Related papers: Thermalization of Classical Weakly Nonintegrable M…
We propose a novel framework to characterize the thermalization of many-body dynamical systems close to integrable limits using the scaling properties of the full Lyapunov spectrum. We use a classical unitary map model to investigate…
We study thermalization of weakly nonintegrable nonlinear unitary lattice dynamics. We identify two distinct thermalization regimes close to the integrable limits of either linear dynamics or disconnected lattice dynamics. For weak…
We investigate prethermalization by studying the statistical properties of the time-dependent largest Lyapunov exponent $\Lambda(t)$ for unitary-circuit maps upon approaching integrability. We follow the evolution of trajectories for…
We study thermalization slowing down of a quantum many-body spin system upon approach to two distinct integrability limits. Motivated by previous studies of classical systems, we identify two thermalization time scales: one quantum Lyapunov…
We study thermalization in closed non-integrable quantum systems using the Krylov basis. We demonstrate that for thermalization to occur, the matrix representation of typical local operators in the Krylov basis should exhibit a specific…
Motivated by dynamical experiments on cold atomic gases, we develop a quantum kinetic approach to weakly perturbed integrable models out of equilibrium. Using the exact matrix elements of the underlying integrable model we establish an…
We study the effects of integrability breaking perturbations on the non-equilibrium evolution of many-particle quantum systems. We focus on a class of spinless fermion models with weak interactions. We employ equation of motion techniques…
When a non-integrable system evolves out of equilibrium for a long time, local observables are expected to attain stationary expectation values, independent of the details of the initial state. However, intriguing experimental results with…
Using a Krylov-subspace time evolution algorithm, we simulate the real-time dynamics of translation invariant non-integrable finite spin rings to quite long times with high accuracy. We systematically study the finite-size deviation between…
Thermalization of classical fields is investigated in a \phi^4 scalar field theory in 1+1 dimensions, discretized on a lattice. We numerically integrate the classical equations of motion using initial conditions sampled from various…
Ability of dynamical systems to relax to equilibrium has been investigated since the invention of statistical mechanics, which establishes the connection between dynamics of many-body Hamiltonian systems and phenomenological thermodynamics.…
It is usually expected and observed that non-integrable isolated quantum systems thermalize. However, for some non-integrable spin chain models, in a numerical study, initial states with oscillations that persisted for some time were found…
We establish an analytical criterion for dynamical thermalization within harmonic systems, applicable to both classical and quantum models. Specifically, we prove that thermalization of various observables, such as particle energies in…
Understanding the microscopic mechanisms of thermalization in closed quantum systems is among the key challenges in modern quantum many-body physics. We demonstrate a method to probe local thermalization in a large-scale many-body system by…
We study the thermalization slowing down of Fermi-Past-Ulam-Tsingou (FPUT) chains and of Toda chains with nonintegrable boundaries. We focus on the transition from FPUT to harmonic chains, from FPUT to Toda chains with fixed boundaries, and…
In their seminal work, Fermi, Pasta, Ulam and Tsingou explored the connection between statistical mechanics and dynamical properties, such as chaos and ergodicity. Even today, seventy years later, the topic is not fully understood: while…
Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…
Localization marks the breakdown of thermalization in subregions of quantum many-body systems in the presence of sufficiently large disorder. In this paper, we use numerical techniques to study thermalization and localization in a many-body…
This paper develops a new approach to the estimation of the degree of boundedness or stability of multidimensional nonlinear systems with time-dependent nonperiodic coefficients-an essential task in various engineering and natural science…
The dynamics of a many-body system can take many forms, from a purely reversible evolution to fast thermalization. Here we show experimentally and numerically that an assembly of spin 1 atoms all in the same spatial mode allows one to…