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:2403.12112 · Physica Scripta

Current, quantum transport and entropic force of bosonic system interacting with two thermal reservoirs

Jayarshi Bhattacharya, Gautam Gangopadhyay, Sunandan Gangopadhyay

Published Dec 20, 2024• 1 citation
arXivHTMLPDF

Abstract

Abstract This paper investigates the dynamics of current and quantum transport factor in a bosonic system consisting of a central system interacting with two reservoirs at different temperatures. We derive a master equation describing the time evolution of the density matrix of the system, accounting for the interactions and energy transfer between the components. We quantify the current, representing the flow of bosons through the system and analyse its dependence on the system's parameters and temperatures of the thermal reservoirs. In the steady state regime, we derived an expression for the quantum transport factor of the energy transfer process. Our analysis show that quantum effects, such as the dependence on temperature can significantly impact this factor. In particular, we observe that the transport factor of the quantum system is greater than the corresponding factor when the temperature goes to infinity, where the factor has an identical form with the Carnot efficiency of an ideal heat engine. We then derived the Fokker-Planck equation to find out the Glauber-Sudarsan P-representation. In the steady state of the equation, the probability distribution comes out to be in Gaussian form. We then calculated the entropic force for this probability distribution which gives the Hooke's law in the steady state, in agreement with the fact that our system is a harmonic oscillator.

DOI
10.1088/1402-4896/ada210

Related papers

Energy transport in the integrable system in contact with various types of phonon reservoirs

Keiji Saito, Shinji Takesue, Seiji Miyashita

We study how energy transport in an integrable system is affected by the spectral densities of heat reservoirs. The model investigated here is the quantum harmonic chain with both ends in contact with two heat reservoirs at different temperatures. The master equation for the reduced density matrix is derived on the assumption that the reservoirs are composed of an infinite number of independent harmonic oscillators. We evaluate temperature profile and energy flux in the stationary state for the master equation and discuss how they depend on the types of spectral densities. When we attach the reservoirs of the same type of spectral density, we find that the temperature profile is independent of the types. On the other hand, when the two reservoirs have different types of spectral densities, the energy profile near the ends of the chain depends on the types. When the coupling is finite, the temperature profile near the ends shows a wide variation of behavior dependent on spectral densities and temperatures of reservoirs. This dependence is discussed with the Fokker-Planck equations obtained in the classical limit.

arXiv:cond-mat/9810069•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Mar 1, 2000•93 citations

Stochastic quantum thermodynamics, entropy production, and transport properties of a bosonic system

Mário J. de Oliveira

The transport properties of a bosonic chain have been calculated by placing the ends of the chain in contact with thermal and particle reservoirs at different temperatures and chemical potentials. The contact with the reservoirs is described by the use of a quantum Fokker-Planck-Kramers equation, which is a canonical quantization of the classical Fokker-Planck-Kramers equation. From the quantum equation we obtain equations for the covariances of the creation and annihilation boson operators and solve them in the stationary state for small interactions. From the covariances we determine the Onsager coefficients and in particular the conductance, which was found to be finite for any chain size leading to an infinite conductivity and the absence of Fourier's law.

Physical review. E•Jan 5, 2018•9 citations

Quantum dynamics of a bosonic mode and a two-level system interacting with several reservoirs

Narges Cheraghpour, Fardin Kheirandish

Abstract In the framework of a novel dissipative scheme, we have investigated the quantum dynamics of an oscillating system interacting with two reservoirs with different temperatures trough different time-dependent coupling functions. The reduced density matrix, quantum optical characteristic functions, and (quasi) distribution functions like Husimi, Glauber–Sudarshan and Wigner functions on the phase space of the oscillator are obtained. The problem has been generalized to the case where the oscillator is interacting with n distinctive reservoirs, and a quantum current and an effective reservoir is introduced. Finally, the quantum dynamics of a two-level system interacting with two reservoirs has been investigated, and the exact reduced density matrix is obtained.

arXiv:2504.13303•Laser Physics•May 1, 2025•0 citations

Steady-state quantum transport through an anharmonic oscillator strongly coupled to two heat reservoirs

