Non-Equilibrium Nano-Physics: A Many-Body Approach

by Jonas Fransson

Overview

The aim of this book is to present a formulation of the non-equilibrium physics in nanoscale systems in terms of many-body states and operators and, in addition, discuss a diagrammatic approach to Green functions expressed by many-body states. The intention is not to give an account of strongly correlated systems as such. Thus, the focus of this book ensues from the typical questions that arise when addressing nanoscale systems from a practical point of view, e.g. current-voltage asymmetries, negative differential conductance, spin-dependent tunneling. The focus is on nanoscale systems constituted of complexes of subsystems interacting with one another, under non-equilibrium conditions, in which the local properties of the subsystems are preferably being described in terms of its (many-body) eigenstates.

Product Details

ISBN-13:	9789048192090
Publisher:	Springer Netherlands
Publication date:	07/08/2010
Series:	Lecture Notes in Physics , #809
Edition description:	2010
Pages:	224
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

About the Author

Author's profile: Fransson developed a diagrammatic Green function approach to treat nanoscale many-body systems under non-equilibrium conditions; [ Phys. Rev. B 66, 195319 (2003), Phys. Rev. B 72, 075314 (2005) ]. Established a theory for asymmetries and negative differential conductance generated by strong electron correlations in nanoscale systems [ Phys. Rev. B 70, 085301 (2004) , Phys. Rev. B 69, 201304 (2004) , J. Phys.: Condens. Matter 16, L85 (2004) ]. Provided a successful theoretical description and explanation for the so-called Pauli exclusion principle spin blockade in double quantum dot systems [Phys. Rev. B73, 205333 (2006)]. Described combined nanomechanical-superconducting device that allows Cooper pair tunneling to interfere with the mechanical motion of a middle superconducting island [Phys. Rev. Lett. 101, 067202 (2008)]. In total he has published 32 peer reviewed papers which are cited ~200 times - the index is currently 8. Sources: ISI Web of Knowledge, APS, and IOP.

Table of Contents

1 Many-body representation of physical systems.- 1.1 Many-body states.- 1.2 Two-level system.- 1.3 Many-body operators.- 1.4 Transition matrix elements.- References.- 2 Occupation number formalism.- 2.1 Perturbing the local levels.- 2.2 Occupations numbers.- 2.3 Single-level system.- 2.4 Two-level system in the Pauli spin blockade.- References.- 3 Many-body operator Green functions.- 3.1 Basic definitions.- 3.2 Equilibrium.- 3.3 Contour ordering.- 3.4 Single-level system.- References.- 4 Non-equilibrium formalism.- 4.1 Occupation number approach.- 4.2 Two-level system: Pauli spin-blockade.- 4.3 Green function approach.- 4.4 Non-equilibrium Green functions.- 4.5 Single-level quantum dot.- References.- 5 Diagram technique.- 5.1 Decoupling procedure.- 5.2 Expansion using functional derivatives.- 5.3 Single-level quantum dot.- 5.4 Current-voltage asymmetry.- References.- 6 Collection of physical examples.- 6.1 Spin-filtering.- 6.2 Current-voltage asymmetry in double quantum dots.- 6.3 Detection of exchange interaction through Fano-like interference effects.- 6.4 Non-equilibrium triplet blockade in T-shaped double quantum dot.- 6.5 Formation of pure triplet in double quantum dot.- References.- 7 Spin system.- 7.1 Equation for local spin >.- 7.2 Dynamics of local spin: semi-classical approach.- 7.3 Signatures of the local spin in the transport.- References.

Editorial Reviews

From the reviews:

“This book aims at an introductory presentation of some many-body aspects of nano-systems under non-equilibrium conditions. … Useful references are … offered at the end of each chapter, and the whole formalism is clearly illustrated through applications to simple single- and two-level systems and single-level quantum dots. … Overall, this book may be regarded as a useful and stimulating introduction to some up-to-date issues in mesoscopic physics.” (Giorgio Cattapan, Mathematical Reviews, Issue 2011 f)

From the Publisher