Understanding Hawking radiation in the framework of open quantum systems
霍金介绍成就英文作文
霍金介绍成就英文作文Stephen Hawking, one of the most renowned scientists of our time, made significant contributions to the fields of theoretical physics and cosmology despite facing immense physical challenges due to his motor neuron disease, amyotrophic lateral sclerosis (ALS). His remarkable achievements have left an indelible mark on our understanding of the universe. 。
Hawking's journey into the realm of science began during his undergraduate years at Oxford University, where he studied physics. He then pursued graduate studies at Cambridge University, where he delved into the mysteries of black holes and the origins of the universe. His groundbreaking doctoral thesis on the nature of black holes catapulted him into the scientific spotlight, earning him widespread recognition in the academic community.One of Hawking's most significant contributions came in the form of his theory of Hawking radiation. This theoryproposed that black holes are not entirely black but emit radiation due to quantum effects near the event horizon. This groundbreaking idea challenged long-held beliefs in physics and provided new insights into the behavior of black holes, which are some of the most enigmatic objectsin the universe.In addition to his theoretical work on black holes, Hawking made significant strides in cosmology. He developed the theory of cosmic inflation, which posits that the early universe underwent a rapid expansion shortly after the Big Bang. This theory not only provided a framework for understanding the large-scale structure of the universe but also offered a solution to several long-standing problems in cosmology.Hawking's popular science books, such as "A Brief History of Time" and "The Universe in a Nutshell," played a crucial role in bringing complex scientific concepts to a wider audience. Through his engaging writing style and ability to explain intricate ideas in simple terms, he inspired millions of people around the world to take aninterest in science and cosmology.Despite being diagnosed with ALS at a young age and being confined to a wheelchair for most of his life, Hawking never allowed his physical limitations to hinderhis intellectual pursuits. He continued to conduct research, write books, and deliver lectures until his passing in 2018. His resilience in the face of adversity serves as a testament to the power of the human spirit and has inspired countless individuals to persevere in the pursuit of knowledge.In recognition of his extraordinary contributions to science and his enduring legacy, Stephen Hawking received numerous awards and honors throughout his lifetime,including the prestigious Albert Einstein Award, the Wolf Prize in Physics, and the Presidential Medal of Freedom.In conclusion, Stephen Hawking's groundbreaking work in theoretical physics and cosmology has revolutionized our understanding of the universe. His theories on black holes, Hawking radiation, and cosmic inflation have reshaped thelandscape of modern physics and inspired generations of scientists. Despite facing formidable challenges, Hawking's intellect, perseverance, and passion for knowledge haveleft an indelible mark on the scientific community and the world at large.。
英雄 霍金 英文作文
英雄霍金英文作文Title: The Inspirational Journey of a Hero: Stephen Hawking。
In the vast expanse of human history, few figures shine as brightly as the remarkable Stephen Hawking. Renowned for his groundbreaking contributions to theoretical physics and cosmology, Hawking's life journey transcended the confines of physical limitations, inspiring generations with his intellect, resilience, and indomitable spirit.Born on January 8, 1942, in Oxford, England, Hawking exhibited early signs of brilliance and curiosity. Despite facing challenges due to a rare motor neuron disease, diagnosed at the age of 21, he pursued his passion for understanding the universe's mysteries with unwavering determination. As his physical abilities declined, his intellectual prowess soared, demonstrating to the world the power of the human mind to transcend its limitations.Hawking's groundbreaking work on black holes revolutionized our understanding of the cosmos. His theory of Hawking radiation, proposed in 1974, suggested that black holes emit radiation and gradually lose mass, challenging previously accepted notions in theoretical physics. This monumental discovery not only contributed to the advancement of scientific knowledge but also captivated the public imagination, cementing Hawking's status as a scientific icon.Beyond his scientific achievements, Hawking'sresilience in the face of adversity served as aninspiration to millions worldwide. Confined to a wheelchair and reliant on a computerized voice synthesizer to communicate, he refused to be defined by his physical condition. Instead, he embraced life with a sense of humor and an insatiable thirst for knowledge, demonstrating the power of the human spirit to triumph over adversity.Throughout his illustrious career, Hawking authored numerous bestselling books, including his seminal work "A Brief History of Time." Written for a general audience, thebook offered readers a glimpse into the complexities of theoretical physics, making profound concepts accessible to the masses. Hawking's ability to communicate complex ideas with clarity and eloquence