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QuantumRelax Report Summary

Project ID: 320975
Funded under: FP7-IDEAS-ERC
Country: Austria

Mid-Term Report Summary - QUANTUMRELAX (Non Equilibrium Dynamics and Relaxation in Many Body Quantum Systems)

Non-equilibrium processes and relaxation occur in many diverse physical systems over many orders of magnitude in length scale and energy, from the very large to the very small, from the very hot to the very cold, from the simple to the very complex. However, very little about the relaxation of non-equilibrium systems is understood. There is no general understanding of if, how and on which timescale such systems reach thermal equilibrium, nor do we understand the transient processes present in their evolution.

Relaxation processes are even more mysterious in isolated Quantum Systems, who’s evolution is ‘Unitary’, that in its mathematical form means there is NO relaxation. Never the less non-equilibrium dynamics and relaxation in many-body quantum systems is at the center of some of the most intriguing phenomena in many diverse areas of physics ranging from inflation in the early universe to the emergence of classical properties in complex quantum systems.

The project QuantumRelax (“Non-equilibrium Dynamics and Relaxation in Many-Body Quantum Systems”) aims at studying some of the fundamental problems in non-equilibrium many-body quantum physics and developing a general toolbox for their analysis and characterization. Model systems built with ultra-cold atoms provide a unique opportunity for studying such complex non-equilibrium quantum many body systems in the laboratory. The coherent quantum evolution can be observed on experimentally accessible timescales and the tunability in interaction, temperature and dimensionality allows the realization of a multitude of different relevant physical situations.

In the first half of the project QuantumRelax, we studied one dimensional quantum many body systems out of equilibrium. We could thereby identify a series of fundamental processes which guide the relaxation.
(1) Relaxation follows through discrete steps, governed by quasi steady states (pre-thermalized states) defined by nearly conserved quantities in the approximate quantum field theoretical descriptions of the many body physics.
(2) The relaxation follows a light cone like evolution, where the pre thermalized state meres locally and spreads throughout the system with an ‘horizon’ defined by the ‘light cone’.
(3) The pre-thermalized state is characterized by a generalized thermodynamic ensemble, a ‘Generalized Gibbs Ensemble’ (GGE).
(4) These pre-thermalized states relax in a further very slow evolution.
We conjecture that the observed stages of relaxation point to a universal behavior for systems that can be described by an effective quantum field theory with long lived quasi particles. The pre-thermalized state corresponds to a non-thermal fix-point in a renormalization group description of non-equilibrium dynamics.

A key goal for the second half of QuntumRelax will be to solidify this conjecture, with diverse experiments. To realize this goal we are developing a novel experimental apparatus which will allow to study a wide variety of non-equilibrium quantum dynamics under conditions ranging from weakly interacting to strongly correlated, from weakly disturbed to quantum turbulent. and search for universal properties in non-equilibrium quantum evolution.

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