Tianqi Chen, Vinitha Balachandran, Chu Guo +1 more

We investigate the transport properties of an anharmonic oscillator, modeled by a single-site Bose-Hubbard model, coupled to two different thermal baths using the numerically exact thermofield based chain-mapping matrix product states (TCMPS) approach. We compare the effectiveness of TCMPS to probe the nonequilibrium dynamics of strongly interacting system irrespective of the system-bath coupling against the global master equation approach in Gorini-Kossakowski-Sudarshan-Lindblad form. We discuss the effect of on-site interactions, temperature bias as well as the system-bath couplings on the steady-state transport properties. Last, we also show evidence of non-Markovian dynamics by studying the nonmonotonicity of the time evolution of the trace distance between two different initial states.

arXiv:2004.05017•Physical review. E•Jul 31, 2020•24 citations

Heat currents in qubit systems

Hans C. Fogedby

Abstract There is a current interest in quantum thermodynamics in the context of open quantum systems. An important issue is the consistency of quantum thermodynamics, in particular the second law of thermodynamics, i.e. the flow of heat from a hot reservoir to a cold reservoir. Here recent emphasis has been on composite system and in particular the issue regarding the application of local or global master equations. In order to contribute to this discussion we discuss two cases, namely as an example a single qubit and as a simple composite system two coupled qubits driven by two heat reservoirs at different temperatures, respectively. Applying a global Lindblad master equation approach we present explicit expressions for the heat currents in agreement with the second law of thermodynamics. The analysis is carried out in the Born–Markov approximation. We also discuss issues regarding the possible presence of coherences in the steady state.

arXiv:2301.13544•Journal of Statistical Mechanics Theory and Experiment•Jul 23, 2024•0 citations

Work extraction from coupled qubits in equilibrium and nonequilibrium thermal reservoirs

Maryam Hadipour, Soroush Haseli

This study investigates the thermodynamic behavior of a two-qubit quantum system, where each qubit is coupled to an independent thermal reservoir, either bosonic or fermionic. Using a master equation approach, we analyze both steady-state and time-dependent ergotropy to understand how different reservoir statistics affect work extraction. In bosonic environments, ergotropy consistently declines with increasing temperature due to thermal noise. In contrast, fermionic reservoirs exhibit more complex behavior, with ergotropy enhanced by particle transport under non-equilibrium conditions. Our results reveal a threshold-like sensitivity to the chemical potential configuration, leading to qualitatively distinct regimes of energy storage performance. Time-resolved analyses show that the system's approach to steady state varies depending on the type of reservoir and the coupling strength between qubits. These insights highlight how carefully engineered reservoir properties and non-equilibrium driving can be leveraged to optimize quantum battery performance.