earned him widespread acclaim and further solidified his status as a scientific luminary.Hawking's contributions extended beyond the realm of academia, as he used his platform to advocate forscientific literacy, environmental conservation, and the exploration of space. His efforts to popularize science and engage the public in discussions about the universe's wonders helped foster a greater appreciation for the beauty and complexity of the cosmos.In 2014, Hawking's extraordinary life story was brought to the silver screen in the biographical film "The Theory of Everything." The film offered a poignant portrayal of Hawking's personal struggles and triumphs, garneringcritical acclaim and further elevating his status as a cultural icon.On March 14, 2018, Stephen Hawking passed away at theage of 76, leaving behind a legacy that continues toinspire and awe. His contributions to science, his resilience in the face of adversity, and his unwavering pursuit of knowledge have left an indelible mark on humanity. Though he may no longer be with us in body, his spirit lives on in the countless lives he touched and the enduring impact of his work.In conclusion, Stephen Hawking's life journey exemplifies the transformative power of intellect, perseverance, and resilience. Despite facing immense challenges, he defied the odds and reshaped our understanding of the universe, leaving behind a legacy that will inspire generations to come. As we reflect on his remarkable achievements, let us honor his memory by continuing to explore, discover, and push the boundaries of human knowledge.。
一个著名的人英语作文
一个著名的人英语作文Sure, here's a composition about a famous person:Stephen Hawking was not just a renowned physicist but also a symbol of resilience and intellectual prowess. Born on January 8, 1942, in Oxford, England, he was diagnosed with amyotrophic lateral sclerosis (ALS) at the age of 21, a condition that gradually paralyzed him over the decades. Despite the physical challenges, his mind remained as sharp as ever, and he made groundbreaking contributions to the field of cosmology and quantum gravity, particularly in the context of black holes.Hawking's most famous work, "A Brief History of Time," published in 1988, became a bestseller and brought complex scientific concepts to the masses. The book delved into the origins of the universe, the nature of time, and the possibility of time travel, captivating readers worldwide. His ability to simplify complex theories and make them accessible to the general public was one of his greatest gifts.His work on the singularity theorems, in collaboration with Roger Penrose, showed that the universe must have had a beginning, which was a significant departure from theprevailing steady-state theory. Hawking also proposed the concept of Hawking radiation, suggesting that black holes could emit radiation and eventually evaporate, a theory that challenged the prevailing understanding of black holes.Beyond his scientific achievements, Hawking was a cultural icon. He appeared in various TV shows and movies, including "The Simpsons" and "Star Trek: The Next Generation." His portrayal of himself in these media highlighted his sense of humor and his ability to engage with the public on a personal level.Hawking's life was a testament to the power of the human spirit. He defied medical predictions and lived to the age of 76, passing away on March 14, 2018. His legacy continues to inspire scientists, students, and the general public alike, reminding us that the human mind is capable of extraordinary feats, even in the face of adversity.In conclusion, Stephen Hawking's life story is one of determination, brilliance, and an unwavering pursuit of knowledge. His contributions to science have expanded our understanding of the universe, and his personal story has inspired countless individuals to overcome their own challenges. His legacy will continue to influence and inspire future generations.This composition provides a brief overview of Stephen Hawking's life, his scientific contributions, and hiscultural impact, highlighting his resilience and intellectual achievements.。
关于霍金一生英语作文
关于霍金一生英语作文Title: The Extraordinary Life of Stephen Hawking。
Stephen Hawking, renowned physicist, cosmologist, and author, captivated the world with his brilliant mind and indomitable spirit throughout his lifetime. Born on January 8, 1942, in Oxford, England, he overcame tremendous physical challenges to become one of the most influential scientists of the modern era.Hawking's journey into the realm of science began during his undergraduate years at Oxford University, where he studied physics. It was during this time that he was diagnosed with amyotrophic lateral sclerosis (ALS), a debilitating neurological disease that gradually paralyzed him. Despite this daunting prognosis, Hawking refused tolet his condition hinder his pursuit of knowledge and academic excellence.After completing his undergraduate studies, Hawkingcontinued his education at Cambridge University, where he earned his Ph.D. in theoretical physics in 1966. His groundbreaking research focused on the origins of the universe, black holes, and the nature of space and time. His doctoral thesis, "Properties of Expanding Universes," laid the groundwork for his future contributions to cosmology.Throughout his career, Hawking made significant discoveries that reshaped our