Formulation Of Statistical Mechanics Based On Thermal Pure Quantum States

Author : Sho Sugiura
Publisher : Springer
ISBN 13 : 9811015066
Total Pages : 73 pages
Book Rating : 4.69/5 ( download)

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Download or read book Formulation of Statistical Mechanics Based on Thermal Pure Quantum States written by Sho Sugiura and published by Springer. This book was released on 2017-10-05 with total page 73 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis introduces the concept of "thermal pure quantum (TPQ) states", which are pure quantum states in equilibrium. The author establishes a new formulation of statistical mechanics based on the TPQ states. This formulation allows us to obtain not only mechanical variables but also thermodynamic variables such as entropy and free energy from a single TPQ state. Furthermore, the formulation provides a new physical description in which all fluctuations including thermally driven ones are uniquely identified to be quantum fluctuations. The use of TPQ formulation has practical advantages in its application to numerical computations and allows for significant reduction in computation cost in numerics. For demonstration purposes, a numerical computation based on TPQ formulation is applied to a frustrated two-dimensional quantum spin model, and the result is also included in this book.

Author : Shu Tanaka
Publisher : World Scientific
ISBN 13 : 9814602388
Total Pages : 292 pages
Book Rating : 4.89/5 ( download)

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Download or read book Physics, Mathematics, and All that Quantum Jazz written by Shu Tanaka and published by World Scientific. This book was released on 2014-03-11 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of contributions from a Summer Workshop on “Physics, Mathematics, and All That Quantum Jazz”. Subjects of the symposium include quantum information theory, quantum annealing, Bose gases, and thermodynamics from a viewpoint of quantum physics. Contributions to this book are prepared in a self-contained manner so that readers with a modest background may understand the subjects. Contents:My Life as a Quantum Physicist (M Nakahara)A Review on Operator Quantum Error Correction — Dedicated to Professor Mikio Nakahara on the Occasion of His 60th Birthday (C-K Li, Y-T Poon and N-S Sze)Implementing Measurement Operators in Linear Optical and Solid-State Qubits (Y Ota, S Ashhab and F Nori)Fast and Accurate Simulation of Quantum Computing by Multi-Precision MPS: Recent Development (A Saitoh)Entanglement Properties of a Quantum Lattice-Gas Model on Square and Triangular Ladders (S Tanaka, R Tamura and H Katsura)On Signal Amplification from Weak-Value Amplification (Y Shikano)Topological Protection of Quantum Information (K Fujii)Quantum Annealing with Antiferromagnetic Fluctuations for Mean-Field Models (Y Seki and H Nishimori)A Method to Change Phase Transition Nature — Toward Annealing Methods (R Tamura and S Tanaka)Computational Analysis of the First Stage of the Photosynthetic System, the Light-Dependent Reaction, by Quantum Chemical Simulation Method (M Tada-Umezaki)Two-Qubit Gate Operation on Selected Nearest Neighboring Qubits in a Neutral Atom Quantum Computer (E Hosseini Lapasar, K Kasamatsu, S Nic Chormaic, T Takui, Y Kondo, M Nakahara and T Ohmi)A Simple Operator Quantum Error Correction Scheme Avoiding Fully Correlated Errors (C Bagnasco, Y Kondo and M Nakahara)Black Hole Predictability, Classical and Quantum (A Ishibashi)Classical Field Simulation of Finite-Temperature Bose Gases (T Sato)Atomic Quantum Simulations of Lattice Gauge Theory: Effect of Gauge Symmetry Breaking (K Kasamatsu, I Ichinose and T Matsui)Recursive Construction of Noiseless Subsystem for Qudits (U Güngördü, C-K Li, M Nakahara, Y-T Poon and N-S Sze)Composite Quantum Gates for Precise Quantum Control (M Bando, T Ichikawa, Y Kondo and M Nakahara)New Formulation of Statistical Mechanics Using Thermal Pure Quantum States (S Sugiura and A Shimizu)Thermodynamics in Unitary Time Evolution (T N Ikeda)Second Law of Thermodynamics with QC-Mutual Information (T Sagawa) Readership: Graduate students and researchers in physics, mathematics, informatics and computer science. Accessible to advanced undergraduate students. Key Features:This book includes wide-ranging areas of quantum physics, e.g., quantum annealing, topological quantum computation, quantum error correction, and foundation of thermodynamicsSome of the authors are PhD students. This book includes very recent topics relating to quantum physicsProminent authors: Professor Mikio Nakahara and Professor Chi-Kwong Li, Professor Akihiro Ishibashi, and Professor Kenichi KasamatsuKeywords:Quantum Information Science;Statistical Physics;Strongly Correlated Systems;Thermodynamics;Mathematics

