Statistical Physics
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Arxiv:1509.06955V1 [Physics.Optics]
Statistical mechanics models for multimode lasers and random lasers F. Antenucci 1,2, A. Crisanti2,3, M. Ib´a˜nez Berganza2,4, A. Marruzzo1,2, L. Leuzzi1,2∗ 1 NANOTEC-CNR, Institute of Nanotechnology, Soft and Living Matter Lab, Rome, Piazzale A. Moro 2, I-00185, Roma, Italy 2 Dipartimento di Fisica, Universit`adi Roma “Sapienza,” Piazzale A. Moro 2, I-00185, Roma, Italy 3 ISC-CNR, UOS Sapienza, Piazzale A. Moro 2, I-00185, Roma, Italy 4 INFN, Gruppo Collegato di Parma, via G.P. Usberti, 7/A - 43124, Parma, Italy We review recent statistical mechanical approaches to multimode laser theory. The theory has proved very effective to describe standard lasers. We refer of the mean field theory for passive mode locking and developments based on Monte Carlo simulations and cavity method to study the role of the frequency matching condition. The status for a complete theory of multimode lasing in open and disordered cavities is discussed and the derivation of the general statistical models in this framework is presented. When light is propagating in a disordered medium, the system can be analyzed via the replica method. For high degrees of disorder and nonlinearity, a glassy behavior is expected at the lasing threshold, providing a suggestive link between glasses and photonics. We describe in details the results for the general Hamiltonian model in mean field approximation and mention an available test for replica symmetry breaking from intensity spectra measurements. Finally, we summary some perspectives still opened for such approaches. The idea that the lasing threshold can be understood as a proper thermodynamic transition goes back since the early development of laser theory and non-linear optics in the 1970s, in particular in connection with modulation instability (see, e.g.,1 and the review2). -
Arxiv:1910.10745V1 [Cond-Mat.Str-El] 23 Oct 2019 2.2 Symmetry-Protected Time Crystals
A Brief History of Time Crystals Vedika Khemania,b,∗, Roderich Moessnerc, S. L. Sondhid aDepartment of Physics, Harvard University, Cambridge, Massachusetts 02138, USA bDepartment of Physics, Stanford University, Stanford, California 94305, USA cMax-Planck-Institut f¨urPhysik komplexer Systeme, 01187 Dresden, Germany dDepartment of Physics, Princeton University, Princeton, New Jersey 08544, USA Abstract The idea of breaking time-translation symmetry has fascinated humanity at least since ancient proposals of the per- petuum mobile. Unlike the breaking of other symmetries, such as spatial translation in a crystal or spin rotation in a magnet, time translation symmetry breaking (TTSB) has been tantalisingly elusive. We review this history up to recent developments which have shown that discrete TTSB does takes place in periodically driven (Floquet) systems in the presence of many-body localization (MBL). Such Floquet time-crystals represent a new paradigm in quantum statistical mechanics — that of an intrinsically out-of-equilibrium many-body phase of matter with no equilibrium counterpart. We include a compendium of the necessary background on the statistical mechanics of phase structure in many- body systems, before specializing to a detailed discussion of the nature, and diagnostics, of TTSB. In particular, we provide precise definitions that formalize the notion of a time-crystal as a stable, macroscopic, conservative clock — explaining both the need for a many-body system in the infinite volume limit, and for a lack of net energy absorption or dissipation. Our discussion emphasizes that TTSB in a time-crystal is accompanied by the breaking of a spatial symmetry — so that time-crystals exhibit a novel form of spatiotemporal order. -
Conclusion: the Impact of Statistical Physics
Conclusion: The Impact of Statistical Physics Applications of Statistical Physics The different examples which we have treated in the present book have shown the role played by statistical mechanics in other branches of physics: as a theory of matter in its various forms it serves as a bridge between macroscopic physics, which is more descriptive and experimental, and microscopic physics, which aims at finding the principles on which our understanding of Nature is based. This bridge can be crossed fruitfully in both directions, to explain or predict macroscopic properties from our knowledge of microphysics, and inversely to consolidate the microscopic principles by exploring their more or less distant macroscopic consequences which may be checked experimentally. The use of statistical methods for deductive purposes becomes unavoidable as soon as the systems or the effects studied are no longer elementary. Statistical physics is a tool of common use in the other natural sciences. Astrophysics resorts to it for describing the various forms of matter existing in the Universe where densities are either too high or too low, and tempera tures too high, to enable us to carry out the appropriate laboratory studies. Chemical kinetics as well as chemical equilibria depend in an essential way on it. We have also seen that this makes it possible to calculate the mechan ical properties of fluids or of solids; these properties are postulated in the mechanics of continuous media. Even biophysics has recourse to it when it treats general properties or poorly organized systems. If we turn to the domain of practical applications it is clear that the technology of materials, a science aiming to develop substances which have definite mechanical (metallurgy, plastics, lubricants), chemical (corrosion), thermal (conduction or insulation), electrical (resistance, superconductivity), or optical (display by liquid crystals) properties, has a great interest in statis tical physics. -
