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arXiv:1302.0232 · Physical Review B

Nonequilibrium mesoscopic Fermi-reservoir distribution and particle current through a coherent quantum system

Shigeru Ajisaka, Felipe Barra

Published May 10, 2013• 32 citations
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Abstract

We study particle current and occupation distribution in a recently proposed model for coherent quantum transport. In this model a system connected to mesoscopic Fermi reservoirs (mesoreservoir) is driven out of equilibrium by the action of superreservoirs with prescribed temperatures and chemical potentials described by a simple dissipative mechanism with the Lindblad equation. We compare exact (numerical) results for the nonequilibrium steady-state particle current with theoretical expectations based on the Landauer formula and show that the model reproduces the behavior of coherent quantum systems in the expected parameter region. We also obtain the mesoreservoir occupation distribution in the nonequilibrium steady-state and compare them with the occupation distribution in the leads in usual description of coherent quantum transport.

DOI
10.1103/physrevb.87.195114

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We study particle current and occupation distribution in a recently proposed model for coherent quantum transport. In this model a system connected to mesoscopic Fermi reservoirs (mesoreservoir) is driven out of equilibrium by the action of superreservoirs with prescribed temperatures and chemical potentials described by a simple dissipative mechanism with the Lindblad equation. We compare exact (numerical) results for the nonequilibrium steady-state particle current with theoretical expectations based on the Landauer formula and show that the model reproduces the behavior of coherent quantum systems in the expected parameter region. We also obtain the mesoreservoir occupation distribution in the nonequilibrium steady-state and compare them with the occupation distribution in the leads in usual description of coherent quantum transport.
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.
We suggest a generalization of the expression of the nonequilibrium (NE) density matrix obtained by Hershfield's method for the cases where both heat and charge steady-state currents are present in a quantum open system. The finite-size quantum system, connected to two temperature and particle reservoirs, is driven out of equilibrium by the presence of both a temperature gradient and a chemical potential gradient between the two reservoirs. We show that the NE density matrix is given by a generalized Gibbs-like ensemble and is in full agreement with the general results of the McLennan-Zubarev nonequilibrium ensembles. The extra nonequilibrium terms are related to the entropy production in the system and characterize the fluxes of heat and particle. An explicit example, for the lowest-order expansion, is provide for a model system of noninteracting fermions.
We aim to bridge the gap between quantum coherence, quantum correlations, and nonequilibrium quantum transport in a quantum double-dot (QDD) system interacting with fermionic reservoirs. The system-reservoir coupling is modeled using a Fano-Anderson-type Hamiltonian. The density operator elements of the QDD system are expressed in terms of expectation values involving various combinations of the fermionic creation and annihilation operators associated with the system. By utilizing the quantum Langevin equation and the Heisenberg equation of motion, we derive the precise temporal behavior of these operator averages in terms of nonequilibrium Green's functions and subsequently obtain the time evolution of the density operator elements. Our approach is valid in both the strong coupling and non-Markovian regimes. Additionally, we examine the time evolution of quantum coherence in the QDD system, quantifying it using standard measures such as the l1-norm and the relative entropy of coherence. As observed, coherence reaches a non-zero steady-state value, highlighting its significant potential for applications in quantum information processing and quantum technologies. Furthermore, we establish a connection between quantum coherence and transport current in a QDD system serially coupled to fermionic reservoirs. We then investigate the effects of coupling strength and reservoir memory by tuning the finite spectral width of the reservoir, examining their impact on both transient and steady-state properties, such as quantum coherence and particle current, which could play a crucial role in ultrafast nanodevice applications.
Abstract Quantum coherence is a fragile quantum resource that is typically degraded by environmental interactions. We demonstrate that, in quantum double dot system connected to fermionic reservoirs, coherence can instead be generated from an initially incoherent state and sustained in the steady state through nonequilibrium particle transport. The dynamics is analyzed within the framework of quantum resource theory by expressing the density operator elements in terms of fermionic operator expectation values. Their time evolution is obtained exactly using the quantum Langevin equation, yielding a treatment that remains valid over a wide range of system-reservoir parameters and naturally incorporates non-Markovian effects. By tuning reservoir parameters such as coupling strength and spectral bandwidth, we identify regimes in which steady-state coherence and particle current are simultaneously enhanced. Our results establish a direct operational connection between coherence and charge transport, providing quantitative guidance for stabilizing coherence in nanoscale devices operating far from equilibrium.