The study of nonequilibrium phenomena in correlated lattice systems has developed into one of the most active and exciting branches of condensed matter physics. This research field provides rich new insights that could not be obtained from the study of equilibrium situations, and the theoretical understanding of the physics often requires the development of new concepts and methods. On the experimental side, ultrafast pump-probe spectroscopies enable studies of excitation and relaxation phenomena in correlated electron systems, while ultracold atoms in optical lattices provide a new way to control and measure the time evolution of interacting lattice systems with a vastly different characteristic time scale compared to electron systems. A theoretical description of these phenomena is challenging because, first, the quantum-mechanical time evolution of many-body systems out of equilibrium must be computed and second, strong-correlation effects which can be of a nonperturbative nature must be addressed. This review discusses the nonequilibrium extension of the dynamical mean field theory (DMFT), which treats quantum fluctuations in the time domain and works directly in the thermodynamic limit. The method reduces the complexity of the calculation via a mapping to a self-consistent impurity problem, which becomes exact in infinite dimensions. Particular emphasis is placed on a detailed derivation of the formalism, and on a discussion of numerical techniques, which enable solutions of the effective nonequilibrium DMFT impurity problem. Insights gained into the properties of the infinite-dimensional Hubbard model under strong nonequilibrium conditions are summarized. These examples illustrate the current ability of the theoretical framework to reproduce and understand fundamental nonequilibrium phenomena, such as the dielectric breakdown of Mott insulators, photodoping, and collapse-and-revival oscillations in quenched systems. Furthermore, remarkable novel phenomena have been predicted by the nonequilibrium DMFT simulations of correlated lattice systems, including dynamical phase transitions and field-induced repulsion-to-attraction conversions.

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Nonequilibrium dynamical mean-field theory and its applications

The authors review the physics of ultrafast dynamics in semiconductors and their heterostructures, including both the observed experimental phenomena and the theoretical description of the processes. These are probed by ultrafast optical excitation, generating nonequilibrium states that can be monitored by time-resolved spectroscopy. Light pulses create coherent superpositions of states, and the dynamics of the associated phase relationships can be directly investigated by means of many-pulse experiments. The commonly used experimental techniques are briefly reviewed. A variety of different phenomena can be described within a common theoretical framework based on the density-matrix formalism. The important interactions of the carriers included in the theoretical description are the phonon interactions, the interactions with classical and quantum light fields, and the Coulomb interaction among the carriers themselves. These interactions give rise to a strong interplay between phase coherence and relaxation, which strongly affects the non equilibrium dynamics. Based on the general theory, the authors review the physical phenomena in various semiconductor structures including superlattices, quantum wells, quantum wires, and bulk media. Particular results which have played a central role in understanding the microscopic origins of the relaxation processes are discussed in detail.

Theory of ultrafast phenomena in photoexcited semiconductors

Semiconductor superlattices: a model system for nonlinear transport

http://cds.cern.ch/record/483091/files/0101103.pdf

The quark-gluon plasma: collective dynamics and hard thermal loops

A kinetic theory for quantum many-particle systems in time-dependent electromagnetic fields is developed based on a gauge-invariant formulation. The resulting kinetic equation generalizes previous results to quantum systems and includes many-body effects. It is, in particular, applicable to the interaction of strong laser fields with dense correlated plasmas.

Quantum kinetic theory of plasmas in strong laser fields

A systematic and unambiguous method of deriving generalized transport equations, i.e., equations for distribution functions having a single-time structure, on the basis of the nonequilibrium Green function is obtained, if the common Kadanoff-Baym (KB) ansatz is replaced by a modification which we call the generalized KB ansatz. This new ansatz is fully consistent with the dynamical structure of the theory and is independent of any specific representation. The resulting equations appear to be the zeroth-order approximation of a systematic expansion in terms of the collision duration. In the case of the electron transport in a strong homogeneous electric field, the generalized ansatz is shown to be in agreement with the superoperator methods, whereas the KB ansatz is known to fail in this case.

Generalized Kadanoff-Baym ansatz for deriving quantum transport equations

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Generalized Kadanoff-Baym ansatz for deriving quantum transport equations