understanding of the cosmos. One of his most notable achievements was his theory of black hole radiation, now known as Hawking radiation. This revolutionary idea challenged long-held beliefs about the behavior of black holes and contributed to the field of quantum mechanics.In addition to his groundbreaking research, Hawking was a prolific author who sought to make complex scientific concepts accessible to the general public. His best-selling book, "A Brief History of Time," became an international sensation, selling millions of copies worldwide and cementing his reputation as a science communicator.Hawking's ability to convey complex ideas with clarity and wit endeared him to readers of all ages and backgrounds.Despite his physical limitations, Hawking continued to push the boundaries of scientific inquiry and inspireothers with his resilience and determination. He traveledthe world, delivering lectures and engaging in discussions with fellow scientists, students, and the public. Hisiconic voice, generated by a computerized speech synthesizer, became synonymous with intellect and curiosity.Beyond his scientific achievements, Hawking was asymbol of hope and perseverance for people living with disabilities. He advocated for greater accessibility and opportunities for individuals with physical impairments, using his platform to raise awareness and promote inclusivity.Throughout his life, Stephen Hawking received numerous accolades and honors for his contributions to science and society. He was awarded the prestigious Albert Einstein Medal, the Wolf Prize, and the Presidential Medal ofFreedom, among many others. His legacy continues to inspire future generations of scientists and thinkers to explore the mysteries of the universe.In March 2018, Stephen Hawking passed away at the age of 76, leaving behind a legacy that transcends the boundaries of time and space. His remarkable intellect, courage, and passion for discovery will forever be remembered as an enduring beacon of light in the vast expanse of the cosmos.In conclusion, Stephen Hawking's life was a testament to the power of the human spirit and the boundless possibilities of the mind. Despite facing unimaginable challenges, he never lost sight of his dreams and continued to push the boundaries of knowledge until the very end. His legacy serves as a reminder that with determination and perseverance, anything is possible.。
英语作文霍金的故事
英语作文霍金的故事Title: The Remarkable Journey of Stephen Hawking。
Stephen Hawking, a name synonymous with brilliance, resilience, and unparalleled contributions to the realm of theoretical physics, embarked on a journey that transcended the boundaries of human limitations and soared into the realms of the cosmos.Born on January 8, 1942, in Oxford, England, Hawking displayed an early fascination with the mysteries of the universe. Graduating from University College, Oxford, with a degree in Natural Science, he delved into the intricate world of theoretical physics. However, his journey was not without its challenges. At the age of 21, he was diagnosed with amyotrophic lateral sclerosis (ALS), a debilitating motor neuron disease that gradually paralyzed him, rendering him wheelchair-bound and unable to speak without assistance.Despite the daunting prognosis, Hawking refused to let his physical limitations hinder his intellectual pursuits. Instead, he defied the odds and embarked on a journey of groundbreaking discoveries that would revolutionize our understanding of the cosmos.One of Hawking's most notable achievements came in 1974 when he proposed the theory of Hawking radiation, which suggested that black holes emit radiation and eventually evaporate. This groundbreaking theory not only challenged conventional wisdom but also bridged the gap between quantum mechanics and general relativity, two pillars of modern physics.Throughout his career, Hawking continued to push the boundaries of scientific inquiry, exploring concepts such as the nature of time, the origin of the universe, and the possibility of time travel. His bestselling book, "A Brief History of Time," became a seminal work in popular science, captivating audiences worldwide with its accessible explanations of complex cosmological concepts.Despite his physical limitations, Hawking remained an active participant in the scientific community, travelingthe globe to deliver lectures and collaborate with fellow researchers. His indomitable spirit and insatiablecuriosity served as an inspiration to millions, provingthat the human mind knows no bounds.In addition to his scientific endeavors, Hawking wasalso a staunch advocate for disability rights and a vocal supporter of efforts to make science more accessible to all. His tireless advocacy efforts helped raise awareness about the challenges faced by individuals with disabilities and paved the way for greater inclusivity in academia and beyond.Hawking's remarkable journey serves as a testament tothe power of the human spirit and the boundless potentialof the human mind. Despite facing unimaginable obstacles,he refused to succumb to despair, choosing instead to embrace life with courage, curiosity, and determination.As we reflect on the life and legacy of Stephen Hawking,we are reminded of the transformative power of perseverance and the enduring impact of scientific exploration. His contributions to our understanding of the cosmos will continue to inspire generations of scientists, thinkers, and dreamers for years to come, ensuring that his legacy remains etched in the stars for eternity.。
