The study of rare or anomalous fluctuations in classical, stochastic systems has lead in recent years to the understanding of dynamical phase transitions – occurring in phenomena where different classes of trajectories enter in competition. Example systems include 'exclusion processes' (lattice gases in which particles interact only through an exclusion rule: particles cannot occupy the same site). In such systems, jammed and non-jammed histories can compete. The dynamical phase transition is reflected at the mathematical level in a singularity of a large deviation function. Although being classical, the dynamics of such systems can be mapped to the thermodynamics of a quantum spin chain. Classical 'rare events' are mapped to quantum typical configurations. This mapping is known at the formal level for many years, but it has not been fully exploited. We discuss (i) how the understanding of finite-size properties of the classical dynamical phase transition brings a new light on an example quantum phase transition and (ii) how standard quantum rotational symmetries allow to map non-equilibrium to equilibrium current fluctuations in the SSEP driven out-of-equilibrium by its boundaries, giving an answer to the existence or not of singularities.

(Joint works with Marc Cheneau, Juanpe Garrahan, Frédéric van Wijland, Cécile Appert-Rolland, Bernard Derrida, Alberto Imparato)

Thimothée Thiery (LPT-ENS)Thu, Feb 25

The study of rare or anomalous fluctuations in classical, stochastic systems has lead in recent years to the understanding of dynamical phase transitions – occurring in phenomena where different classes of trajectories enter in competition. Example systems include 'exclusion processes' (lattice gases in which particles interact only through an exclusion rule: particles cannot occupy the same site). In such systems, jammed and non-jammed histories can compete. The dynamical phase transition is reflected at the mathematical level in a singularity of a large deviation function. Although being classical, the dynamics of such systems can be mapped to the thermodynamics of a quantum spin chain. Classical 'rare events' are mapped to quantum typical configurations. This mapping is known at the formal level for many years, but it has not been fully exploited. We discuss (i) how the understanding of finite-size properties of the classical dynamical phase transition brings a new light on an example quantum phase transition and (ii) how standard quantum rotational symmetries allow to map non-equilibrium to equilibrium current fluctuations in the SSEP driven out-of-equilibrium by its boundaries, giving an answer to the existence or not of singularities.

(Joint works with Marc Cheneau, Juanpe Garrahan, Frédéric van Wijland, Cécile Appert-Rolland, Bernard Derrida, Alberto Imparato)