Influence of Thermal Fluctuations on Active Diffusion at Large Péclet Numbers
Influence of thermal fluctuations on active diffusion at large Péclet numbers Cite as: Phys. Fluids 33, 051904 (2021); https://doi.org/10.1063/5.0049386 Submitted: 04 March 2021 . Accepted: 15 April 2021 . Published Online: 14 May 2021 O. T. Dyer, and R. C. Ball COLLECTIONS This paper was selected as Featured ARTICLES YOU MAY BE INTERESTED IN Numerical and theoretical modeling of droplet impact on spherical surfaces Physics of Fluids 33, 052112 (2021); https://doi.org/10.1063/5.0047024 Phase-field modeling of selective laser brazing of diamond grits Physics of Fluids 33, 052113 (2021); https://doi.org/10.1063/5.0049096 Collective locomotion of two uncoordinated undulatory self-propelled foils Physics of Fluids 33, 011904 (2021); https://doi.org/10.1063/5.0036231 Phys. Fluids 33, 051904 (2021); https://doi.org/10.1063/5.0049386 33, 051904 © 2021 Author(s). Physics of Fluids ARTICLE scitation.org/journal/phf Influence of thermal fluctuations on active diffusion at large Peclet numbers Cite as: Phys. Fluids 33, 051904 (2021); doi: 10.1063/5.0049386 Submitted: 4 March 2021 . Accepted: 15 April 2021 . Published Online: 14 May 2021 O. T. Dyera) and R. C. Ball AFFILIATIONS Department of Physics, University of Warwick, Coventry, CV4 7AL, United Kingdom a)Author to whom correspondence should be addressed: [email protected] ABSTRACT Three-dimensional Wavelet Monte Carlo dynamics simulations are used to study the dynamics of passive particles in the presence of microswimmers—both represented by neutrally buoyant spheres—taking into account the often-omitted thermal motion alongside the hydrody- namic flows generated by the swimmers. -
Research Statement Statistical Physics Methods and Large Scale
Research Statement Maxim Shkarayev Statistical physics methods and large scale computations In recent years, the methods of statistical physics have found applications in many seemingly un- related areas, such as in information technology and bio-physics. The core of my recent research is largely based on developing and utilizing these methods in the novel areas of applied mathemat- ics: evaluation of error statistics in communication systems and dynamics of neuronal networks. During the coarse of my work I have shown that the distribution of the error rates in the fiber op- tical communication systems has broad tails; I have also shown that the architectural connectivity of the neuronal networks implies the functional connectivity of the afore mentioned networks. In my work I have successfully developed and applied methods based on optimal fluctuation theory, mean-field theory, asymptotic analysis. These methods can be used in investigations of related areas. Optical Communication Systems Error Rate Statistics in Fiber Optical Communication Links. During my studies in the Ap- plied Mathematics Program at the University of Arizona, my research was focused on the analyti- cal, numerical and experimental study of the statistics of rare events. In many cases the event that has the greatest impact is of extremely small likelihood. For example, large magnitude earthquakes are not at all frequent, yet their impact is so dramatic that understanding the likelihood of their oc- currence is of great practical value. Studying the statistical properties of rare events is nontrivial because these events are infrequent and there is rarely sufficient time to observe the event enough times to assess any information about its statistics. -
Statistical Physics II
Statistical Physics II. Janos Polonyi Strasbourg University (Dated: May 9, 2019) Contents I. Equilibrium ensembles 3 A. Closed systems 3 B. Randomness and macroscopic physics 5 C. Heat exchange 6 D. Information 8 E. Correlations and informations 11 F. Maximal entropy principle 12 G. Ensembles 13 H. Second law of thermodynamics 16 I. What is entropy after all? 18 J. Grand canonical ensemble, quantum case 19 K. Noninteracting particles 20 II. Perturbation expansion 22 A. Exchange correlations for free particles 23 B. Interacting classical systems 27 C. Interacting quantum systems 29 III. Phase transitions 30 A. Thermodynamics 32 B. Spontaneous symmetry breaking and order parameter 33 C. Singularities of the partition function 35 IV. Spin models on lattice 37 A. Effective theories 37 B. Spin models 38 C. Ising model in one dimension 39 D. High temperature expansion for the Ising model 41 E. Ordered phase in the Ising model in two dimension dimensions 41 V. Critical phenomena 43 A. Correlation length 44 B. Scaling laws 45 C. Scaling laws from the correlation function 47 D. Landau-Ginzburg double expansion 49 E. Mean field solution 50 F. Fluctuations and the critical point 55 VI. Bose systems 56 A. Noninteracting bosons 56 B. Phases of Helium 58 C. He II 59 D. Energy damping in super-fluid 60 E. Vortices 61 VII. Nonequillibrium processes 62 A. Stochastic processes 62 B. Markov process 63 2 C. Markov chain 64 D. Master equation 65 E. Equilibrium 66 VIII. Brownian motion 66 A. Diffusion equation 66 B. Fokker-Planck equation 68 IX. Linear response 72 A. -