黑洞介绍英语作文带翻译
黑洞介绍英语作文带翻译标题，Exploring the Mysteries of Black Holes。
Introduction:Black holes have long been a subject of fascination and wonder for scientists and laypeople alike. These enigmatic cosmic phenomena, characterized by their immense gravitational pull and ability to devour everything intheir path, continue to captivate our imagination. In this essay, we will delve into the depths of black holes, exploring their formation, properties, and the profound impact they have on the universe.正文：1. What are Black Holes?Black holes are regions in space where thegravitational pull is so strong that nothing, not evenlight, can escape from them. They are formed when massive stars undergo gravitational collapse at the end of theirlife cycle. As the star's core runs out of fuel, it can no longer support its own weight against gravity, causing itto collapse in on itself. This collapse creates a singularity—a point of infinite density—surrounded by an event horizon, beyond which no information can escape.1. 黑洞的形成。
Hawking Radiation in the Dilaton Gravity with a Non-Minimally Coupled Scalar Field
a r X i v :h e p -t h /9909138v 1 20 S e p 1999IF-UFRJ/99HAWKING RADIATION IN THE DILATON GRAVITY WITH A NON-MINIMALLY COUPLED SCALAR FIELD M.ALVES ⋆Instituto de Fisica -UFRJ Rio de Janeiro-RJ Brazil ABSTRACT We discuss the two-dimensional dilaton gravity with a scalar field as the source matter where the coupling with gravity is given,besides the minimal one,through an external field.This coupling generalizes the conformal anomaly in the same way as those found in recent literature,but with a diferent motivation.The modification to the Hawkingradiation is calculated explicity and show an additional term that introduces a dependence on the (effective)mass of the black-hole.PACS:04.60.+n;11.17.+y;97.60.Lf⋆e-mail:MSALVES@if.ufrj.br1INTRODUCTIONIt is widely recognized that two-dimensional models of gravity can give us a better understanding of the gravitational quantum effects.These models,derived either from a string motivated effective action[1]or from some low-dimensional version of the Einstein equations[2],have a rich structure in spite of their relative simplicity.Gravitational collapse,black holes and quantum effects are examples of subjects whose description is rather complicated in four-dimensional gravity while their lower-dimensional versions turn out to be more treatable,sometimes completely solved.This is the case of the seminal work of Callan,Giddings,Harvey and Strominger(CGHS)[1],where black-hole solutions are found and analysed semi-classically,giving us a two dimensional version of the Hawking effect.In the CGHS model,the starting point is the four-dimensional Einstein-Hilbert action in the spherically symmetric metric,where the Schwarzchild one is the simplest case. Then,the assumption of dependence in two variables for all thefields is done and,with a suitable form of the metric,it is possible to integrate the angular dependence.The final result is a two-dimensional action with a newfield,besides the gravitational one, called the dilaton,that can be taken as the relic of the integrated coordinates.This is the two-dimensional dilaton gravity.Some improvements have been done[3]to circumvent difficulties that arise from its quantum version,but leaving the initial purpose unchanged.Black-hole solutions are found to be formed from non-singular initial conditions, namely a source of scalar matter coupled minimally with the two-dimensional gravity sector(the terminology will be clarified later).There is also a linear vacuum region, which turns to be relevant to these models.Since these results are classical,the next step is the search for quantum effects:it is well known that whereas classical black-holes radiate nothing the semi-classical ones render a thermal radiation by a proccess called Hawking-Beckestein effect.An important feature of the semi-classical version for this effect is the conformal anomaly,since the Hawking radiation can be derived from this quantity.Recently,a series of works[10]givesatention to the generalization of the conformal anomaly to the CGHS model,with diferent coupling between the scalarfield and gravitation.By semi-classical version of this theory we mean the scalarfield quantized in the curved,classical,background.However,as pointed out before[6,7,8],we must be careful with thefield variable to be considered when we use the Fujikawa method.In the present case we make a redefinition of the scalarfield variable that,in the two dimensional case, results in a more general expression for the trace anomaly.We discuss here how this redefinition generates the same expression to the generalized anomaly found in[10]in a simple and direct way.This is one of the results of this work.On other hand,since the anomaly is used to calculate the Hawking radiation in the two dimensional case,we can expect new contributions to this quantity from the new terms of the conformal anomaly.In the CGHS model,these new terms give a generalization to the expression of the Hawking radiation that depend of the effective mass of the black-hole, absent in the original calculation.This article is organized as follows:in the next section we discuss the motivation