Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1005.5097 · The European Physical Journal Special Topics

New theoretical approaches for correlated systems in nonequilibrium

Martin Eckstein, Andreas Hackl, Stefan K. Kehrein, Marcus Kollar, Michael Moeckel, Philipp Werner, F. Alexander Wolf

Published Dec 1, 2009• 59 citations
arXivHTMLPDF
DOI
10.1140/epjst/e2010-01219-x

Related papers

New Theoretical Approaches to Strongly Correlated Systems

Springer eBooks•Jan 1, 2001•61 citations

Nonequilibrium Aspects of Integrable Models

Colin Rylands, Natan Andrei

Driven by breakthroughs in experimental and theoretical techniques, the study of nonequilibrium quantum physics is a rapidly expanding field with many exciting new developments. Among the manifold ways the topic can be investigated, one-dimensional systems provide a particularly fine platform. The trifecta of strongly correlated physics, powerful theoretical techniques, and experimental viability have resulted in a flurry of research activity over the past decade or so. In this review, we explore the nonequilibrium aspects of one-dimensional systems that are integrable. Through a number of illustrative examples, we discuss nonequilibrium phenomena that arise in such models, the role played by integrability, and the consequences these have for more generic systems.

arXiv:1904.09259•Annual Review of Condensed Matter Physics•Oct 25, 2019•16 citations

Theory of Strongly Correlated Systems

Rishabh Jha

arXiv:2507.07195•Lecture notes in physics•Jan 1, 2026•0 citations

Nonequilibrium dynamical mean-field theory and its applications

Hideo Aoki, Naoto Tsuji, Martin Eckstein +3 more

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.

arXiv:1310.5329•Reviews of Modern Physics•Jun 24, 2014•775 citations

Nonequilibrium critical relaxation with coupling to a conserved density

Klaus Oerding, H. K. Janssen

The authors study nonequilibrium critical relaxation properties of model C (purely dissipative relaxation of an order parameter coupled to a conserved density) starting from a macroscopically prepared initial state with short-range correlations. Using a field-theoretic renormalization group approach they show that all the stages of growth of the correlation length display universal behaviour governed by a new critical exponent theta . This exponent is calculated to second order in in =4-d where d is the spatial dimension of the system.

Journal of Physics A Mathematical and General•Jul 21, 1993•49 citations

Nonequilibrium behavior in strongly correlated electron systems

Dragana Popovi 'c

Bulletin of the American Physical Society•Mar 20, 2013•0 citations
Driven by breakthroughs in experimental and theoretical techniques, the study of nonequilibrium quantum physics is a rapidly expanding field with many exciting new developments. Among the manifold ways the topic can be investigated, one-dimensional systems provide a particularly fine platform. The trifecta of strongly correlated physics, powerful theoretical techniques, and experimental viability have resulted in a flurry of research activity over the past decade or so. In this review, we explore the nonequilibrium aspects of one-dimensional systems that are integrable. Through a number of illustrative examples, we discuss nonequilibrium phenomena that arise in such models, the role played by integrability, and the consequences these have for more generic systems.
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.
The authors study nonequilibrium critical relaxation properties of model C (purely dissipative relaxation of an order parameter coupled to a conserved density) starting from a macroscopically prepared initial state with short-range correlations. Using a field-theoretic renormalization group approach they show that all the stages of growth of the correlation length display universal behaviour governed by a new critical exponent theta . This exponent is calculated to second order in in =4-d where d is the spatial dimension of the system.