Scientific Reports•Aug 28, 2025•1 citation
Abstract This paper investigates the dynamics of current and quantum transport factor in a bosonic system consisting of a central system interacting with two reservoirs at different temperatures. We derive a master equation describing the time evolution of the density matrix of the system, accounting for the interactions and energy transfer between the components. We quantify the current, representing the flow of bosons through the system and analyse its dependence on the system's parameters and temperatures of the thermal reservoirs. In the steady state regime, we derived an expression for the quantum transport factor of the energy transfer process. Our analysis show that quantum effects, such as the dependence on temperature can significantly impact this factor. In particular, we observe that the transport factor of the quantum system is greater than the corresponding factor when the temperature goes to infinity, where the factor has an identical form with the Carnot efficiency of an ideal heat engine. We then derived the Fokker-Planck equation to find out the Glauber-Sudarsan P-representation. In the steady state of the equation, the probability distribution comes out to be in Gaussian form. We then calculated the entropic force for this probability distribution which gives the Hooke's law in the steady state, in agreement with the fact that our system is a harmonic oscillator.
We study how energy transport in an integrable system is affected by the spectral densities of heat reservoirs. The model investigated here is the quantum harmonic chain with both ends in contact with two heat reservoirs at different temperatures. The master equation for the reduced density matrix is derived on the assumption that the reservoirs are composed of an infinite number of independent harmonic oscillators. We evaluate temperature profile and energy flux in the stationary state for the master equation and discuss how they depend on the types of spectral densities. When we attach the reservoirs of the same type of spectral density, we find that the temperature profile is independent of the types. On the other hand, when the two reservoirs have different types of spectral densities, the energy profile near the ends of the chain depends on the types. When the coupling is finite, the temperature profile near the ends shows a wide variation of behavior dependent on spectral densities and temperatures of reservoirs. This dependence is discussed with the Fokker-Planck equations obtained in the classical limit.
The transport properties of a bosonic chain have been calculated by placing the ends of the chain in contact with thermal and particle reservoirs at different temperatures and chemical potentials. The contact with the reservoirs is described by the use of a quantum Fokker-Planck-Kramers equation, which is a canonical quantization of the classical Fokker-Planck-Kramers equation. From the quantum equation we obtain equations for the covariances of the creation and annihilation boson operators and solve them in the stationary state for small interactions. From the covariances we determine the Onsager coefficients and in particular the conductance, which was found to be finite for any chain size leading to an infinite conductivity and the absence of Fourier's law.
Abstract In the framework of a novel dissipative scheme, we have investigated the quantum dynamics of an oscillating system interacting with two reservoirs with different temperatures trough different time-dependent coupling functions. The reduced density matrix, quantum optical characteristic functions, and (quasi) distribution functions like Husimi, Glauber–Sudarshan and Wigner functions on the phase space of the oscillator are obtained. The problem has been generalized to the case where the oscillator is interacting with n distinctive reservoirs, and a quantum current and an effective reservoir is introduced. Finally, the quantum dynamics of a two-level system interacting with two reservoirs has been investigated, and the exact reduced density matrix is obtained.
We investigate the transport properties of an anharmonic oscillator, modeled by a single-site Bose-Hubbard model, coupled to two different thermal baths using the numerically exact thermofield based chain-mapping matrix product states (TCMPS) approach. We compare the effectiveness of TCMPS to probe the nonequilibrium dynamics of strongly interacting system irrespective of the system-bath coupling against the global master equation approach in Gorini-Kossakowski-Sudarshan-Lindblad form. We discuss the effect of on-site interactions, temperature bias as well as the system-bath couplings on the steady-state transport properties. Last, we also show evidence of non-Markovian dynamics by studying the nonmonotonicity of the time evolution of the trace distance between two different initial states.
Abstract There is a current interest in quantum thermodynamics in the context of open quantum systems. An important issue is the consistency of quantum thermodynamics, in particular the second law of thermodynamics, i.e. the flow of heat from a hot reservoir to a cold reservoir. Here recent emphasis has been on composite system and in particular the issue regarding the application of local or global master equations. In order to contribute to this discussion we discuss two cases, namely as an example a single qubit and as a simple composite system two coupled qubits driven by two heat reservoirs at different temperatures, respectively. Applying a global Lindblad master equation approach we present explicit expressions for the heat currents in agreement with the second law of thermodynamics. The analysis is carried out in the Born–Markov approximation. We also discuss issues regarding the possible presence of coherences in the steady state.
This study investigates the thermodynamic behavior of a two-qubit quantum system, where each qubit is coupled to an independent thermal reservoir, either bosonic or fermionic. Using a master equation approach, we analyze both steady-state and time-dependent ergotropy to understand how different reservoir statistics affect work extraction. In bosonic environments, ergotropy consistently declines with increasing temperature due to thermal noise. In contrast, fermionic reservoirs exhibit more complex behavior, with ergotropy enhanced by particle transport under non-equilibrium conditions. Our results reveal a threshold-like sensitivity to the chemical potential configuration, leading to qualitatively distinct regimes of energy storage performance. Time-resolved analyses show that the system's approach to steady state varies depending on the type of reservoir and the coupling strength between qubits. These insights highlight how carefully engineered reservoir properties and non-equilibrium driving can be leveraged to optimize quantum battery performance.