Heat transport through lattices of quantum harmonic oscillators in arbitrary dimensions

Abstract

In d-dimensional lattices of coupled quantum harmonic oscillators, we analyze the heat current caused by two thermal baths of different temperatures, which are coupled to opposite ends of the lattice, with a focus on the validity of Fourier's law of heat conduction. We provide analytical solutions of the heat current through the quantum system in the nonequilibrium steady state using the rotating-wave approximation and bath interactions described by a master equation of Lindblad form. The influence of local dephasing in the transition of ballistic to diffusive transport is investigated.

Thermal conductance of a two-level atom coupled to two quantum harmonic oscillators

“…More precisely one oscillator is in contact with a heat reservoir at a higher temperature and the other oscillator is in contact with a heat reservoir at a lower temperature. This arrangement allows us to calculate the thermal conductance [16][17][18][19] as well as the rate of the entropy production [18][19][20][21] and the atomic population [2], which are the main purpose of the present study. This calculation is achieved by the use of a quantum Fokker-Planck-Kramers (FPK) equation [19], understood as the canonical quantization of the ordinary FKP equation.…”

“…This calculation is achieved by the use of a quantum Fokker-Planck-Kramers (FPK) equation [19], understood as the canonical quantization of the ordinary FKP equation. The calculation of the conductance and the atomic population were also performed by the use of a master equation in the Lindblad form [17,22]. In both approaches the calculations were performed for small values of the coupling constant.…”

Nonequilibrium generalised Langevin equation for the calculation of heat transport properties in model 1D atomic chains coupled to two 3D thermal baths

“…For information, we present in Figure 9 most of the results we have obtained for the heat current J heat flowing across all chains (length N = 7, 11,15,19,23,27) and for all sets of temperatures T L and T R . From these results, it can be seen that the heat current increases with increasing temperature differences ∆T = T L − T R (as expected).…”

“…No temperature gradient is formed in the bulk of the system, since the dominating energy "carriers" are not scattered and propagate ballistically. A large variety of harmonic (integrable) classical [8][9][10][11][12][13][14][15][16][17] and quantum 10,13,[18][19][20][21][22][23] systems have been studied using analytical and/or numerical approaches. All these studies show that there is no temperature gradient inside the system (except for small regions in the vicinity of the contacts between the central system and the baths).…”

“…All these studies show that there is no temperature gradient inside the system (except for small regions in the vicinity of the contacts between the central system and the baths). One usually obtains a constanttemperature profile [8][9][10][11][12]15,[17][18][19][20][21][22][23] in the central system around the averaged temperature T av = (T L + T R )/2.…”