Author : Osvaldo Civitarese
Publisher : Springer Nature
ISBN 13 : 3030536580
Total Pages : 185 pages
Book Rating : 4.89/5 ( download)

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Download or read book Methods in Statistical Mechanics written by Osvaldo Civitarese and published by Springer Nature. This book was released on 2020-09-07 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a variety of techniques for tackling phenomena that are not amenable to the conventional approach based on the concept of probabilities. The methods described rely on the use of path integration, thermal Green functions, time-temperature propagators, Liouville operators, second quantization, and field correlators at finite density and temperature. Also exploring the statistical mechanics of unstable quantum systems, the book is intended as a supplementary or reference text for use in one-semester graduate courses on Quantum Mechanics, Thermodynamics, Electromagnetism, and Mathematical Methods in Physics.

Author : Peter T. Landsberg
Publisher : Courier Corporation
ISBN 13 : 0486167585
Total Pages : 480 pages
Book Rating : 4.89/5 ( download)

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Download or read book Thermodynamics and Statistical Mechanics written by Peter T. Landsberg and published by Courier Corporation. This book was released on 2014-03-05 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exceptionally articulate treatment of negative temperatures, relativistic effects, black hole thermodynamics, gravitational collapse, much more. Over 100 problems with worked solutions. Geared toward advanced undergraduates and graduate students.

Author : Kuzemsky Alexander Leonidovich
Publisher : World Scientific
ISBN 13 : 981314565X
Total Pages : 1260 pages
Book Rating : 4.58/5 ( download)

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Download or read book Statistical Mechanics And The Physics Of Many-particle Model Systems written by Kuzemsky Alexander Leonidovich and published by World Scientific. This book was released on 2017-02-24 with total page 1260 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the study of the correlation effects in many-particle systems. It presents the advanced methods of quantum statistical mechanics (equilibrium and nonequilibrium), and shows their effectiveness and operational ability in applications to problems of quantum solid-state theory, quantum theory of magnetism and the kinetic theory. The book includes description of the fundamental concepts and techniques of analysis following the approach of N N Bogoliubov's school, including recent developments. It provides an overview that introduces the main notions of quantum many-particle physics with the emphasis on concepts and models. This book combines the features of textbook and research monograph. For many topics the aim is to start from the beginning and to guide the reader to the threshold of advanced researches. Many chapters include also additional information and discuss many complex research areas which are not often discussed in other places. The book is useful for established researchers to organize and present the advanced material disseminated in the literature. The book contains also an extensive bibliography. The book serves undergraduate, graduate and postgraduate students, as well as researchers who have had prior experience with the subject matter at a more elementary level or have used other many-particle techniques.

Author : Peter Hertel
Publisher : Springer
ISBN 13 : 3319585959
Total Pages : 368 pages
Book Rating : 4.56/5 ( download)

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Download or read book Quantum Theory and Statistical Thermodynamics written by Peter Hertel and published by Springer. This book was released on 2017-08-16 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents a concise yet detailed introduction to quantum physics. Concise, because it condenses the essentials to a few principles. Detailed, because these few principles – necessarily rather abstract – are illustrated by several telling examples. A fairly complete overview of the conventional quantum mechanics curriculum is the primary focus, but the huge field of statistical thermodynamics is covered as well. The text explains why a few key discoveries shattered the prevailing broadly accepted classical view of physics. First, matter appears to consist of particles which, when propagating, resemble waves. Consequently, some observable properties cannot be measured simultaneously with arbitrary precision. Second, events with single particles are not determined, but are more or less probable. The essence of this is that the observable properties of a physical system are to be represented by non-commuting mathematical objects instead of real numbers. Chapters on exceptionally simple, but highly instructive examples illustrate this abstract formulation of quantum physics. The simplest atoms, ions, and molecules are explained, describing their interaction with electromagnetic radiation as well as the scattering of particles. A short introduction to many particle physics with an outlook on quantum fields follows. There is a chapter on maximally mixed states of very large systems, that is statistical thermodynamics. The following chapter on the linear response to perturbations provides a link to the material equations of continuum physics. Mathematical details which would hinder the flow of the main text have been deferred to an appendix. The book addresses university students of physics and related fields. It will attract graduate students and professionals in particular who wish to systematize or refresh their knowledge of quantum physics when studying specialized texts on solid state and materials physics, advanced optics, and other modern fields.

