Convergence of the quantum Boltzmann map (Q1062690)

We consider a non-linear map on the space of density matrices, which we call the Boltzmann map \(\tau\). It is the composition of a doubly stochastic map T on the space of n-body states, and the conditional expectation onto the one-body space. When T is ergodic, then the iterates of \(\tau\) take any initial state to the uniform distribution. If the energy levels are equally spaced and T conserves energy and is ergodic on each energy shell, then iterates of \(\tau\) take any initial state of finite energy to a canonical distribution.