R j(t) =2k B Tζjiδ(t) includes coupling(space),but no memory. Simple Langevinm i˙v i(t)=−∂V mf∂x i−ζi v i(t)+R i(t)withR i(0)R j(t) =2k B Tζiδ(t)δij includes neither coupling nor memory.'$ Espoo Feb2004BROWNIAN DYNAMICS-1If systematic force does not change much on the time scale of the ve-locity correlation function,we can average over a time∆t>τc.The average acceleration becomes small and can be neglected(non-inertial dynamics):0≈F i(x)−jζij v j(t)+R iwithR i= t+∆ttR(t )dtR i(0)R j(t) =2k B Tζjiδ(t)Be aware that the average acceleration is not zero if there is a cooperative motion with large massHence v j(t)can be solved from matrix equationζv=F+R(t)Solve in time steps∆tRandom force R i withR i =0R i R j =2k B Tζji∆tR i and R j are correlated random numbers,chosen from bivariate gaus-sian distributions.'$ Espoo Feb2004BROWNIAN DYNAMICS-2Without hydrodynamic coupling:v i=F iζi+r ir i is random number chosen from(gaussian)distribution with variance 2k B T∆t/ζi.x i(t+∆t)=x i(t)+v i∆tVelocity can be eliminated.Write D=k B T/ζ(diﬀusion constant) yields Brownian dynamicsx(t+∆t)=x(t)+Dk B TF(t)∆t+r(t)r =0r2 =2D∆tF must assumed to be constant during∆t.The longer∆t,the smaller the noise.For slow processes in macroscopic times the noise goes to zero.Espoo Feb2004'$ REDUCED PARTICLE DYNAMICSSuperatom approachLump a number of atoms together into one particle(e.g.10monomersof a homopolymer).Design forceﬁeld for those superatoms including bonding and nonbonding terms.For polymer:•soft harmonic spring between particles,representing Gaussian distri-bution of superatom-distance distributions•harmonic angular term in chain,representing stiﬀness•Lennard-Jones type interactions between particles•solvent:LJ particleDerive parameters from•experimental data(density,heat of vaporization,solubility,surfacetension,...,•atomic simulations of small system(radius of gyration,end-to-enddistance distribution,radial distribution functions,....Perform normal Molecular Dynamics.Adding friction and noise hasinﬂuence on dynamics,but is not needed for equilibrium properties. Example:Nielsen et al.,J.Chem.Phys.119(2003)2043.Espoo Feb2004'$DPDWe can also describe the space and time-dependent densities as the im-portant variables(e.g.described on a grid of points),and consider all detailed degrees of freedom as unimportant.This leadsﬁrst to meso-scopic dynamics(still including noise),and for even coarser averagingto the macroscopic Navier-Stokes equation.The Navier-Stokes equation is normally solved on a grid of points. Dissipative Particle Dynamics attempts to solve the Navier-Stokes equations using an ensemble of special particles.Originally proposed by Hoogerbrugge and Koelman,Europhys.Lett.19 (1992)155.Improved by Espa˜n ol,Warren,Flekkoy,Coveney.See article by Espa˜n ol in SIMU Newsletter Issue4,Chapter III,http://simu.ulb.ac.be/newsletters/N4III.pdf。

基于陶瓷纳米纤维的柔性压力传感器

视野VISION 创新 INNOVATION仿生胶原蛋白支架可诱导肺组织原位再生●创新点肺组织结构非常复杂，一旦发生损伤就很难进行自我修复。

例如，肺泡毛细血管膜屏障被破坏后会引起肺部水肿、炎症以及纤维化等，这会进一步导致肺部微环境紊乱、再生困难。

因此，对于严重的急性肺损伤，原位修复是一个巨大的挑战。

目前，肺移植术是有效的治疗方法，但面临供体来源有限以及免疫排斥等风险，限制了其临床应用。

人工肺植入技术是一种新兴的替代策略，但如何在人工肺支架中重建肺组织再生的微环境仍是一个挑战。

利用再生医学技术促进肺组织再生是当前的研究热点。

最近，中国科学院遗传与发育生物学研究所戴建武研究员所带领的再生医学研究团队构建了一种智能的胶原蛋白支架，首次在仿生支架材料的指导下进行肺再生研究，并证实该支架能促进肺组织原位再生。

●方法和结果研究人员采用组织工程的策略来研究肺组织的再生。

首先，他们制备了一种与天然肺组织组成、表面结构、孔径、孔隙率和力学特性类似的三维多孔胶原蛋白支架，该仿生支架具备良好的生物相容性和生物降解性。

然后，他们又构建一个包含胶原蛋白结合结构域（CBD）和肝细胞生长因子（HGF）的融合蛋白,该融合蛋白可特异性结合三维胶原蛋白支架，并在体内外持续缓释能改善肺再生微环境的HGF。

基于此策略，研究人员开发出了高效的人工肺再生微环境系统。

最后，研究团队构建了大鼠右肺中叶部分切除模型，并将该仿生支架植入残留的肺组织边缘，发现该支架能够对损伤的肺组织进行有效的保护和修复。

研究结果显示，三维仿生胶原蛋白支架能够抑制炎症和纤维化，促进急性肺损伤后损伤区域的恢复、肺泡再生和血管生成。

仿生支架的多孔结构一方面起到分隔作用，另一方面为细胞的黏附提供有效支撑。

在移植早期，CBD-HGF 一方面可诱导宿主血管内皮细胞的迁移、增殖，从而促进微血管的形成；另一方面还可以促进内源性的肺泡前体细胞进入支架，形成类肺泡样结构，最终促进支架内功能性肺泡样结构的再生以及残肺总体形态和功能的恢复。

