We present a formalism to study many-particle quantum transport across a lattice locally connected to two finite, nonstationary (bosonic or fermionic) reservoirs, both of which are in a thermal state. We show that, for conserved total particle number, a system of nonlinear quantum-classical master equations describes the concurrent many-particle time evolution on the lattice and in the reservoirs. The finiteness of the reservoirs makes a macroscopic current emerge, which decreases exponentially in time and asymptotically drives the many-particle configuration into an equilibrium state where the particle flow ceases. We analytically derive the timescale of this equilibration process, and, furthermore, investigate the imprint of many-particle interferences on the transport process.
Abstract We introduce a concept of non-coherent evolution of macroscopic quantum systems. We show that for weakly interacting systems such evolution is a Markovian stochastic process. The transition rates between system states, which characterize the process, are determined by Fermi’s golden rule. Such evolution is time-irreversible and leads to the equidistribution of probabilities across every state of the system. Furthermore, we investigate the time dependence of the mean numbers of particles in single-particle states and find that, under the given assumptions, it is governed by the Boltzmann collision integral. The proposed mechanism that transforms time-reversible unitary evolution into time-irreversible stochastic evolution is non-coherence. In the presented theory, the non-coherence is not associated with interaction with a heat bath, but rather with the finite spectral width of quantum states. This understanding of non-coherence is analogous to the one used in wave optics. Thus, we present a novel approach to the famous arrow of time problem.
We use the free evolution propagator to determine the quantum probability representation (i.e., the general expression of the tomogram) of any one-dimensional system described by a density state. The evolution operator for the considered quantum system is additionally used to establish the corresponding time dependent tomogram. Applications are given for a Gaussian wave packet, the quantum shutter related with the phenomenon of diffraction in time, the double quantum shutter, and a finite potential. A generalisation to describe
N particle systems is also presented and, in particular, we find the tomogram associated to the 2 particle case occupying in general non-orthogonal states. In the latter case, for a bipartite quantum system, the entanglement properties are established by considering quantum information concepts such as the linear entropy.