Open Bose-Hubbard chain: Pseudoclassical approach

Abstract

We analyze stationary current of bosonic carriers in the Bose-Hubbard chain of length L where the first and the last sites of the chain are attached to reservoirs of Bose particles acting as the particle source and sink, respectively. The analysis is curried out by using the pseudoclassical approach which reduces the original quantum problem to the classical problem for L coupled nonlinear oscillators. It is shown that an increase of oscillator nonlinearity (which is determined by the strength of inter-particle interactions) results in a transition from the ballistic transport regime, where the stationary current is independent of the chain length, to the diffusive regime, where the current is inverse proportional to L.

Resonant transport of bosonic carriers through a quantum device

“…In the latter system one measures the atomic current across the lattice connecting two atomic reservoirs with different chemical potentials, in spirit of the laboratory experiment [10] conducted with the Fermi atoms. The unique feature of the bosonic system, however, is that with the increase of the carriers density it shows a transition from quantum to classical regime where the BH chain can be viewed as system of coupled classical oscillators [11]. This quantum-to-classical transition for the identical particles motivates further studying transport phenomena with bosonic carriers.…”

“…In our previous works [8,11] we analyzed the current of Bose particles within the framework of the standard open BH model where the effect of reservoirs is taken into account by introducing the gain and loss Lindbladian operators acting on the first and the last sites of the chain. In the classical approach this corresponds to the situation where the first and the last oscillators are subject to the friction and are excited by white noise whose intensity is determined by the mean particle density of the respective reservoir [11]. Unfortunately, the standard open BH model implies validity of the Markov approximation which is not justified for low-temperature reservoirs with nearly condensed Bose particles.…”

“…The pseudoclassical approach substitute the master equation Eq. ( 1) by the Fokker-Planck equation for the classical distribution function f [11]. Considering for the moment the case of a single ring (generalization onto the case of two ring is given in the beginning of Sec.…”

“…( 13) describes the diffusion. Thus, one can put into correspondence to the Fokker-Planck equation (11) the following Langevin equation…”

Dynamics of a nonlinear quantum oscillator under non-Markovian pumping

“…Interaction of quantum systems with thermal reservoirs is one of the most important problems in contemporary physics. It is of vital importance in the context of physics of cold and ultracold quantum gases [1][2][3][4][5], quantum computation [6], quantum fluids with a photonic component [7,8], atomtronics [9] and many other fields [10] where finite-temperature effects play a significant role.…”