Thermalization of closed chaotic many-body quantum systems

Abstract

We investigate thermalization of a closed chaotic many-body quantum system by combining the Hartree–Fock approach with the Bohigas–Giannoni–Schmit conjecture. The conjecture implies that locally, the residual interaction causes the statistics of eigenvalues and eigenfunctions of the full Hamiltonian to agree with random-matrix predictions. The agreement is confined to an interval Δ (the correlation width). The results are used to calculate Tr(Aρ(t)) . Here ρ(t) is the time-dependent density matrix of the system, and A represents an observable. In the semiclassical regime, the average ⟨Tr(Aρ(t))⟩ decays on the time scale ℏ/Δ toward an asymptotic value. If the energy spread of the system is of order Δ, that value is given by Tr(Aρeq) where ρeq is the density matrix of statistical equilibrium. The correlation width Δ is the central parameter of our approach. We argue that Δ occurs generically in chaotic quantum systems and plays the same central role.