From the Preface: "The purpose of this book is to present and apply a language and to discuss methods which make it very convenient to exploit such analogies, and which are uniquely suited to describe and explain non-equilibrium phenomena in a rich variety of many-particle systems: the language of time correlation functions and linear response theory."
From the Preface: "The purpose of this book is to present and apply a language and to discuss methods which make it very convenient to exploit such analogies, and which are uniquely suited to describe and explain non-equilibrium phenomena in a rich variety of many-particle systems: the language of time correlation functions and linear response theory."
The book is devoted to the fundamental aspects of the non-equilibrium statistical mechanics of many-particle systems. The concept of Zubarev's approach, which generalizes the notion of Gibbs' ensembles, and introduces a nonequilibrium statistical operator, providing an adequate basis for dealing with strongly correlated systems that are governed by nonperturbative phenomena, such as the formation of bound states, quantum condensates and the instability of the vacuum. Besides a general introduction to the formalism, this book contains contributions devoted to the applications of Zubarev's method to the solution of modern problems in different fields of physics: transport theory, hydrodynamics, high-energy physics, quark-gluon plasma and hadron production in heavy-ion collisions. The book provides valuable information for researchers and students in these fields, requiring powerful concepts to solve fundamental problems of non-equilibrium phenomena in strongly
Abstract In quantum statistics based on many-body Green’s functions, the effective medium is represented by the selfenergy. This book aims to discuss the selfenergy from this point of view. The knowledge of the exact selfenergy is equivalent to the knowledge of the exact correlation function from which one can evaluate any single-particle observable. Complete interpretations of the selfenergy are as rich as the properties of the many-body systems. It will be shown that classical features are helpful to understand the selfenergy, but in many cases we have to include additional aspects describing the internal dynamics of the interaction. The inductive presentation introduces the concept of Ludwig Boltzmann to describe correlations by the scattering of many particles from elementary principles up to refined approximations of many-body quantum systems. The ultimate goal is to contribute to the understanding of the time-dependent formation of correlations. Within this book an up-to-date most simple formalism of nonequilibrium Green’s functions is presented to cover different applications ranging from solid state physics (impurity scattering, semiconductor, superconductivity, Bose–Einstein condensation, spin-orbit coupled systems), plasma physics (screening, transport in magnetic fields), cold atoms in optical lattices up to nuclear reactions (heavy-ion collisions). Both possibilities are provided, to learn the quantum kinetic theory in terms of Green’s functions from the basics using experiences with phenomena, and experienced researchers can find a framework to develop and to apply the quantum many-body theory straight to versatile phenomena.
It is a happy situation when similar concepts and theoretical techniques can be applied to widely different physical systems because of a deep similarity in the situations being studied. The book illustrates this well; it focuses on the description of correlations in quantum systems out of equilibrium at very short time scales, prompted by experiments with short laser pulses in semiconductors, and in complex reactions in heavy nuclei. In both cases the experiments are characterized by nonlinear dynamics and by strong correlations out of equilibrium. In some systems there are also important finite-size effects. The book comprises several independent contributions of moderate length, and I sometimes felt that a more intensive effort in cross-coordination of the different contributions could have been of help. It is divided almost equally between theory and experiment. In the theoretical part, there is a thorough discussion both of the kinematic aspects (description of correlations) and the dynamical ones (evaluation of correlations). The experimental part is naturally divided according to the nature of the system: the interaction of pulsed lasers with matter on the one hand, and the correlations in finite-size systems (nanoparticles and nuclei) on the other. There is also a discussion on the dynamics of superconductors, a subject currently of great interest. Although an effort has been made to keep each contribution self-contained, I must admit that reading level is uneven. However, there are a number of thorough and stimulating contributions that make this book a useful introduction to the topic at the level of graduate students or researchers acquainted with quantum statistical mechanics.
The experimental progress in cold atomic gases and mesoscopic systems has allowed unprecedented access to low dimensional correlated quantum systems far from equilibrium. This has revealed a variety of novel phenomena such as many-body localization, time crystals and dynamical phase transitions. The theoretical description of such systems has remained a challenge: The numerically exact solution of generic, correlated quantum systems requires computational effort that scales exponentially in the number of fermions, rendering larger systems and therefore collective behavior inaccessible. This necessitates approximations. In low dimensions, infrared divergences prohibit the use of a purely perturbative approach. Renormalization group based techniques, where energy scales are treated successively remedy some of these shortcomings. We therefore propose the use of the functional renormalization group to access correlation functions far from equilibrium in large, interacting systems. Such techniques were previously successfully applied in the investigation of quantum impurity problems and quenches in tight-binding chains and are widely used in the study of equilibrium phase diagrams. After a presentation of the Keldysh formalism, that constitutes a natural language out of equilibrium, we present perturbation theory and the functional renormalization group approach in a diagrammatic language. We then develop, optimize and apply flexible fRG techniques to four different problems in one-dimensional tight-binding chains with short-ranged two-particle interaction. First, we discuss the emergence of anomalous transport in the presence of a quasiperiodic potential by analyzing linear response and a far-from-equilibrium quench protocol. We then develop a variant of the fRG to access pure excited eigenstates. We use this algorithm to investigate many-body states in large tight-binding chains and show that generic excitations appear thermal while some states show unique spectral properties. To study the influence of inelastic scattering on the transport properties in such a chain we then go beyond an effective single-particle picture; to that end, we present an algorithm, that includes scattering in long chains. Finally, we discuss infinite chains coupled to a substrate while driven out of equilibrium by an electric field. Exploiting the inherent symmetries, we develop efficient algorithms and apply them to a simple tight-binding chain with nearest-neighbor interaction to explore the interplay of spontaneous symmetry breaking and driving. We demonstrate, that ordering is suppressed and provide results that indicate unconventional transport in the driven system.
There exists a regime of overlap between the equilibrium and non-equilibrium behavior of a system, the non-equilibrium behavior of weakly perturbed states. When a system is perturbed ever so slightly, its response will be linear in the perturbation, say the current of the conduction electrons in a metal will be proportional to the strength of the applied electric field. This regime is called the linear response regime, and though the system is in a non-equilibrium state all its characteristics can be inferred from the properties of its equilibrium state. In the next chapter we shall go beyond the linear regime by showing how to obtain quantum kinetic equations. The kinetic-equation approach to transport is a general method, and allows in principle nonlinear effects to be considered. However, in many practical situations one is interested only in the linear response of a system to an external force. The linear response limit is a tremendous simplification in comparison with general non-equilibrium conditions, and is the subject matter of this chapter. In particular the linear response of the density and current of an electron gas are discussed. The symmetry properties of response functions, and the fluctuation–dissipation theorem are established. Lastly we demonstrate how correlation functions can be measured in scattering experiments, as illustrated by considering neutron scattering from matter. Needless to say, in measurements of (say) the current in a macroscopic body, far less information in the current correlation function is probed. Linear response In this section we consider the response of an arbitrary property of a system to a general perturbation.