Necessity of eigenstate thermalization for equilibration towards unique expectation values when starting from generic initial states

We investigate dynamical equilibration of expectation values in closed quantum systems for realistic non-equilibrium initial states. Thereby we find that the corresponding long time expectation values depend on the initial expectation values if eigenstate thermalization is violated. An analytical expression for the deviation from the expected ensemble value is derived for small displacements from equilibrium. Additional numerics for magnetization and energy equilibration in an asymmetric anisotropic spin-1/2-ladder demonstrate that the analytical predictions persist beyond the limits of the theory. The results suggest eigenstate thermalization as physically necessary condition for initial state independent equilibration.Comment: 5 pages, 4 figure

Boltzmann equation approach to transport in finite modular quantum systems

We investigate the transport behavior of finite modular quantum systems. Such systems have recently been analyzed by different methods. These approaches indicate diffusive behavior even and especially for finite systems. Inspired by these results we analyze analytically and numerically if and in which sense the dynamics of those systems are in agreement with an appropriate Boltzmann equation. We find that the transport behavior of a certain type of finite modular quantum systems may indeed be described in terms of a Boltzmann equation. However, the applicability of the Boltzmann equation appears to be rather limited to a very specific type of model