Statistical Mechanics
3 d rB rB 3 d rA rA Statistical Mechanics Daniel F. Styer December 2007 Statistical Mechanics Dan Styer Department of Physics and Astronomy Oberlin College Oberlin, Ohio 44074-1088 [email protected] http://www.oberlin.edu/physics/dstyer December 2007 Although, as a matter of history, statistical mechanics owes its origin to investigations in thermodynamics, it seems eminently worthy of an independent development, both on account of the elegance and simplicity of its principles, and because it yields new results and places old truths in a new light. | J. Willard Gibbs Elementary Principles in Statistical Mechanics Contents 0 Preface 1 1 The Properties of Matter in Bulk 4 1.1 What is Statistical Mechanics About? . 4 1.2 Outline of Book . 4 1.3 Fluid Statics . 5 1.4 Phase Diagrams . 7 1.5 Additional Problems . 7 2 Principles of Statistical Mechanics 10 2.1 Microscopic Description of a Classical System . 10 2.2 Macroscopic Description of a Large Equilibrium System . 14 2.3 Fundamental Assumption . 15 2.4 Statistical Definition of Entropy . 17 2.5 Entropy of a Monatomic Ideal Gas . 19 2.6 Qualitative Features of Entropy . 25 2.7 Using Entropy to Find (Define) Temperature and Pressure . 34 2.8 Additional Problems . 44 3 Thermodynamics 46 3.1 Heat and Work . 46 3.2 Heat Engines . 50 i ii CONTENTS 3.3 Thermodynamic Quantities . 52 3.4 Multivariate Calculus . 55 3.5 The Thermodynamic Dance . 60 3.6 Non-fluid Systems . 67 3.7 Thermodynamics Applied to Fluids . 68 3.8 Thermodynamics Applied to Phase Transitions . -
Chapter 7 Equilibrium Statistical Physics
Chapter 7 Equilibrium statistical physics 7.1 Introduction The movement and the internal excitation states of atoms and molecules constitute the microscopic basis of thermodynamics. It is the task of statistical physics to connect the microscopic theory, viz the classical and quantum mechanical equations of motion, with the macroscopic laws of thermodynamics. Thermodynamic limit The number of particles in a macroscopic system is of the order of the Avogadro constantN 6 10 23 and hence huge. An exact solution of 1023 coupled a ∼ · equations of motion will hence not be possible, neither analytically,∗ nor numerically.† In statistical physics we will be dealing therefore with probability distribution functions describing averaged quantities and theirfluctuations. Intensive quantities like the free energy per volume,F/V will then have a well defined thermodynamic limit F lim . (7.1) N →∞ V The existence of a well defined thermodynamic limit (7.1) rests on the law of large num- bers, which implies thatfluctuations scale as 1/ √N. The statistics of intensive quantities reduce hence to an evaluation of their mean forN . →∞ Branches of statistical physics. We can distinguish the following branches of statistical physics. Classical statistical physics. The microscopic equations of motion of the particles are • given by classical mechanics. Classical statistical physics is incomplete in the sense that additional assumptions are needed for a rigorous derivation of thermodynamics. Quantum statistical physics. The microscopic equations of quantum mechanics pro- • vide the complete and self-contained basis of statistical physics once the statistical ensemble is defined. ∗ In classical mechanics one can solve only the two-body problem analytically, the Kepler problem, but not the problem of three or more interacting celestial bodies. -
Verification, Validation, and Predictive Capability in Computational Engineering and Physics
SAND REPORT SAND2003-3769 Unlimited Release Printed February 2003 Verification, Validation, and Predictive Capability in Computational Engineering and Physics William L. Oberkampf, Timothy G. Trucano, and Charles Hirsch Prepared by Sandia National Laboratories Albuquerque, New Mexico 87185 and Livermore, California 94550 Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under Contract DE-AC04-94-AL85000. Approved for public release; further dissemination unlimited. Issued by Sandia National Laboratories, operated for the United States Department of Energy by Sandia Corporation. NOTICE: This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government, nor any agency thereof, nor any of their employees, nor any of their contractors, subcontractors, or their employees, make any warranty, express or implied, or assume any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represent that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government, any agency thereof, or any of their contractors or subcontractors. The views and opinions expressed herein do not necessarily state or reflect those of the United States Government, any agency thereof, or any of their contractors. Printed in the United States of America. This report has been reproduced directly from the best available copy. -
