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arXiv:2609.11741

Quantum transport along a tight-binding chain connected to Markovian reservoirs

P. S. Muraev, A. R. Kolovsky, D. N. Maksimov

quant-phSubmitted Sep 10, 2026• Announced Sep 11, 2026• 0 citations
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Abstract

We consider quantum transport of non-interacting particles in a tight-binding chain coupled to Markovian reservoirs at its boundaries and subject to uniform on-site dephasing. Using the masterequation approach, we derived the exact analytic solution for the mean current along the chain. This analytic solution is obtained in the framework of single-particle quantum mechanics and, thus, equally applies for transport of non-interacting bosons and fermions. In the absence of phase damping, the results are extended to the complete many-body solution for bosonic problem in the form of anti-normally ordered characteristic function. This function allows us to calculate the distribution function for the current at each bond in the chain as well as the inter-bond current correlation functions.

Comments
11 pages, 3 figures

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We consider quantum transport of non-interacting particles in a tight-binding chain coupled to Markovian reservoirs at its boundaries and subject to uniform on-site dephasing. Using the masterequation approach, we derived the exact analytic solution for the mean current along the chain. This analytic solution is obtained in the framework of single-particle quantum mechanics and, thus, equally applies for transport of non-interacting bosons and fermions. In the absence of phase damping, the results are extended to the complete many-body solution for bosonic problem in the form of anti-normally ordered characteristic function. This function allows us to calculate the distribution function for the current at each bond in the chain as well as the inter-bond current correlation functions.
We propose a simple, yet feasible, model for quantum transport of fermionic carriers across tight-binding chain connecting two reservoirs maintained at arbitrary temperatures and chemical potentials. The model allows for elementary derivation of the master equation for the reduced single particle density matrix (SPDM) in a closed form in both Markov and Born approximations. In the Markov approximation the master equation is solved analytically, whereas in the Born approximation the problem is reduced to an algebraic equation for the SPDM in the Redfield form. The non-Markovian equation is shown to lead to resonant transport similar to Landauer's conductance. It is shown that in the deep non-Markovian regime the transport current can be matched with that obtained by the non-equilibrium Green's function method.
We analyze the current of Bose particles across a tight-binding chain connected at both ends to the particles' reservoirs. Unlike the standard open Bose-Hubbard model, where the presence of reservoirs is taken into account by the Lindbladians acting on the first and last sites of the chain, we use semimicroscopic models for the reservoirs. This allows us to address the case of arbitrary reservoir temperature. In particular, we discuss the phenomenon of the resonant transmission for nearly condensed bosons, where the current across the chain is significantly enhanced for certain values of the gate voltage.
A pure-dephasing reservoir acting on an individual quantum system induces loss of coherence without energy exchange. When acting on composite quantum systems, dephasing reservoirs can lead to a radically different behavior. Transport of heat between two pure-dephasing Markovian reservoirs is predicted in this work. They are connected through a chain of coupled sites. The baths are kept in thermal equilibrium at distinct temperatures. Quantum coherence between sites is generated in the steady-state regime and results in the underlying mechanism sustaining the effect. A quantum model for the reservoirs is a necessary condition for the existence of stationary heat transport. A microscopic derivation of the non-unitary system-bath interaction is employed, valid for arbitrary inter-site coupling regime. The model assumes that each site-reservoir coupling is local.
We derive a non-Markovian master equation for the evolution of a class of open quantum systems consisting of quadratic fermionic systems coupled to wideband reservoirs. This is done by providing an explicit correspondence between master equations and nonequilibrium Green's function approaches. Our findings permit us to address non-Markovian regimes characterized by negative decoherence rates and to characterize the dynamics with respect to a recently proposed measurement of ``non-Markovianity.'' We study the real-time dynamics and the steady-state solution of two illustrative models: a tight-binding electronic model and XY\mathit{XY}XY spin chains. The rich set of nonequilibrium steady-state phases encountered extends previous results to the non-Markovian regime.
We build an exact framework to evaluate heat, energy, and particle transport between Gaussian reservoirs mediated by a quadratic quantum system. By combining full counting statistics with newly developed non-Markovian master equation approaches, we introduce an effective master equation whose solution can be used to generate arbitrary moments of the heat statistics for any number of reservoirs. This theory applies equally to fermionic and bosonic systems, holds at arbitrarily strong coupling, and resolves out-of-equilibrium transient dynamics determined by the system's initial state. In the steady-state, weak-coupling limit, we recover results analogous to those of the well-known Landauer-Büttiker formalism. We conclude our discussion by demonstrating an application of the method to a prototypical fermionic system. Our results uncover a regime of transient negative heat conductance contingent upon the initial system preparation, providing a clear signature of non-trivial out-of-equilibrium dynamics.
Quantum master equations form an important tool in the description of transport problems in open quantum systems. However, they suffer from the difficulty that the shape of the Lindblad dissipator depends sensibly on the system Hamiltonian. Consequently, most of the work done in this field has focused on phenomenological dissipators which act locally on different parts of the system. In this paper we show how to construct Lindblad dissipators to model a one-dimensional bosonic tight-binding chain connected to two baths at the first and last site, kept at different temperatures and chemical potentials. We show that even though the bath coupling is local, the effective Lindblad dissipator stemming from this interaction is inherently nonlocal, affecting all normal modes of the system. We then use this formalism to study the current of particles and energy through the system and find that they have the structure of Landauer's formula, with the bath spectral density playing the role of the transfer integral. Finally, we consider infinitesimal temperature and chemical potential gradients and show that the currents satisfy Onsager's reciprocal relations, which is a consequence of the fact that the microscopic quantum dynamics obeys detailed balance.