for the definition of a newfield variable,the modification in the original action and the resulting expression for the trace anomaly in a direct way.After that,we present without details the main results of the CGHS model concerning the black hole radiation tofix notation,then,following the same steps as in[1],we calculate the new expression for the Hawking radiation derived from the modified anomaly.Discussions andfinal remarks are in the conclusion.2THE2d DILATON GRAVITY WITH NON-MINIMAL COUPLING The semi-classical quantization via functional method requires the integration over fields(the scalar one in this particular case).On the other hand,we are interested in theories that have the full quantized version free of anomalies.This paradigm can be worked out via the BRST analysis of the theory by using the Fujikawa’s technique[6,7]. In this framework,the quantized theory is anomaly-free provided the functional measure is BRST-invariant.It follows that this invariance requires a redefinition of thefield variables,the so-called gravitational dressing,and we must consider these newfields as the variables of the model that we are studying.We stress that without this modification the conservation of the quantized energy-momentum tensor(EMT)is not verified[7]. Another remarkable fact is that the trace anomaly would be null(only in the2d case).For the present case,2d scalarfield f,this redefinition meansf→˜f=(−g)(12π d2x√2πd2x∇µ˜f∇µ˜f(2)It is straightforward to see that the action for the new variables is not conformal invariant,since by a transformation asg′µν=e2αgµν(3) thefield˜f transform as˜f→˜f′=eα˜f.(4) Now,let us use the conformal gaugegµν=e2ρηµν(−g)(1and write˜f′=(eρf)′=eαeρf(6) so,in this gauge,a conformal transformation on f′is equivalent to makeρ→ρ′=ρ+α(7)Using these relations,we can define a non-minimal coupling to thefield variable through a gauge typefield,namely˜∇µ˜f=(∇µ−Aµ)˜f(8) whereAµ=∇µρ(9) tranforms asA′µ=Aµ+∇µα(10) With the definition(8),we can write a conformally invariant action to thefields˜f and gµν:1S[˜f,gµν]=d2x˜f(∇µ∇µ−AµAµ+∇µAµ)˜f(12)2πThis modification leads to a generalization of the value of trace anomaly which is easily calculated,since thefield Aµis not quantized and can be considered as an externalfield. The resulting anomaly is[8]:R→R(generalized)=R+β(AµAµ−∇µAµ)(13)Here,the parameterβshows us the presence of non-minimal coupling(β=1)or its absence(β=0).Antecipating a result from the next section,to wit the conformal factorρequal to the dilatonfieldφ,we have:R(generalized)=R+β(∇µφ∇µφ+∇µ∇µφ)(14) There are many recent works[10]dealing with this general value for the2d trace anomaly,some of them with others but related motivation,rendering different numerical values for the extra terms in(14).This does not change our analysis.3THE CGHS MODEL FOR THE2d DILATON GRAVITY AND THE HAWKING RADIATIONIntending to compare results,we present in this section the CGHS model for the two dimensional gravity and,specifically,the expression of the radiation of the black hole, derived from the semi-classical version following the same steps as in[1].The starting point is the actionS=1−g e−2φR+4(∇φ)2+4λ2 .(15)Here,R is the bidimensional scalar curvature andλis to be considered as a cosmologi-cal constant.As mentioned before,the dilatonfieldφ,that in two dimensional space time is a scalar,came from the angular part of the original4d metric,so that this action must be considered as the pure gravitational part.Stressing this affirmative is the possibility to make the dilaton equal to the gravitationalfield,at least classically.Using the light-cone coordinates and the conformal gauge,the metric becomesg+−=−1λ−λ2x−x+(17) for x+>x+0and for x+<x+0we have the vacuum.M=ax+0λis identified with the mass of the hole.Note thatρ=φis a consequence of the calculation and it will be used later.Up to this point,all the results are classical and to obtain information about the Hawking radiation we must consider quantum effects.This can be done through the relation between the trace anomaly and the components of the vacuum expectation value(VEV)of the energy momentum tensor(EMT)[9].In two dimensions,the VEV for the masslessfield is given byTµµ =Nλeλy+and x−=−1λ2.(22)These definitions result in a new metric but conformally related with theflat one like the former or,in others words,they preserve the conformal gauge.This new metric is obtained by writing(17)in terms of the variables y+and y−giving the conformal factor ase2ρ=(1+aλeλ(y−−y++y+0))−1for y+>y+0,(23)whereλx+0=eλy+0.The requeriment that these expressions vanish in the vacuun(x+<x+0)gives us the values of t+and t−and can be calculated at the limits e−λy−→∞and e−λy−→−a4(1−(1+aλ2or e−λy−→0,(25)Using(24)and(20),thefinal expression is:T horizon −−=λ2T+−=α∂+∂−ρ+β∂+ρ∂−ρ,(28) where the constantsαandβwere redefined in terms of those ones of(13).In this way,it is simple to see that the new contribution comes from the second term in RHS of(28).Following the same steps as before,namely using(28)in the(18)and(19),we have, e.g,for the T−−componentT−−=Tβ=0−−+β[14(12e4ρ−2ρ),(30)with t(y−)β=0given by(26)andρby(23).Finally,taking the appropriated limits,we arrive at the desired expression,T horizon −−=λ2a)](31)where the constantsαandβwere redefined again for simplicity.The modification of the expression of the Hawking radiation(31)was already expected, since the expression to the