Asymptotic relaxation of a system of a large number of interacting particles

I.V. Simenog

Valentin Nikolaevich Ryzhov, Elena Evgen'evna Tareeva

I. V. Vovchenko, Vladislav Yu. Shishkov, A. A. Zyablovsky +1 more

Existing Markov models of the relaxation of quantum-mechanical systems are applicable in the approximations where the difference between eigenfrequencies is either much larger than the relaxation rates (global approach) or much lower than these rates (local approach). In this work, a model has been proposed to describe relaxation in systems where the difference between some eigenfrequencies is close to the relaxation rates. It has been shown that the master equation for the density matrix contains coefficients explicitly depending on the time in the interaction representation. Equations for the occupation numbers of the modes of the system have been derived by example of two interacting oscillators. It has been shown that occupation numbers in the proposed approach in the limits of small and large differences between eigenfrequencies compared to the relaxation rates asymptotically match the occupation numbers in the local and global approaches, respectively.

Pasquale Calabrese, Mihail Mintchev, Ettore Vicari

We derive exact relations between the Rényi entanglement entropies and the particle-number fluctuations of (connected and disjoint) spatial regions in systems of N non-interacting fermions in arbitrary dimension. We prove that the asymptotic large- N behavior of the entanglement entropies is proportional to the variance of the particle number. We also consider 1D Fermi gases with a localized impurity, where all particle cumulants contribute to the asymptotic large- N behavior of the entanglement entropies. The particle cumulant expansion turns out to be convergent for all integer-order Rényi entropies (except for the von Neumann entropy) and the first few cumulants provide already a good approximation. Since the particle cumulants are accessible to experiments, these relations may provide a measure of entanglement in these systems.

И. В. Александров