关于Biolin动态接触角

对于动态接触角，人们有多种状态定义：其一，对于让处于非平衡状态的液滴在固体表面上自由铺展，动态接触角又分为前进角和后退角，前进角是液体在未被润湿过的固体表面进行铺展润湿，后退角是液体在已被润湿过的固体表面进行铺展，测试前进后退角是针对于疏水材料，亲水材料测试无意义。

其二，液体在固体表面接触角随时间变化而变化的过程，也是动态接触角。

谈起接触角，一定避不开的牌子就是百欧林，这个瑞典的老牌子。

瑞典百欧林科技有限公司是一家先进科研仪器生产商，在北欧的瑞典，丹麦和芬兰都有主要产品的研发和生产基地。

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可用测试：静态接触角、动态接触角（自动）、表面/界面张力、粗糙度修正接触角、界面流变、表面自由能：Zisman Plot, OWRK/Extended Fowkes, van Oss Acid-Base, Wu, Neumann’s Equation of State, Schultz 1 and 2可用测试方法：坐滴法、批处理坐滴法、捕泡法、倒置悬滴法、半月面法、动态接触角（自动）、震荡液滴法、3D形貌法、高压液滴形状拟合方法：Young-Laplace (CA, ST/IT, M)、Bashforth-Adams (ST/IT)、Circular (CA)、Polynomial (CA, M)软件及系统：所提供软件: OneAttension推荐系统配置: 2 GHz processor, 1 GB RAM*, 40 GB hard disk drive (20 GB free), 1024 * 768 resolution, 1 USB port*, 1 Gigabit Ethernet port with Theta, *2 GB RAM recommended and 1 additional USB port required with 3D topography module 操作系统要求：Windows 7 & 8 (32 or 64 bit), Windows Vista (32 bit), Windows XP SP3 (32 bit)OneAttension软件：OneAttension软件将直观的用户界面和高水平的多功能化结合起来。

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a r X i v :c o n d -m a t /0612396v 2 [c o n d -m a t .m e s -h a l l ] 27 J u n 2007epl draft
Introduction.–The problem of a two-level system (TLS)suﬀering from environmental decohering eﬀects is ubiquitous to many physical and chemical situations [1–3].Standard examples involve electron and proton transfer reaction in condensed phases [4],defect tunneling in met-als [5]or tunneling systems in glasses [6,7].Recently,sev-eral realizations of TLSs have been experimentally demon-strated in superconducting [8]and semiconducting [9]de-vices as possible unit (quantum bit)for future quantum computers.In these solid state systems,decoherence is a major obstacle towards the realization of a usable quan-tum computer [10–12].Hence,a proper understanding of dissipation over a broad parameter regime is of outermost importance.
For a description of the dissipative dynamics the spin-boson model,in which the TLS is bilinearly coupled to a harmonic bath,is very frequently used.It reads [1–3]
ˆH (t )= 2ˆσz ˆX +ˆH B .(1)The basis states |R and |L are the localized eigenstates of the ”position”operator ˆσz ,∆describes the coupling between the two-states due to tunneling,and ε(t )is an ex-ternal control ﬁeld.The Hamiltonian ˆH B = i ωi (ˆb †i ˆb i +1/2)represents a bath of bosons,and the collective vari-able ˆX = i c i (ˆb i +ˆb †i )/2describes the bath polarization.Despite the huge amounts of works on the subject [1–3],the existing schemes for a portrayal of the time-evolution of the TLS reduced density matrix mostly reduce to two main roads of approximation.On the one hand the so termed noninteracting-blip approximation (NIBA)[1,2],or equivalent projection operator techniques [13]based on an expansion to leading order in the tunneling ma-trix element ∆,has been proved to be successful in the regimes of high temperatures and/or strong friction.On the other hand the weak coupling and low-temperature regime,where NIBA fails for an asymmetric TLS,is typ-ically tackled within an expansion to lowest order in the TLS-bath coupling.In this latter case path-integral meth-ods [14,15]as well as the Bloch-Redﬁeld formalism are used [16](the two methods have been demonstrated to yield the same dynamics for weak Ohmic damping [17]),or a Born approximation [18].To date,only numerical ab-initio calculations [12,19–21]can provide a description of the TLS dynamics smoothly interpolating between a weak and a strong coupling situation.In this work,we present an interpolating approximation scheme,enabling to describe the weak and strong coupling regimes in a unique scheme.We call it weakly-interacting blip approximation (WIBA),within which the dynamics of the population diﬀerence ˆσz t ≡P (t )is ˙P (t )=− t
dt ′[K a (t,t ′)−W (t,t ′)+K s (t,t ′)P (t ′)].(2)
ωω2 coth
2
),(14)
implying localization of the TLS(P∞N=−1)at zero tem-perature even for inﬁnitesimal asymmetries.In order to overcome the NIBA shortcomings,a weak-coupling ap-proximation(WCA)has been proposed in[2,14,15]with WCA kernels being linear inδs and nonperturbative in∆. Within the WCA,the TLS dynamics shows damped coher-ent oscillations with a renormalized energy splitting Ω,withΩ2=∆2eﬀ[1−2Re u(iE/ )]+ε20,towards the equi-librium value
P∞WCA=−
ε0
2
).(15)
Here,the frequency shift is related to the frequency in-
tegral u(z)=1
ω2+z2
[coth( βω/2)−1].Moreover, E=
2(1−α)(∆/ωc)α。