anomaly was modified.The dependence with the effective mass arises due the nonlinearity of the extra term in(27)and is a direct consequence of the new couplings introduced before.This is another result of this work.4CONCLUSIONS AND FINAL REMARKSIn this paper,we use the non-minimal coupling between the scalarfield and2d gravi-tation that gives rise to a generalization to the trace anomaly.The non-minimal coupling includes a type-gaugefield,given in terms of the gravitation(or the dilaton in the CGHS model)field.The motivation of the introduction of this extra coupling is the requirement of the conformal invariance of the action for the redefinedfield that,differently to the original,is not conformally invariant.The semiclassical quantization allows us to consider this gaugefield as an external one,rendering the calculation of the anomaly very simple:we just need to add the new terms that appear in the equation of motion derived from(12).The expression for the auxiliaryfield is due to the fact that in two dimensions we allways can use the conformal gauge.In higher dimensions,this choice would be very restrictive but,in this case,it is not nescessary to redefine the matterfield to satisfy(19) and the definition of the conformal gaugefield is straightfoward[13].Actually,in the4d case,(19)is used tofix some of numerical values of the EMT[5].In two dimensional space-time the calculation of the Hawking radiation is easily ob-tained via its relation with the trace anomaly[9].The calculations using the CGHS model yield a expression for black hole radiation that do not depend on the mass of the hole.On the contrary,in the Schwarzchild black hole,there is such dependence and has important consequences on the behaviour of these objects[9].When we use the generalized conformal anomaly the resulting expression to the Hawk-ing radiation has a dependence with the mass.The modification in the Hawking radiation was expected because the relations(13)and(18)and we can expect a more general be-haviour for these structures.We mention also that,in the CGHS model,the dependence of the radiation with the temperature is assured by the relation with theλparameter, since the temperature in this case is given by[12]:λT=and it is found to be the same as in the four dimensional case,to wit,T−−∼T2(in this case,T∼M and T−−∼M2).However,the modification in(31)breaks the relation between radiation and temperature so this result must be taken as a higher order term and not as the complete expression.Finally,it must be interesting to study others models using the non-minimal coupling to see what are the consequences of this choice.Works in this direction are in progress.ACKNOWLEDGEMENTSThe author is grateful to Prof.Carlos Farina for reading the manuscript and useful comments.This work was partially supported by Funda¸c˜a o Universit´a ria Jos´e Bonif´a cio, FUJB.REFERENCES[1]C.G.Callan,S.B.Giddings and J.A.Strominger,Phys.Rev.D45(1992)R1005;J.A. Strominger,in Les Houches Lectures on Black Holes(1994),hep-th/9501071.[2]R.Mann,A.Shiekm and L.Tarasov,Nucl.Phys.B341(1992)134;R.Jackiw,in Quantum Theory of Gravity,ed.S.Christensen(Adam Hilger,Bristol,1984),p.403;C. Teitelboim,ibid,p.327.[3]J.Russo,L.Susskind and L.Thorlacius,Phys.Rev.D45(1992)3444;47(1993)533[4]J.Maharana and J.H.Schwarz,Nucl.Phys.B390(1993)3;J.Scherk and J.H.Schwarz, Nucl.Phys.B153(1979)61;J.Maharana,Phys.Rev.Lett.75,2(1995)205.[5]N.D.Birrel and P.C.Davies,in Quantum Fields in Curved Spacetime(Cambridge University Press,Cambridge,1984)[6]K.Fujikawa in Quantum Gravity and Cosmology,ed.H.Sato and T.Inami(Singapore: World scientific);Phys.Rev.D25(1982)2584.[7]K.Fujikawa,U.Lindstrom,N.K.Rocek and P.van Nieuwenhuizen,Phys.Rev.D37 (1988)391.[8]M.Alves and C.Farina,Class.Quantum Grav.9(1992)1841;M.Alves,Class.Quantum Grav.13(1996)171.[9]S.M.Christensen and S.A.Fulling,Phis.Rev.D15(1977)2088.[10]S.Hawking and R.Boussos,hep-th/9705236;J.S.Dowker,hep-th/9802029;S.Ichinoise and S.Odintsov,hep-th/9802043.[11]S.Hawking,Commun.math.Phys.43,199(1975);G.Gibbons and S.Hawking,Phys.Rev.D 15(1976)2738.[12]See,for example,A.Gosh,hep-th/9604056and references therein.[13]M.Alves and J.Barcelos-Neto,Class.Quantum Grav.5(1988)377.。
英语专四总结霍金作文
英语专四总结霍金作文Title: A Summary of Stephen Hawking's Contribution to Science。
Introduction:Stephen Hawking, a renowned theoretical physicist, cosmologist, and author, has left an indelible mark on the world of science. His groundbreaking work in the fields of cosmology, black holes, and theoretical physics has reshaped our understanding of the universe. In this essay, we will delve into some of his most significant contributions and their implications for science and humanity.Hawking Radiation:One of Hawking's most revolutionary contributions to physics is his theory of Hawking radiation. In the 1970s, he proposed that black holes are not completely black, butrather emit radiation due to quantum effects near the event horizon. This groundbreaking idea challenged conventional wisdom and sparked intense debate among physicists. Hawking radiation has profound implications for our understandingof black holes and the fundamental nature of space and time.The Nature of Black Holes:Hawking's work on black holes also extended to their thermodynamic properties and entropy. Through his research, he demonstrated that black holes possess entropy, a measure of their disorder, and obey the