Field theory of non-equilibrium systems (Q2888983)

During the last years, among physicists interested in non-equilibrium many-body systems a new, universal and common language has appeared, i.e., quantum field theory. Initially this theory was used in the study of superconducting kinetics and laser physics, but, as each living language does, it has kept changing and evolving towards new challenges allowing solutions to new problems that have appeared in other branches of physics. This development was caused by many reasons, one of the most important ones is the fact that, the over last two decades, mesoscopic normal metals and superconductors have demonstrated that non-equilibrium conditions may be achieved in controlled and reproducible ways. Moreover, one can observe that these systems are rarely truly at equilibrium but also exhibit many phenomena that need theoretical description -- some kind of ``standardized package'' that will be part of theoretical physics. Such a ``package'' may be given by quantum field theory and the considered book is devoted to a presentation of many important aspects of this new paradigm.NEWLINENEWLINEThe author takes into account many different aspects of the whole context and tries to pay special attention to specific peculiarities (especially relating to the notion of equilibrium) of non-equilibrium quantum field theory. His presentation starts with the simplest systems and develops through the successive chapters towards more and more complex cases. Usually equilibrium theory is interested in such cases where the experimental states are unchanged and a linear response is present. One can also see the equilibrium approach as a special case of the non-equilibrium one, thus, in this book, whenever it is possible, connections to the huge field of classical stochastic systems are made. We will illustrate this by a short outline of the book's contents.NEWLINENEWLINEAfter the Introduction, Chapter 2 is devoted to one of the simplest many-body systems, i.e., bosonic particles occupying a single quantum state. Its introduction allows to exploit in Chapter 3 the analogy between this simple model and the harmonic oscillator. This is done in order to formulate single-particle quantum mechanics as a path integral of closed time contours. In the next chapter, this particle is coupled to a bath. All these considerations are limited to systems with one or a few degrees of freedom (sometimes coupled to an external bath). In the case of these chapters, one can say that they are given with the purpose to introduce necessary notations, conventions and the mathematical apparatus that is used throughout the rest of the book.NEWLINENEWLINEThe next three chapters are devoted to considerations of specific examples. In Chapter 6, the collisionless dynamics of a classical plasma described by Vlasov equations and Landau damping is given. The proposed approach is presented in terms of the quantum formalism. Chapter 7 introduces the low-temperature weakly interacting Bose gas using the Gross-Pitaevskii description of the condensate as a stationary point approximation of the corresponding functional integral. The last chapter in this group is devoted to the dynamics of phase transitions by examples of the nucleation dynamics of critical droplets, reaction-diffusion models and Kardar-Parisi-Zhang considerations.NEWLINENEWLINEThen, Chapters 9--14 are devoted to fermions. The first two chapters of this part show a fermionic version of the degree of freedom model presented in Chapter 2, whereas Chapter 10 presents a discussion of non-equilibrium quantum transport in terms of the fermionic formalism. Next, the author gives some examples of fermionic systems, namely the kinetic equation approach and the diffusive dynamics of density fluctuations; mesoscopic fluctuations due to differences in disorder configurations in metallic samples; electron-electron interactions in disordered systems; the physics of disordered superconductors.NEWLINENEWLINEThis book is directed at advanced graduate students or post-docs in order to enhance their knowledge about non-equilibrium physics. There are no exercises, but many interesting examples can be found which may be very useful for those interested in this field. For those interested in broadening their knowledge about quantum field theory of non-equilibrium systems, this is a very valuable book and a must-read.