Stefano Lepri

We investigate thermalization in a tight-binding chain with an on-site defect subject to local dephasing noise implemented as random phase kicks. For a single linear defect of strength ε , we obtain an exact analytical description of the system spectrum and formulate the dephasing-induced dynamics in the eigenstate basis. We derive an approximate kinetic equation for mode populations that describes a continuous-time random walk in action space. The walk transition rates are defined by the overlap matrix encoding the spatial structure of eigenstates that can be computed exactly. Analyzing the spectral properties of the equation, we show that defect-induced localized modes act as bottlenecks that strongly slow down relaxation, with rates scaling as ε − 2 for strong defects. Using large-deviation theory, we characterize rare dynamical trajectories and identify distinct relaxation pathways associated with low- and high-activity regimes in action space. We provide numerical evidence that the large-deviation function exhibits a dynamical phase transition in the limit ε → ∞ . We then extend our analysis to the nonlinear case, considering a single nonlinear defect embedded in either a linear or a fully nonlinear discrete Schrödinger equation. Numerical simulations reveal a qualitatively faster approach to equilibrium than in the corresponding linear-defect model, driven by the amplitude-dependent weakening of the defect. Our results provide a unified framework for understanding thermalization, rare fluctuations, and relaxation pathways in stochastic tight-binding systems.

A novel approach is proposed to characterize the dynamics of perturbed many-body integrable systems. Focusing on the paradigmatic case of the Toda chain under non-integrable Hamiltonian perturbations, this study introduces a method based the time evolution of the Lax eigenvalues as a proxy of the quasi-particles velocities and of the perturbed Toda actions. A set of exact equations of motion for the is derived that closely resemble those for eigenenergies of a quantum problem (also known as the Pechukas-Yukawa gas). Numerical simulations suggest that the invariant measure of such dynamics is basically the thermal density of states of the Toda lattice, regardless of the form of the perturbation.

We study non-equilibrium properties of a chain of N oscillators with both long-ranged harmonic interactions and long-range conservative noise that exchange momenta of particle pairs. We derive exact expressions for the (deterministic) energy-current auto-correlation at equilibrium, based on the kinetic approximation of the normal mode dynamics. In all cases the decay is algebraic in the thermodynamic limit. We distinguish four distinct regimes of correlation decay depending on the exponents controlling the range of deterministic and stochastic interactions. Surprisingly, we find that long-range noise breaks down the long-range correlations characteristic of low dimensional models, suggesting a normal regime in which heat transport becomes diffusive. For finite systems, we do also derive exact expressions for the finite-size corrections to the algebraic decay of the correlation. In certain regimes, these corrections are considerably large, rendering hard the estimation of transport properties from numerical data for the finite chains. Our results are tested against numerical simulations, performed with an efficient algorithm.

We investigate the behavior of heat conduction in two-dimensional (2D) electron gases without and with a magnetic field. We perform simulations with the multiparticle collision approach, suitably adapted to account for the Lorenz force acting on the particles. For zero magnetic field, we find that the heat conductivity κ diverges with the system size L following the logarithmic relation κ∼lnL (as predicted for 2D systems) for small L values; however, in the thermodynamic limit the heat conductivity tends to follow the relation κ∼L^{1/3}, as predicted for one-dimensional (1D) fluids. This suggests the presence of a dimensional-crossover effect in heat conduction in electronic systems that adhere to standard momentum conservation. Under the magnetic field, time-reversal symmetry is broken and the standard momentum conservation in the system is no longer satisfied but the pseudomomentum of the system is still conserved. In contrast with the zero-field case, both equilibrium and nonequilibrium simulations indicate a finite heat conductivity independent on the system size L as L increases. This indicates that pseudomomentum conservation can exhibit normal diffusive heat transport, which differs from the abnormal behavior observed in low-dimensional coupled charged harmonic oscillators with pseudomomentum conservation in a magnetic field. These findings support the validity of the hydrodynamic theory in electron gases and clarify that pseudomomentum conservation is not enough to ensure the anomalous behavior of heat conduction.