Correlations in classical and quantum systems far from thermal equilibrium

Hermann Haken

Jürgen Berges, Alexander Rothkopf, J. Schmidt

Strongly correlated systems far from equilibrium can exhibit scaling solutions with a dynamically generated weak coupling. We show this by investigating isolated systems described by relativistic quantum field theories for initial conditions leading to nonequilibrium instabilities, such as parametric resonance or spinodal decomposition. The nonthermal fixed points prevent fast thermalization if classical-statistical fluctuations dominate over quantum fluctuations. We comment on the possible significance of these results for the heating of the early Universe after inflation and the question of fast thermalization in heavy-ion collision experiments.

Nikolai Nikolaevich Bogoliubov, D. N. Zubarev, V. V. Tolmatchev +1 more

Claude‐Alain Pillet

Koopmanism -- the spectral theory of dynamicalsystems -- reduces the study of dynamical properties of a classical or quantum system S to the spectral analysis of its Liouvillean L_S . By definition, the operator L_S implements the dynamics on a suitable representation of the observable algebra of S. Near thermal equilibrium,this representation can often be constructed explicitely. Recent developments have shown that, in this situation, spectral analysis becomes a powerful tool in the study of thermal relaxation processes. Far from thermal equilibrium, the explicit construction of stationary states and of the corresponding representations is usually not possible. Nevertheless, important physical properties of the system S can be obtained from a fairly simple mathematical analysis. In this work, I investigate entropy production in open systems driven away from equilibrium by thermodynamic forces.

Juan Camilo Castillo

Adilet Imambekov, Jörg Schmiedmayer, Takuya Kitagawa +1 more

Quantum noise correlations have been employed in several areas in physics including condensed matter, quantum optics and ultracold atom to reveal non-classical states of the systems. So far, such analysis mostly focused on systems in equilibrium. In this paper, we show that quantum noise is also a useful tool to characterize and study the non-equilibrium dynamics of one dimensional system. We consider the Ramsey sequence of one dimensional, two-component bosons, and obtain simple, analytical expressions of time evolutions of the full distribution functions for this strongly-correlated, many-body system. The analysis can also be directly applied to the evolution of interference patterns between two one dimensional quasi-condensates created from a single condensate through splitting. Using the tools developed in this paper, we demonstrate that one dimensional dynamics in these systems exhibits the phenomenon known as "prethermalization", where the observables of non-equilibrium, long-time transient states become indistinguishable from those of thermal equilibrium states.