Thermalization in a closed many-body quantum system

Haibin Li, Yang Yang, Pei Wang +1 more

We propose a quantity called modulus fidelity to measure the closeness of two quantum pure states. We use it to investigate the closeness of eigenstates in one-dimensional hard-core bosons. When the system is integrable, eigenstates close to their neighbor or not, which leads to a large fluctuation in the distribution of modulus fidelity. When the system becomes chaos, the fluctuation is reduced dramatically, which indicates all eigenstates become close to each other. It is also found that two kind of closeness, i.e., closeness of eigenstates and closeness of eigenvalues, are not correlated at integrability but correlated at chaos. We also propose that the closeness of eigenstates is the underlying mechanism of eigenstate thermalization hypothesis (ETH) which explains the thermalization in quantum many-body systems.

Felix M. Izrailev

Juniper J. Bauroth-Sherman

An explanation of the thermalization of closed quantum systems is the eigenstate thermalization hypothesis, which states that all eigenstates are thermal. Quantum many-body scars are a relatively newly discovered phenomenon, which describe a band of nonthermal eigenstates that have high overlap with the initial state. These states impede the thermalization of systems. This paper looks at a system of ultracold Rubidium Rydberg atoms that interact via dipole-dipole interactions. This system has apparently normal thermalization when the dipole interactions are primarily two-body interactions, however when they are primarily three-body interaction the system thermalizes slower than expected. Simulations results are presented which suggest that scars states affect the time evolution of the system.

Osamu Fukushima

Cenap Ates, Juan P. Garrahan, Igor Lesanovsky

Thermalization has been shown to occur in a number of closed quantum many-body systems, but the description of the actual thermalization dynamics is prohibitively complex. Here, we present a model-in one and two dimensions-for which we can analytically show that the evolution into thermal equilibrium is governed by a Fokker-Planck equation derived from the underlying quantum dynamics. Our approach does not rely on a formal distinction of weakly coupled bath and system degrees of freedom. The results show that transitions within narrow energy shells lead to a dynamics which is dominated by entropy and establishes detailed balance conditions that determine both the eventual equilibrium state and the nonequilibrium relaxation to it.

Léa Ferreira dos Santos, Eduardo Jonathan Torres-Herrera, Francisco Pérez-Bernal +2 more