Green's Functions in Quantum Physics

ISBN-13: 9783642066917 / Angielski / Miękka / 2010 / 480 str.

Eleftherios N. Economou

Opis

In this third edition the book has been expanded in three directions: 1. Problems have been added at the end of each chapter (40% of which are solved in the last section of the book) together with suggestions for further reading. Furthermore, the number of appendices (marked with a grey stripe) has been substantially enlarged in order to make the book more self-su?cient. These additions, together with many clari?cations in the text, render the book more suitable as a companion in a course on Green s functions and their applications. 2. Theimpressivedevelopmentsofthe1980sand1990sinmesoscopicphysics, and in particular in transport properties, found their way to a c- tain extent in the new Chaps.8 and 9 (which also contain some of the material of the old Chap.7). This is a natural expansion, since Green s functions have played an important role as a theoretical tool in this new ?eld of physics, a role that continues in nanoregime research (see, e.g., recent publications dealing with carbon nanotubes). Thus, the powerful and unifying formalism of Green s functions ?nds applications not only in standard physics subjects such as perturbation and scattering theory, bound-state formation, etc., but also at the forefrontof current and, most likely, future developments. 3. Over the last 15 yearsor so Green s functions havefound applications not only in condensed matter electronicmotion but in classicalwavepropa- tion in both periodic and random media; photonic and phononic crystals aretheoutcomesofthislineofresearchwhoseunderlyingbasictheoretical principles are summarized in Sect.7.2.4."

Recenzje

From the reviews of the third edition:

"The main purpose of this book is to provide graduate students, and also experienced researchers, with a clear and quite detailed survey of the applications of Green's functions in different modern fields of quantum physics. ... In summary, this book is a good manual for people who want to understand the physics and the various applications of Green's functions in modern fields of physics. It can also be used as a starting point for studying numerical analysis in condensed matter theory." (Jean-Yves-Fortin, Mathematical Reviews, Issue, 2007 i)

Spis treści

Green’s Functions in Mathematical Physics.- Time-Independent Green’s Functions.- Time-Dependent Green’s Functions.- Green’s Functions in One-Body Quantum Problems.- Physical Significance of G. Application to the Free-Particle Case.- Green’s Functions and Perturbation Theory.- Green’s Functions for Tight-Binding Hamiltonians.- Single Impurity Scattering.- Two or More Impurities; Disordered Systems.- Electrical Conductivity and Green’s Functions.- Localization, Transport, and Green’s Functions.- Green’s Functions in Many-Body Systems.- Definitions.- Properties and Use of the Green’s Functions.- Calculational Methods for g.- Applications.

Blurb

The main part of this book is devoted to the simplest kind of Green's functions, namely the solutions of linear differential equations with a -function source. It is shown that these familiar Green's functions are a powerful tool for obtaining relatively simple and general solutions of basic problems such as scattering and bound-level information. The bound-level treatment gives a clear physical understanding of "difficult" questions such as superconductivity, the Kondo effect, and, to a lesser degree, disorder-induced localization. The more advanced subject of many-body Green's functions is presented in the last part of the book.