The Green Function Method in Statistical Mechanics

The Green Function Method in Statistical Mechanics
Author: V.L. Bonch-Bruevich
Publisher: Courier Dover Publications
Total Pages: 276
Release: 2015-11-18
Genre: Science
ISBN: 0486797155

Concise monograph devoted to techniques of solving many-body problems in physics using the quantum-mechanical Green function method. Requires some familiarity with the basic theory of quantum mechanics and statistical mechanics. 1962 edition.

Green’s Functions in Quantum Physics

Green’s Functions in Quantum Physics
Author: Eleftherios N. Economou
Publisher: Springer Science & Business Media
Total Pages: 325
Release: 2013-03-14
Genre: Science
ISBN: 3662023695

In this edition the second and main part of the book has been considerably expanded as to cover important applications of the formalism. In Chap.5 a section was added outlining the extensive role of the tight binding (or equivalently the linear combination of atomic-like orbitals) approach to many branches of solid-state physics. Some additional informa tion (including a table of numerical values) regarding square and cubic lattice Green's functions were incorporated. In Chap.6 the difficult subjects of superconductivity and the Kondo effect are examined by employing an appealingly simple connection to the question of the existence of a bound state in a very shallow potential well. The existence of such a bound state depends entirely on the form of the un perturbed density of states near the end of the spectrum: if the density of states blows up there is always at least one bound state. If the density of states approaches zero continuously, a critical depth (and/or width) of the well must be reached in order to have a bound state. The borderline case of a finite discontinuity (which is very important to superconductivity and the Kondo effect) always produces a bound state with an exponentially small binding energy.

The Non-Equilibrium Green's Function Method for Nanoscale Device Simulation

The Non-Equilibrium Green's Function Method for Nanoscale Device Simulation
Author: Mahdi Pourfath
Publisher: Springer
Total Pages: 268
Release: 2014-07-05
Genre: Technology & Engineering
ISBN: 370911800X

For modeling the transport of carriers in nanoscale devices, a Green-function formalism is the most accurate approach. Due to the complexity of the formalism, one should have a deep understanding of the underlying principles and use smart approximations and numerical methods for solving the kinetic equations at a reasonable computational time. In this book the required concepts from quantum and statistical mechanics and numerical methods for calculating Green functions are presented. The Green function is studied in detail for systems both under equilibrium and under nonequilibrium conditions. Because the formalism enables rigorous modeling of different scattering mechanisms in terms of self-energies, but an exact evaluation of self-energies for realistic systems is not possible, their approximation and inclusion in the quantum kinetic equations of the Green functions are elaborated. All the elements of the kinetic equations, which are the device Hamiltonian, contact self-energies and scattering self-energies, are examined and efficient methods for their evaluation are explained. Finally, the application of these methods to study novel electronic devices such as nanotubes, graphene, Si-nanowires and low-dimensional thermoelectric devices and photodetectors are discussed.

Annotations to Quantum Statistical Mechanics

Annotations to Quantum Statistical Mechanics
Author: In-Gee Kim
Publisher: CRC Press
Total Pages: 258
Release: 2018-03-14
Genre: Science
ISBN: 1351767526

This book is a rewritten and annotated version of Leo P. Kadanoff and Gordon Baym’s lectures that were presented in the book Quantum Statistical Mechanics: Green’s Function Methods in Equilibrium and Nonequilibrium Problems. The lectures were devoted to a discussion on the use of thermodynamic Green’s functions in describing the properties of many-particle systems. The functions provided a method for discussing finite-temperature problems with no more conceptual difficulty than ground-state problems, and the method was equally applicable to boson and fermion systems and equilibrium and nonequilibrium problems. The lectures also explained nonequilibrium statistical physics in a systematic way and contained essential concepts on statistical physics in terms of Green’s functions with sufficient and rigorous details. In-Gee Kim thoroughly studied the lectures during one of his research projects but found that the unspecialized method used to present them in the form of a book reduced their readability. He started the tedious work of rewriting and annotating them to fully understand the formalism of nonequilibrium quantum statistical mechanics. While doing so, he realized they can be a useful resource for students of modern physics but will have to be upgraded to match pace with the evolved curricula. Being aware that besides completing the course work and passing the relevant examinations, it is necessary for graduate students of modern physics to make the knowledge of a topic concrete in their minds. This book is a systematically prepared summary of those lectures and will be extremely useful for graduate students as well as senior researchers to settle down the key knowledge of the subject.

Statistical Mechanics And The Physics Of Many-particle Model Systems

Statistical Mechanics And The Physics Of Many-particle Model Systems
Author: Alexander Leonidovich Kuzemsky
Publisher: World Scientific
Total Pages: 1259
Release: 2017-02-24
Genre: Science
ISBN: 981314565X

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.

Methods in Statistical Mechanics

Methods in Statistical Mechanics
Author: Osvaldo Civitarese
Publisher: Springer Nature
Total Pages: 185
Release: 2020-09-07
Genre: Science
ISBN: 3030536580

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.