Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2109.14824 · Physical Review A

Resonant transport of bosonic carriers through a quantum device

Pavel S. Muraev, Дмитрий Н. Максимов, Andrey R. Kolovsky

Published Jan 11, 2022• 9 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.105.013307

Related papers

Open Bose-Hubbard chain: Pseudoclassical approach

Anna A. Bychek, Pavel S. Muraev, Дмитрий Н. Максимов +1 more

We analyze the 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 a particle source and sink, respectively. The analysis is carried 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 interparticle 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 inversely proportional to L.

arXiv:1909.06213•Physical review. E•Jan 13, 2020•19 citations

Ballistic transport of interacting Bose particles in a tight-binding chain

Pavel S. Muraev, Дмитрий Н. Максимов, Andrey R. Kolovsky

It is known that the quantum transport of noninteracting Bose particles across a tight-binding chain is ballistic in the sense that the current does not depend on the chain length. We address the question whether the transport of strongly interacting bosons can be ballistic as well. We find such a regime and show that, classically, it corresponds to the synchronized motion of local nonlinear oscillators. It is also argued that, unlike the case of noninteracting bosons, the transporting state responsible for the ballistic transport of interacting bosons is metastable, i.e., the current decays in the course of time. An estimate for the decay time is obtained.

arXiv:2206.08711•Physical review. E•Dec 6, 2022•2 citations

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

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

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.

quant-pharXiv:2609.11741•Sep 11, 2026•0 citations

Non-Markovian master equation for quantum transport of fermionic carriers

Дмитрий Н. Максимов, S. V. Aksenov, Andrey R. Kolovsky

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.

arXiv:2207.01943•Journal of Physics Condensed Matter•Oct 13, 2023•5 citations

Landauer-Büttiker equation for bosonic carriers

Andrey R. Kolovsky, Zakari Denis, Sandro Wimberger

We study the current of Bose particles between two reservoirs connected by a one-dimensional channel. We analyze the problem from first principles by considering a microscopic model of conductivity in the noninteracting limit. Equations for the transient and the stationary current are derived analytically. The asymptotic current has a form similar to the Landauer-B\"uttiker equation for electronic current in mesoscopic devices.

arXiv:1811.01626•Physical Review A•Oct 19, 2018•24 citations

Microscopic theory of a nonequilibrium open bosonic chain

Jader P. Santos, Gabriel Teixeira Landi

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.

arXiv:1610.05126•Physical review. E•Dec 28, 2016•38 citations
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.
We analyze the 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 a particle source and sink, respectively. The analysis is carried 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 interparticle 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 inversely proportional to L.
It is known that the quantum transport of noninteracting Bose particles across a tight-binding chain is ballistic in the sense that the current does not depend on the chain length. We address the question whether the transport of strongly interacting bosons can be ballistic as well. We find such a regime and show that, classically, it corresponds to the synchronized motion of local nonlinear oscillators. It is also argued that, unlike the case of noninteracting bosons, the transporting state responsible for the ballistic transport of interacting bosons is metastable, i.e., the current decays in the course of time. An estimate for the decay time is obtained.
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.
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.