Slow relaxations and nonequilibrium dynamics in classical and quantum systems

Abstract

I wish to thank the organisers of the Les Houches Summer School of Physics Strongly Interacting Quantum Systems Out of Equilibrium for their invitation to lecture. It was a great opportunity to thoroughly think on several topics on out of equilibrium dynamics.Much of what I learned on out of equilibrium dynamics, and that I retransmitted to the students, is due to collaborations and interactions with colleagues and friends. I will not list all their names here (a too long list . . . I had a lot to learn) but I thank them all. Last but not least, special thanks are due to T. Giamarchi and L.F. Cugliandolo for their encouragements (and patience!). Contents 1 Coupling to the Environment: What is a Reservoir? 1.1 What does a reservoir do to a system? 1.2 The simplest reservoir: linearly coupled Harmonic oscillators 1.3 Noise and irreversibility 1.4 The environment 2 Field Theory, Time-Reversal Symmetry and Fluctuation Theorems 2.1 Martin-Siggia-Rose-DeDominicis-Janssen field theory 2.2 Meaning of the fields 2.3 Generalizations 2.4 Relationship with Schwinger-Keldysh field theory 2.5 Time-reversal symmetry 2.6 Time-reversal symmetry breaking and fluctuation relations out of equilibrium 2.7 Quantum systems 3 Thermalization 3.1 The meaning of thermalization 3.2 Classical systems coupled to a bath 3.3 Quantum systems coupled to a bath 3.4 Isolated systems 4 Quenches and Coarsening 4.1 Thermal Quenches 4.2 Coarsening 4.3 Curvature-driven Domain Growth 4.4 Kibble-Zurek Mechanism and Slow Thermal Quenches 4.5 Quantum fluctuations 5 Quenched Disorder and Slow Dynamics 5.1 Broad distribution of relaxation times 5.2 Broad distribution of low energy excitations 5.3 Activated dynamics scaling and zero temperature fixed points 5.4 Domain growth and coarsening in disordered systems 5.5 Infinite randomness fixed points 6 Effective Temperatures 6.1 Metastable equilibrium 6.2 Driven and Active Systems 6.3 Glassy systems viii Contents References 55

Dimensional crossover of Bose-Einstein-condensation phenomena in quantum gases confined within slab geometries

“…Such phenomena are of great interest in many different physical contexts, at both first-order and continuous transitions, where one may observe hysteresis and coarsening phenomena, the Kibble-Zurek (KZ) defect production, etc, see, e.g., Refs. [30,33,57,58,[91][92][93][94][95][96][97][98][99][100][101][102]. The correlation functions obey general off-equilibrium scaling (OS) laws in the limit of large time scale t s of the variations across the transition, which are controlled by the universal static and dynamic exponents of the equilibrium transition [94,96,102].…”

“…They were able to check the initial 3D behavior, without a clear identification of the subsequent quasi-2D behavior. The computation of the defect production arising from the Kibble-Zurek mechanism is further complicated by later-time coarsening phenomena [92,96,98].…”

Off-equilibrium scaling behaviors driven by time-dependent external fields in three-dimensionalO(N)vector models

“…These phenomena are of great interest in many different physical contexts, see, e.g., Refs. [1][2][3][4][5][6][7].…”

Complexity of energy barriers in mean-field glassy systems

“…Many complex systems in physics, biology and computer science are characterized by high-dimensional landscapes full of local minima and saddles of any order. Characterizing the statistical properties of critical points in these energy landscapes is instrumental to explain and predict the static and dynamic behavior of such systems [1,2]. Much of the current understanding of this problem comes from the research on the glass transition and spin-glasses, which played a major role in developing methods to study the generic properties of rough high-dimensional landscapes.…”