Title: A quantum model for a particle source
Abstract:
This talk will present an analysis of a time evolution for a
density matrix, describing a quantum source for noninteracting
particles, either bosons or fermions. Concerning the particle number
(trace of the density matrix), I will present examples of sublinear,
linear or exponential growth in time, depending on the
bosonic/fermionic character of the particles and the spectral
properties of the one-particle Hamiltonian $H$ and the source state
$\phi$. I will also show that, with an appropriate scaling for the
coordinates and the source activity, the limit of the corresponding
Wigner transform will be governed by the phase space equation for a
classical particle source. The talk is based on a joint work with
Herbert Spohn [M. Butz and H. Spohn, Dynamical phase transition for a
quantum particle source, preprint arXiv:0908.2912v1].