Nonequlibrium particle and energy currents in quantum chains connected to mesoscopic Fermi reservoirs

Abstract

We propose a model of nonequilibrium quantum transport of particles and energy in a system connected to mesoscopic Fermi reservoirs (mesoreservoir). The mesoreservoirs are in turn thermalized to prescribed temperatures and chemical potentials by a simple dissipative mechanism described by the Lindblad equation.As an example, we study transport in monoatomic and diatomic chains of noninteracting spinless fermions. We show numerically the breakdown of the Onsager reciprocity relation due to the dissipative terms of the model.

Nonequilibrium thermal transport and its relation to linear response

“…This is not surprising since we are simulating a closed quantum system, but gives rise to the questions: (1) why does the current saturate except for b > 0, implying that it is not determined by local temperature gradients and (2) would we obtain the same steady-state current if we kept the "reservoirs" at a fixed temperature? 33 Both are reasonable if it does not matter over which length scale L the temperature difference T L − T R is applied; qualitatively, this should be the case if the thermal transport properties of the chain are length-independent, i.e., if the thermal conductance G of a finite system does not decrease with its length L, or equivalently, if the conductivity σ = GL of an infinite chain L → ∞ is infinite. More quantitatively, we conjecture a relation between nonequilibrium and linear response: the nonequilibrium energy current relaxes to a finite steady-state value if the linear-response thermal conductivity is infinite, i.e., if the Drude weight D is nonzero.…”

“…8,9,[18][19][20][21][22][23][24][25] Studying nonequilibrium thermal (or charge) transport is complicated in general-one reason being that is not even clear whether the long-time dynamics can be described by a low-energy theory-and constitutes one of the most active areas of research in strongly correlated condensed matter physics. [26][27][28][29][30][31][32][33][34][35][36][37] The primary goal of our work is to obtain quantitative results on steady-state energy flow both near and far from equilibrium and to understand the effects of integrability and correlations. This is motivated by the experiments listed above and by recent technical advances in dynamical simulations.…”

Full density matrix dynamics for large quantum systems: interactions, decoherence and inelastic effects

“…We also extend the QLE method to include a probe, and time evolve the system. Since our calculations provide the real-time dynamics of the full DM, the process of equilibration and thermalization in a finite quantum system can now be studied [30][31][32][33]. In particular, we find that when only decoherence effects are allowed, the system approaches a non-canonical equilibrium state.…”

Non-additive dissipation in open quantum networks out of equilibrium

“…Alternatively, one can use a 'local' approach, where each generator  a acts non-trivially only on one part of the network s S Ì a , driving it towards thermal equilibrium while leaving its complement s ā unaffected. That is, Generators satisfyingequation (8) may either be derived microscopically using various approximations [19,24,47,49], or directly postulated on phenomenological grounds [63][64][65][66]. In the local approach, S r ¥ is not necessarily diagonal in the energy eigenbasis, and therefore provides a consistent model for the internal current dynamics as required by equation (3).…”