Relaxation due to random collisions with a many-qudit environment
Giuseppe Gennaro, Giuliano Benenti, G. Massimo Palma · Physical Review A · 2009
We analyze the dynamics of a system qudit of dimension $\ensuremath{\mu}$ sequentially interacting with the $\ensuremath{ u}$-dimensional qudits of a chain playing the role of an environment. Each pairwise collision has been modeled as a random unitary transformation. The relaxation to equilibrium of the purity of the system qudit, averaged over random collisions, is analytically computed by means of a Markov chain approach. In particular, we show that the steady state is the one corresponding to the steady state for random collisions with a single environment qudit of effective dimension ${\ensuremath{ u}}_{e}=\ensuremath{ u}\ensuremath{\mu}$. Finally, we numerically investigate aspects of the entanglement dynamics for qubits $(\ensuremath{\mu}=\ensuremath{ u}=2)$ and show that random unitary collisions can create multipartite entanglement between the system qudit and the qudits of the chain.