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Non Equilibrium Dynamics and Relaxation in Many Body Quantum Systems

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

Non-equilibrium Dynamics and Relaxation in Many-body Quantum Systems (QuantumRelax)

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, whose 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 centre 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 allow the realization of a multitude of different relevant physical situations.

In our experiments, we could identify a series of fundamental processes which guide the relaxation.

In our first set of experiments employing weak quenches we found:
(1) Relaxation is governed by the dephasing of many-body states and follows through 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 emerges locally and spreads throughout the system with a ‘horizon’ defined by the ‘light cone’.
(3) The pre-thermalized state is characterized by a generalized ‘classical’ thermodynamic ensemble, a ‘Generalized Gibbs Ensemble’ (GGE). This demonstrates that classical physics and thermodynamics at the macro scale emerges naturally from quantum physics through the dynamics of complex many-body systems.
(4) These pre-thermalized states relax in a further very slow evolution.
(5) Even though the system in a GGE looks classical quantum physics is fully alive underneath, as demonstrated by quantum revivals.
We conjecture that the observed stages of relaxation point to a universal behaviour for systems that can be described by an effective quantum field theory with long-lived quasi-particles.

In the second set of experiments, we demonstrated universal scaling in evolution starting from a very far off equilibrium state of a ‘quantum turbulent’ 1d system after and thereby established first evidence of a general description of non-equilibrium evolution by non-equilibrium renormalization group and non-thermal fixed points. This might lead to a classification of non-equilibrium systems in universality classes with similar potential to the classification of equilibrium phase transitions.

In addition, we got first insights into the connection between universality from non-thermal fixed points in far off equilibrium evolution and the Kibble-Zurek mechanism for close to equilibrium phase transitions.

We established high order correlation functions and their factorization as a general new tool to probe the many-body states of complex (strongly) correlated quantum systems and to characterize their emergent physical descriptions. We could thereby show that the quantum Sine-Gordon model emerges as an effective field theory description of two tunnel coupled superfluids.

Through our investigations, we hope to pave the way for a general, even universal, understanding of non-equilibrium many-body quantum systems across the plethora of research fields.

The demonstration of the emergence of a classical statistical ensemble in the evolution of an isolated quantum many-body systems sheds new light into the division between quantum world and the classical world, and will help putting the, often philosophical, discussions about this subject to a much more robust physics footing and have the potential to profoundly change our understanding of the relation between the quantum world and our classical perception of the macroscopic world.