Out of equilibrium dynamics of classical and quantum complex systems

Abstract

Equilibrium is a rather ideal situation, the exception rather than the rule in Nature. Whenever the external or internal parameters of a physical system are varied its subsequent relaxation to equilibrium may be either impossible or take very long times. From the point of view of fundamental physics no generic principle such as the ones of thermodynamics allows us to fully understand their behaviour. The alternative is to treat each case separately. It is illusionary to attempt to give, at least at this stage, a complete description of all non-equilibrium situations. Still, one can try to identify and characterise some concrete but still general features of a class of out of equilibrium problems - yet to be identified - and search for a unified description of these. In this report I briefly describe the behaviour and theory of a set of non-equilibrium systems and I try to highlight common features and some general laws that have emerged in recent years.

36 pages, to be published in Compte Rendus de l'Academie de Sciences, T. Giamarchi ed

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• Non-ergodic extended phase of the Quantum Random Energy model
• Spatio-temporal spread of perturbations in power-law models at low temperatures: Exact results for OTOC
• Ac dynamic reorganization and non-equilibrium phase transition in driven vortex matter
• Full and fractional defects across the Berezinskii-Kosterlitz-Thouless transition in a driven-dissipative spinor quantum fluid
• Fragmented perspective of self-organized criticality and disorder in log gravity
• Structural heterogeneity: a topological characteristic to track the time evolution of soft matter systems