Hamiltonian time evolution of the density matrix

Edward R. Pike, Sarben Sarkar, J.S. Satchell

Ronald F. Fox

An equation for the time evolution of the density matrix for a nonrelativistic quantum mechanical system is presented. It involves a Hamiltonian which contains a stochastic contribution. Before stochastic averaging is performed, it is shown that the density matrix equation is time reversal invariant, whereas after stochastic averaging is performed, it is shown that the averaged density matrix equation is not time reversal invariant.

Ladislav Šamaj

Vinayak, Marko Žnidarič

We study time evolution of a subsystem's density matrix under unitary evolution, generated by a sufficiently complex, say quantum chaotic, Hamiltonian, modeled by a random matrix. We exactly calculate all coherences, purity and fluctuations. We show that the reduced density matrix can be described in terms of a noncentral correlated Wishart ensemble for which we are able to perform analytical calculations of the eigenvalue density. Our description accounts for a transition from an arbitrary initial state towards a random state at large times, enabling us to determine the convergence time after which random states are reached. We identify and describe a number of other interesting features, like a series of collisions between the largest eigenvalue and the bulk, accompanied by a phase transition in its distribution function.

Omar Gamel

We find the effective Hamiltonian for the evolution of the time-averaged density matrix of a quantum system, along with nonunitary decoherence terms in Lindblad form. Theory applied to AC Stark Shift, and 3-level Raman Transitions.

G. N. Brodimas, A. D. Jannussis, N. Patargias