Canonical Density Matrices from Eigenstates of Mixed Systems.

One key issue of the foundation of statistical mechanics is the emergence of equilibrium ensembles in isolated and closed quantum systems. Recently, it was predicted that in the thermodynamic (N→∞) limit of large quantum many-body systems, canonical density matrices emerge for small subsystems from almost all pure states. This notion of canonical typicality is assumed to originate from the entanglement between subsystem and environment and the resulting intrinsic quantum complexity of the many-body state.

Semiclassical wave functions for open quantum billiards.

We present a semiclassical approximation to the scattering wave function Ψ(r,k) for an open quantum billiard, which is based on the reconstruction of the Feynman path integral. We demonstrate its remarkable numerical accuracy for the open rectangular billiard and show that the convergence of the semiclassical wave function to the full quantum state is controlled by the mean path length or equivalently the dwell time for a given scattering state. In the numerical implementation a cutoff length in the maximum path length or, equivalently, a maximum dwell time τ(max) included implies a finite energy resolution ΔE~τ(max)(-1).