laws of thermodynamics.This insight provided a deeper understanding of black hole dynamics and their role in the universe's evolution.The Theory of Everything:Hawking dedicated much of his career to the quest for a unified theory of physics, often referred to as the "Theory of Everything." He sought to reconcile the disparate lawsof quantum mechanics and general relativity into a single framework that could explain the fundamental forces of theuniverse. While he made significant progress in this endeavor, a complete theory remains elusive. Nevertheless, Hawking's contributions laid the groundwork for future generations of physicists to continue the search for a unified theory.Popularizing Science:In addition to his groundbreaking research, Hawking played a crucial role in popularizing science and making complex concepts accessible to the general public. Through his bestselling book "A Brief History of Time" and numerous public lectures and appearances, he inspired millions of people around the world to engage with the wonders of the cosmos. Hawking's ability to communicate complex ideas with clarity and humor earned him widespread admiration and cemented his legacy as a scientific icon.Conclusion:Stephen Hawking's contributions to science are immense and far-reaching. From his groundbreaking theories on blackholes and Hawking radiation to his efforts to unify the laws of physics, his work has fundamentally transformed our understanding of the universe. Moreover, his passion for communicating science to the public has inspired countless individuals to explore the wonders of the cosmos. As we reflect on his legacy, we are reminded of the boundless potential of human intellect and the enduring quest for knowledge that defines our species.。
介绍一位身残志坚的人英语作文
A Person of Unyielding Determination Despite DisabilityIn the annals of human resilience and perseverance, one name stands out as a beacon of inspiration: Stephen Hawking. Despite being physically handicapped, Hawking's spirit and intellectual prowess were boundless, making him a legend in the scientific community.Born in 1942, Hawking's life was marked by challenges from the very beginning. He was diagnosed with amyotrophic lateral sclerosis (ALS) at the age of 21, a degenerative disease that gradually paralyzed his body. However, this diagnosis did not dampen his enthusiasm for life or his pursuit of knowledge. On the contrary, it seemed to ignite a fire within him, driving him to pursue his studies in physics and cosmology with even greater determination.Hawking's brilliant mind and perseverance led him to groundbreaking discoveries in the field of black hole physics. His theories on the radiation emitted by black holes, now known as Hawking radiation, revolutionized our understanding of these mysterious objects in the universe. His contributions to cosmology and theoretical physics were recognized worldwide, earning him numerous honors and accolades.Despite his physical limitations, Hawking never gave up on his dreams or his love for life. He traveled the world, giving lectures and inspiring countless individuals with his story of resilience and courage. His books, such as "A Brief History of Time," simplified complex scientific concepts for the general reader, making him a household name.Stephen Hawking's life was a testament to the power of the human spirit. Despite being physically handicapped, he achieved remarkable success in the field of science, leaving an indelible mark on the world. Hisstory is a powerful reminder that no matter what challenges life throws at us, with determination and perseverance, we can overcome any obstacle and achieve our dreams. Hawking's legacy will forever inspire generations to come.。
有关霍金的英语作文
Stephen Hawking,a name synonymous with genius and the mysteries of the universe,was born on January8,1942,in Oxford,England.His life was a testament to the power of the human mind and the resilience of the human spirit.Despite being diagnosed with amyotrophic lateral sclerosis ALS at the age of21,Hawking defied all odds and contributed immensely to the field of theoretical physics.Hawkings most significant work was in the area of cosmology and quantum gravity, particularly in the context of black holes.His groundbreaking research on the nature of black holes and the radiation that they emit,now known as Hawking radiation, revolutionized our understanding of these celestial bodies.This discovery was based on the idea that black holes are not entirely black but can emit particles due to quantum effects near the event horizon.In1988,Hawking published A Brief History of Time,a book that aimed to explain complex scientific concepts to the general public.The book became an international bestseller and brought the wonders of the cosmos to the masses.It covered topics such as the Big Bang,the nature of time,and the possibility of time travel.Hawkings ability to simplify complex ideas and make them accessible to a wider audience demonstrated his commitment to making science more inclusive.Throughout his career,Hawking held various prestigious positions,including the Lucasian Professor of Mathematics at the University of Cambridge,a position once held by Sir Isaac Newton.He was also a Fellow of the Royal Society and a recipient of numerous awards and honors for his contributions to science.Hawkings personal life was marked by his unwavering determination to live life to the fullest despite his physical limitations.He was known for his sense of humor and his appearances in popular culture,including the television show The Simpsons and the film The Theory of Everything,which depicted his life and work.Stephen Hawking passed away on March14,2018,but his legacy lives on through his groundbreaking research,his inspirational life story,and his commitment to making science accessible to everyone.He once said,Remember to look up at the stars and not down at your feet.His words continue to inspire people to explore the universe and to seek knowledge,even in the face of adversity.。