Subject Benchmark Statement: Physics, Astronomy and Astrophysics
QAA MEMBERSHIP Subject Benchmark Statement Physics, Astronomy and Astrophysics October 2019 Contents How can I use this document? ................................................................................................. 1 About the Statement ................................................................................................................ 2 Relationship to legislation ......................................................................................................... 2 Summary of changes from the previous Subject Benchmark Statement (2017) ....................... 2 1 Introduction ..................................................................................................................... 3 2 Nature and extent of physics, astronomy and astrophysics ............................................. 4 3 Subject-specific knowledge and understanding ............................................................... 6 4 Teaching, learning and assessment ................................................................................ 9 5 Benchmark standards ................................................................................................... 11 Appendix: Membership of the benchmarking and review groups for the Subject Benchmark Statement for Physics, Astronomy and Astrophysics ............................................................. 13 How can I use this document? This is the Subject Benchmark Statement for Physics, Astronomy and Astrophysics. It defines the academic standards that can be expected -
STATISTICAL PHYSICS Dr. A.K. DWIVEDI
STATISTICAL PHYSICS (Part-1) B.Sc. III (paper-1) Unit-II Dr. A.K. DWIVEDI DEPARTMENT OF PHYSICS HARISH CHANDRA P. G. COLLEGE VARANASI 1 STATISTICAL PHYSICS THE STATICAL BASIC OF THERMODYNAMICS Introduction The primary goal of statistical thermodynamics (also known as equilibrium statistical mechanics) is to derive the classical thermodynamics of materials in terms of the properties of their constituent particles and the interactions between them. In other words, statistical thermodynamics provides a connection between the macroscopic properties of materials in thermodynamic equilibrium, and the microscopic behaviors and motions occurring inside the material. Whereas statistical mechanics proper involves dynamics, here the attention is focused on statistical equilibrium (steady state). Statistical equilibrium does not mean that the particles have stopped moving (mechanical equilibrium), rather, only that the ensemble is not evolving. Fundamental postulate A sufficient (but not necessary) condition for statistical equilibrium with an isolated system is that the probability distribution is a function only of conserved properties (total energy, total particle numbers, etc.).There are many different equilibrium ensembles that can be considered, and only some of them correspond to thermodynamics.] Additional postulates are necessary to motivate why the ensemble for a given system should have one form or another. A common approach found in many textbooks is to take the equal a priori probability postulate. This postulate states that For an isolated system with an exactly known energy and exactly known composition, the system can be found with equal probability in any microstate consistent with that knowledge. The equal a priori probability postulate therefore provides a motivation for the microcanonical ensemble described below. -
Lecture 6: Entropy
Matthew Schwartz Statistical Mechanics, Spring 2019 Lecture 6: Entropy 1 Introduction In this lecture, we discuss many ways to think about entropy. The most important and most famous property of entropy is that it never decreases Stot > 0 (1) Here, Stot means the change in entropy of a system plus the change in entropy of the surroundings. This is the second law of thermodynamics that we met in the previous lecture. There's a great quote from Sir Arthur Eddington from 1927 summarizing the importance of the second law: If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equationsthen so much the worse for Maxwell's equations. If it is found to be contradicted by observationwell these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of ther- modynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation. Another possibly relevant quote, from the introduction to the statistical mechanics book by David Goodstein: Ludwig Boltzmann who spent much of his life studying statistical mechanics, died in 1906, by his own hand. Paul Ehrenfest, carrying on the work, died similarly in 1933. Now it is our turn to study statistical mechanics. There are many ways to dene entropy. All of them are equivalent, although it can be hard to see. In this lecture we will compare and contrast dierent denitions, building up intuition for how to think about entropy in dierent contexts. The original denition of entropy, due to Clausius, was thermodynamic.