Thermalization of closed chaotic many-body quantum systems

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 Delta (the correlation width). The results are used to calculate Tr ( A rho ( t ) ) . Here rho ( t ) is the time-dependent density matrix of the system, and A represents an observable. In the semiclassical regime, the average ⟨ Tr ( A rho ( t ) ) ⟩ decays on the time scale PLANCK CONSTANT OVER TWO PI / Delta toward an asymptotic value. If the energy spread of the system is of order Delta, that value is given by Tr ( A rho eq ) where rho eq is the density matrix of statistical equilibrium. The correlation width Delta is the central parameter of our approach. We argue that Delta occurs generically in chaotic quantum systems and plays the same central role.