Revisiting classical and quantum disordered systems from the unifying perspective of large deviations

Abstract

The theory of large deviations is already the natural language for the statistical physics of equilibrium and non-equilibrium. In the field of disordered systems, the analysis via large deviations is even more useful to describe within a unified perspective the typical events and the rare events that occur on various scales. In the present pedagogical introduction, we revisit various emblematic classical and quantum disordered systems in order to highlight the common underlying mechanisms from the point of view of large deviations.

v2=revised version (30 pages)

References in corpus (10)

• Anderson Transitions
• The large deviation approach to statistical mechanics
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Fluctuation theorems for stochastic dynamics
• Large Deviations of Extreme Eigenvalues of Random Matrices
• Extreme Value Statistics of Eigenvalues of Gaussian Random Matrices
• Large Deviations of the Maximum Eigenvalue for Wishart and Gaussian Random Matrices
• Steady state statistics of driven diffusions
• Dynamical scaling for critical states: is Chalker's ansatz valid for strong fractality?
• Random Transverse Field Spin-Glass Model on the Cayley tree : phase transition between the two Many-Body-Localized Phases

Cited by in corpus (26)

• Critical properties of the Anderson transition in random graphs: two-parameter scaling theory, Kosterlitz-Thouless type flow and many-body localization
• Large deviations for Markov processes with stochastic resetting : analysis via the empirical density and flows or via excursions between resets
• Large deviations of the Lyapunov exponent in 2D matrix Langevin dynamics with applications to one-dimensional Anderson Localization models
• Role of current fluctuations in nonreversible samplers
• Inference of Markov models from trajectories via Large Deviations at Level 2.5 with applications to random walks in disordered media
• Statistical physics of long dynamical trajectories for a system in contact with several thermal reservoirs
• Large deviations at various levels for run-and-tumble processes with space-dependent velocities and space-dependent switching rates
• Large deviations for the Skew-Detailed-Balance Lifted-Markov processes to sample the equilibrium distribution of the Curie-Weiss model
• Jump-Drift and Jump-Diffusion Processes : Large Deviations for the density, the current and the jump-flow and for the excursions between jumps
• Conditioned diffusion processes with an absorbing boundary condition for finite or infinite horizon
• Large deviations for metastable states of Markov processes with absorbing states with applications to population models in stable or randomly switching environment
• Real-Space Renormalization for disordered systems at the level of Large Deviations
• Conditioning diffusion processes with killing rates
• Large deviations for the Pearson family of ergodic diffusion processes involving a quadratic diffusion coefficient and a linear force
• Microcanonical conditioning of Markov processes on time-additive observables
• Revisiting boundary-driven non-equilibrium Markov dynamics in arbitrary potentials via supersymmetric quantum mechanics and explicit large deviations at various levels
• Large deviations and conditioning for chaotic non-invertible deterministic maps: analysis via the forward deterministic dynamics and the backward stochastic dynamics
• Inhomogeneous asymmetric exclusion processes between two reservoirs : large deviations for the local empirical observables in the Mean-Field approximation
• Large deviations at level 2.5 and for trajectories observables of diffusion processes : the missing parts with respect to their random-walks counterparts
• Explicit dynamical properties of the Pelikan random map in the chaotic region and at the intermittent critical point towards the non-chaotic region
• Large deviations for trajectory observables of diffusion processes in dimension $d>1$ in the double limit of large time and small diffusion coefficient
• A supersymmetric quantum perspective on the explicit large deviations for reversible Markov jump processes, with applications to pure and random spin chains
• Inverse problem in the conditioning of Markov processes on trajectory observables : what canonical conditionings can connect two given Markov generators ?
• Traveling/non-traveling phase transition and non-ergodic properties in the random transverse-field Ising model on the Cayley tree
• Asymmetric scaling in large deviations for rare values bigger or smaller than the typical value
• Conditioning two diffusion processes with respect to their first-encounter properties