Author : D.Y. Petrina
Publisher : Springer Science & Business Media
ISBN 13 : 940110185X
Total Pages : 460 pages
Book Rating : 4.51/5 ( download)

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Download or read book Mathematical Foundations of Quantum Statistical Mechanics written by D.Y. Petrina and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to quantum statistical mechanics. It can be regarded as a continuation of the book "Mathematical Foundations of Classical Statistical Mechanics. Continuous Systems" (Gordon & Breach SP, 1989) written together with my colleagues V. I. Gerasimenko and P. V. Malyshev. Taken together, these books give a complete pre sentation of the statistical mechanics of continuous systems, both quantum and classical, from the common point of view. Both books have similar contents. They deal with the investigation of states of in finite systems, which are described by infinite sequences of statistical operators (reduced density matrices) or Green's functions in the quantum case and by infinite sequences of distribution functions in the classical case. The equations of state and their solutions are the main object of investigation in these books. For infinite systems, the solutions of the equations of state are constructed by using the thermodynamic limit procedure, accord ing to which we first find a solution for a system of finitely many particles and then let the number of particles and the volume of a region tend to infinity keeping the density of particles constant. However, the style of presentation in these books is quite different.

Author : Ivo Sachs
Publisher : Cambridge University Press
ISBN 13 : 1139452460
Total Pages : 347 pages
Book Rating : 4.65/5 ( download)

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Download or read book Elements of Statistical Mechanics written by Ivo Sachs and published by Cambridge University Press. This book was released on 2006-05-11 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2006 textbook provides a concise introduction to the key concepts and tools of statistical mechanics. It also covers advanced topics such as non-relativistic quantum field theory and numerical methods. After introducing classical analytical techniques, such as cluster expansion and Landau theory, the authors present important numerical methods with applications to magnetic systems, Lennard-Jones fluids and biophysics. Quantum statistical mechanics is discussed in detail and applied to Bose-Einstein condensation and topics in astrophysics and cosmology. In order to describe emergent phenomena in interacting quantum systems, canonical non-relativistic quantum field theory is introduced and then reformulated in terms of Feynman integrals. Combining the authors' many years' experience of teaching courses in this area, this textbook is ideal for advanced undergraduate and graduate students in physics, chemistry and mathematics.

Author : Shu Tanaka
Publisher : World Scientific Publishing Company Incorporated
ISBN 13 : 9789814602365
Total Pages : 273 pages
Book Rating : 4.61/5 ( download)

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Download or read book Physics, Mathematics, and All That Quantum Jazz written by Shu Tanaka and published by World Scientific Publishing Company Incorporated. This book was released on 2014-03-11 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: My life as a quantum physicist / M. Nakahara -- A review on operator quantum error correction - Dedicated to Professor Mikio Nakahara on the occasion of his 60th birthday / C.-K. Li, Y.-T. Poon and N.-S. Sze -- Implementing measurement operators in linear optical and solid-state qubits / Y. Ota, S. Ashhab and F. Nori -- Fast and accurate simulation of quantum computing by multi-precision MPS: Recent development / A. Saitoh -- Entanglement properties of a quantum lattice-gas model on square and triangular ladders / S. Tanaka, R. Tamura and H. Katsura -- On signal amplification from weak-value amplification / Y. Shikano -- Topological protection of quantum information / K. Fujii -- Quantum annealing with antiferromagnetic fluctuations for mean-field models / Y. Seki and H. Nishimori -- A method to change phase transition nature - Toward annealing methods / R. Tamura and S. Tanaka -- Computational analysis of the first stage of the photosynthetic system, the light-dependent reaction, by quantum chemical simulation method / M. Tada-Umezaki -- Two-qubit gate operation on selected nearest neighboring qubits in a neutral atom quantum computer / E. Hosseini Lapasar ... [et al.] -- A simple operator quantum error correction scheme avoiding fully correlated errors / C. Bagnasco, Y. Kondo and M. Nakahara -- Black hole predictability, classical and quantum / A. Ishibashi -- Classical field simulation of finite-temperature Bose gases / T. Sato -- Atomic quantum simulations of lattice gauge theory: Effect of gauge symmetry breaking / K. Kasamatsu, I. Ichinose and T. Matsui -- Recursive construction of noiseless subsystem for qudits / U. Gungordu ... [et al.] -- Composite quantum gates for precise quantum control / M. Bando ... [et al.] -- New formulation of statistical mechanics using thermal pure quantum states / S. Sugiura and A. Shimizu -- Thermodynamics in unitary time evolution / T. N. Ikeda -- Second law of thermodynamics with QC-mutual information / T. Sagawa

Author : ATTARD
Publisher : IOP Publishing Limited
ISBN 13 : 9780750340533
Total Pages : 300 pages
Book Rating : 4.33/5 ( download)

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Download or read book Quantum Statistical Mechanics in Classical Phase Space written by ATTARD and published by IOP Publishing Limited. This book was released on 2021-11-30 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum and classical physics are presented as distinct and unrelated. Transformation to classical phase space gives researchers access to algorithms derived from classical statistical mechanics that promise results on much more favourable terms. This book offers a framework for understanding the quantum world and collective molecular behaviour.