Relaxation phenomena at criticality

Abstract

The collective behaviour of statistical systems close to critical points is characterized by an extremely slow dynamics which, in the thermodynamic limit, eventually prevents them from relaxing to an equilibrium state after a change in the thermodynamic control parameters. The non-equilibrium evolution following this change displays some of the features typically observed in glassy materials, such as ageing, and it can be monitored via dynamic susceptibilities and correlation functions of the order parameter, the scaling behaviour of which is characterized by universal exponents, scaling functions, and amplitude ratios. This universality allows one to calculate these quantities in suitable simplified models and field-theoretical methods are a natural and viable approach for this analysis. In addition, if a statistical system is spatially confined, universal Casimir-like forces acting on the confining surfaces emerge and they build up in time when the temperature of the system is tuned to its critical value. We review here some of the theoretical results that have been obtained in recent years for universal quantities, such as the fluctuation-dissipation ratio, associated with the non-equilibrium critical dynamics, with particular focus on the Ising model with Glauber dynamics in the bulk. The non-equilibrium dynamics of the Casimir force acting in a film is discussed within the Gaussian model.

Talk delivered at Statphys23, Genova, Italy, July 9-13, 2007. 8 pages, 7 figures

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• Critical Casimir effect in classical binary liquid mixtures
• The Casimir effect: from quantum to critical fluctuations
• Nonequilibrium critical Casimir interactions in binary fluids
• Critical Casimir Effect: Exact Results
• Critical Casimir forces steered by patterned substrates
• The out of equilibrium behavior of Casimir type fluctuation induced forces for free classical fields
• Stresses in non-equilibrium fluids: Exact formulation and coarse grained theory
• Relaxation of the thermal Casimir force between net neutral plates containing Brownian charges
• Universal short-time dynamics: boundary functional renormalization group for a temperature quench
• Transient Casimir forces from quenches in thermal and active matter
• Dynamic critical behavior of model A in films: Zero-mode boundary conditions and expansion near four dimensions
• Non-equilibrium forces following quenches in active and thermal matter
• Forces exerted by a correlated fluid on embedded inclusions
• Out of equilibrium thermal Casimir effect in a model polarizable material
• Dynamical approach to the Casimir effect
• Dynamics and steady states of a tracer particle in a confined critical fluid
• Surface-induced non-equilibrium dynamics and critical Casimir forces for model B in film geometry
• Inducing oscillations of trapped particles in a near-critical Gaussian field
• Dynamics of the critical Casimir force for a conserved order parameter after a critical quench
• Work, work fluctuations, and the work distribution in a thermal non-equilibrium steady state
• Correlations and forces in sheared fluids with or without quenching
• Viscosity of a sheared correlated (near-critical) model fluid in confinement
• Fluctuations of the critical Casimir force
• Interplay of quenching temperature and drift in Brownian dynamics
• Repulsive thermal van der Waals interaction in multi-species asymmetric electrolytes driven by external electric fields
• The role of dimensionality and geometry in quench-induced nonequilibrium forces
• Solving Lyapunov equations for electrically driven ternary electrolytes -- application to long-range van der Waals interactions