The Flow Equation Approach to Many-Particle Systems / Edition 1

by Stefan Kehrein

Overview

Over the past decade, the flow equationmethod has developed into a new versatile theoretical approach to quantum many-body physics. Its basic concept was conceived independently by Wegner [1] and by Glazek and Wilson [2, 3]: the derivation of a unitary flow that makes a many-particle Hamiltonian increasingly energy-diagonal. This concept can be seen as a generalization of the conventional scaling approaches in many-body physics, where some ultra-violet energy scale is lowered down to the experimentally relevant low-energy scale [4]. The main difference between the conventional scaling approach and the flow equation approach can then be traced back to the fact that the flow equation approach retains all degrees of freedom, i. e. the full Hilbert space, while the conventional scaling approach focusses on some low-energy subspace. One useful feature of the flow equation approach is therefore that it allows the calculation of dynamical quantities on all energy scales in one unified framework. Since its introduction, a substantial body of work using the flow equation approach has accumulated. It was used to study a number of very different quantum many-body problems from dissipative quantum systems to correlated electron physics. Recently, it also became apparent that the flow equation approach is very suitable for studying quantum many-body n- equilibrium problems, which form one of the current frontiers of modern theoretical physics. Therefore the time seems ready to compile the research literature on flow equations in a consistent and accessible way, which was my goal in writing this book.

Product Details

ISBN-13:	9783540340676
Publisher:	Springer Berlin Heidelberg
Publication date:	08/18/2006
Series:	Springer Tracts in Modern Physics , #217
Edition description:	2006
Pages:	172
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

Transformation of the Hamiltonian.- Evaluation of Observables.- Interacting Many-Body Systems.- Modern Developments.

Editorial Reviews

From the reviews:

“The book exposes the flow equation approach to many-particle systems … . The book is well written, in a pedagogical manner. It works out in detail exactly solvable models, like the potential scattering and the resonant level models, to develop the ideas and concepts, and then proceeds to their application to those nontrivial problems, making comparisons to other approaches and pointing out the advantages of this method. It contains many up-to-date references. The book can be used in a graduate course on many-particle systems.” (Vitor R. Vieira, Mathematical Reviews, Issue 2012 d)

From the Publisher