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Hongwei Yu and Jialin Zhang Department of Physics and Institute of Physics,
arXiv:0806.3602v1 [gr-qc] 23 Jun 2008
Hunan Normal University, Changsha, Hunan 410081, China
(Dated: June 23, 2008)
Abstract
We study the Hawking radiation in the framework of open quantum systems by examining the time evolution of a detector (modelled by a two-level atom) interacting with vacuum massless scalar fields. The dynamics of the detector is governed by a master equation obtained by tracing over the field degrees of freedom from the complete system. The nonunitary effects are studied by analyzing the time behavior of a particular observable of the detector, i.e., its admissible state, in the Unruh, Hartle-Hawking, as well as Boulware vacua outside a Schwarzschild black hole. We find that the detector in both the Unruh and Hartle-Hawking vacua would spontaneously excite with a nonvanishing probability the same as what one would obtain if there is thermal radiation at the Hawking temperature from the black hole, thus reproducing the basic results concerning the Hawking effect in the framework of open quantum systems.
II.
THE MASTER EQUATION
We shall consider the evolution in the proper time of a static detector (two-level atom) interacting with vacuum massless scalar fields outside a Schwarzschild black hole and assume the combined system (detector + external vacuum fields) to be initially prepared in a factorized state, with the detector held static in the exterior region of the black hole and the fields in their vacuum states. Our derivation of the master equation in this Section follows closely to that in Ref. [10]. The atom is assumed to be fully described in terms of a two-dimensional Hilbert space, so that its states can be represented by a 2 × 2 density matrix ρ, which is mathematically sound, derivation of the reduced dynamics of the detector, we shall assume that the interaction between the detector and the scalar fields are weak so that the finitetime evolution describing the dynamics of the detector takes the form of a one-parameter semigroup of completely positive maps [11, 12]. Without loss of generality, we take the total Hamiltonian for the complete system to have the form H = Hs + Hφ + λ H ′ . Here Hs is the Hamiltonian of the atom, which in the most generic case takes the form ω0 Hs = 2
PACS numbers: 04.70.Dy, 03.65.Yz, 04.62.+v
1
I.
I intriguing objects and are worth studying in all possible varieties. The idea of black holes has been proven to be highly fruitful. In particular, Hawking’s discovery that black holes are not, after all, completely black, but quantum mechanically, emit radiation with a thermal spectrum [1], has provided us with the understanding that black holes may play the role of “Rosetta stone” to relate gravity, quantum theory and thermodynamics. Therefore, Hawking radiation, as one of the most striking effects that arise from the combination of quantum theory and general relativity, has attracted widespread interest in physics community and it has been extensively examined from different prospectives, yielding different derivations of it. These derivations include (but not limited to) Hawking’s original one which calculates the Bogoliubov coefficients between the quantum scalar field modes of the in vacuum states and those of the out vacuum [1, 2], an Euclidean quantum gravity derivation [3] which has been interpreted as a calculation of tunnelling through classically forbidden trajectory [4], an approach based upon string theory [5, 6], an interesting proposal which ties its existence to the cancellation of gravitational anomalies at the horizon [7], and a recent study which reveals an interesting relationship between the existence of Hawking radiation and the spontaneous excitation of atoms using the DDC formalism [8] that separates the contributions of vacuum fluctuations and radiation reaction to the rate of change of the mean atomic energy [9]. In the current paper, we shall try to understand the Hawking radiation by examining the time behavior of a static detector (modelled by a two-level atom) outside a Schwarzschild black hole immersed in vacuum massless scalar fields using the well-known techniques developed in the study of open quantum systems. As for any open system, the full dynamics of the detector can be obtained from the complete time evolution describing the total system (detector plus external fields) by integrating over the field degrees of freedom, which are in fact not observed. It is worth noting here that an examination of a similar issue, i.e., the Unruh effect associated with uniformly accelerated atoms in the paradigm of open quantum system has been already been carried out [10].