Quantum Effects in the Steady State of the Dissipative Standard Map
Thomas Dittrich, R. Graham · Europhysics Letters (EPL) · 1987
The time evolution of the density matrix generated by a quantum map which corresponds to the classical dissipative standard map is studied numerically. The system approaches a steady state which is the quantum analogue of a classical ensemble on an attractor. The quantum-statistical steady state is represented both as Wigner quasi-probability density and as the diagonal elements of the density matrix in coherent states. It is compared with the corresponding results for a stochastic classical map that is equivalent to the semi-classical limit of the quantum map.