Abstract We study a cascaded system of two subsystems repeatedly interacting with a bath prepared in various non-thermal states. Effects of different types of bath coherence on dynamics of the system heat flux are explored. For a single-qubit bath with the displacement coherence, heat flux of each subsystem is divided into dissipative and coherent parts. In the stationary regime, the dissipative heat fluxes are the same for the two subsystems, but the coherent parts are not due to the cascaded feature. In the transient regime, heat fluxes occur even when the system and the bath have the same temperature and, more surprisingly, heat flow reversal appears when temperatures of the system and the bath differ. For a two-qubit bath we consider two types of coherence: the squeezing and the heat-exchange ones. In the stationary regime, the squeezing coherence establishes correlations between the subsystems, each of which is evolving to its thermal state with a temperature identical to the bath’s. The squeezing coherence slightly influences only the dynamics of the subsystem that interacts with the bath later. As for the heat-exchange coherence, it forces the total system to thermalize to a state with the temperature related to both magnitude and relative phase of the coherence. Particularly, depending on the relative phases, the heat-exchange coherence can amplify or suppress the heat flux during the time evolution.
Abstract We study a cascaded system of two subsystems repeatedly interacting with a bath prepared in various non-thermal states. Effects of different types of bath coherence on dynamics of the system heat flux are explored. For a single-qubit bath with the displacement coherence, heat flux of each subsystem is divided into dissipative and coherent parts. In the stationary regime, the dissipative heat fluxes are the same for the two subsystems, but the coherent parts are not due to the cascaded feature. In the transient regime, heat fluxes occur even when the system and the bath have the same temperature and, more surprisingly, heat flow reversal appears when temperatures of the system and the bath differ. For a two-qubit bath we consider two types of coherence: the squeezing and the heat-exchange ones. In the stationary regime, the squeezing coherence establishes correlations between the subsystems, each of which is evolving to its thermal state with a temperature identical to the bath’s. The squeezing coherence slightly influences only the dynamics of the subsystem that interacts with the bath later. As for the heat-exchange coherence, it forces the total system to thermalize to a state with the temperature related to both magnitude and relative phase of the coherence. Particularly, depending on the relative phases, the heat-exchange coherence can amplify or suppress the heat flux during the time evolution.
We study the dynamics of heat flux in the thermalization process of a pair of identical quantum systems that interact dissipatively with a reservoir in a cascaded fashion. Despite that the open dynamics of the bipartite system S is globally Lindbladian, one of the subsystems ``sees'' the reservoir in a state modified by the interaction with the other subsystem and hence it undergoes a non-Markovian dynamics. As a consequence, the heat flow exhibits a nonexponential time behavior which can greatly deviate from the case where each party is independently coupled to the reservoir. We investigate both thermal and correlated initial states of S and show that the presence of correlations at the beginning can considerably affect the heat-flux rate. We carry out our study in two paradigmatic cases---a pair of harmonic oscillators with a reservoir of bosonic modes and two qubits with a reservoir of fermionic modes---and compare the corresponding behaviors. In the case of qubits and for initial thermal states, we find that the trace distance discord is at any time interpretable as the correlated contribution to the total heat flux.
Abstract Understanding how coherence of quantum systems affects thermodynamic quantities, such as work and heat, is essential for harnessing quantumness effectively in thermal quantum technologies. Here, we study the unique contributions of quantum coherence among different subsystems of a multipartite system, specifically in non-equilibrium steady states, to work and heat currents. Our system comprises two coupled ensembles, each consisting of N particles, interacting with two baths of different temperatures, respectively. The particles in an ensemble interact with their bath either simultaneously or sequentially, leading to non-local dissipation and enabling the decomposition of work and heat currents into local and non-local components. We find that the non-local heat current, as well as both the local and non-local work currents, are linked to the system quantum coherence. We provide explicit expressions of coherence-related quantities that determine the work currents under various intrasystem interactions. Our scheme is versatile, capable of functioning as a refrigerator, an engine, and an accelerator, with its performance being highly sensitive to the configuration settings. These findings establish a connection between thermodynamic quantities and quantum coherence, supplying valuable insights for the design of quantum thermal machines.
We consider a system consisting of two interacting qubits that are individually coupled to separate heat baths at different temperatures. The quantum effects in heat transport are investigated in a numerically rigorous manner with a hierarchial equations of motion (HEOM) approach for non-perturbative and non-Markovian system-bath coupling cases under non-equilibrium steady-state conditions. For a weak interqubit interaction, the total system is regarded as two individually thermostatted systems, whereas for a strong interqubit interaction, the two-qubit system is regarded as a single system coupled to two baths. The roles of quantum coherence (or entanglement) between the two qubits (q-q coherence) and between the qubit and bath (q-b coherence) are studied through the heat current calculated for various strengths of the system-bath coupling and interqubit coupling for high and low temperatures. The same current is also studied using the time convolutionless (TCL) Redfield equation and using an expression derived from the Fermi golden rule (FGR). We find that the HEOM results exhibit turnover behavior of the heat current as a function of the system-bath coupling strength for all values of the interqubit coupling strength, while the results obtained with the TCL and FGR approaches do not exhibit such behavior, because they do not possess the capability of treating the q-b and q-q coherences. The maximum current is obtained in the case that the q-q coherence and q-b coherence are balanced in such a manner that coherence of the entire heat transport process is realized. We also find that the heat current does not follow Fourier's law when the temperature difference is very large, due to the non-perturbative system-bath interactions.
Understanding how coherence of quantum systems affects thermodynamic quantities, such as work and heat, is essential for harnessing quantumness effectively in thermal quantum technologies. Here, we study the unique contributions of quantum coherence among different subsystems of a multipartite system, specifically in non-equilibrium steady states, to work and heat currents. Our system comprises two coupled ensembles, each consisting of N particles, interacting with two baths of different temperatures, respectively. The particles in an ensemble interact with their bath either simultaneously or sequentially, leading to non-local dissipation and enabling the decomposition of work and heat currents into local and non-local components. We find that the non-local heat current, as well as both the local and non-local work currents, are linked to the system quantum coherence. We provide explicit expressions of coherence-related quantities that determine the work currents under various intrasystem interactions. Our scheme is versatile, capable of functioning as a refrigerator, an engine, and an accelerator, with its performance being highly sensitive to the configuration settings. These findings establish a connection between thermodynamic quantities and quantum coherence, supplying valuable insights for the design of quantum thermal machines.
Abstract Whether genuine quantum effects, particularly quantum coherences, can offer an advantage to quantum devices is a topic of much interest. Here, we study a minimal model, the three-level V system coupled to two heat baths, and investigate the role of quantum coherences in heat transport in both the transient regime and in the nonequilibrium steady-state. In our model, energy is exchanged between the baths through two parallel pathways, which can be made distinct through the nondegeneracy of excited levels (energy splitting Δ) and a control parameter α , which adjusts the strength of one of the arms. Using a nonsecular quantum master equation of Redfield form, we succeed in deriving closed-form expressions for the quantum coherences and the heat current in the steady state limit for closely degenerate excited levels. By including three ingredients in our analysis: nonequilibrium baths, nondegeneracy of levels, and asymmetry of pathways, we show that quantum coherences are generated and sustained in the V model in the steady-state limit if three conditions, conjoining thermal and coherent effects are simultaneously met: (i) the two baths are held at different temperatures. (ii) Bath-induced pathways do not interfere destructively. (iii) Thermal rates do not mingle with the control parameter α to destroy interference through an effective local equilibrium condition. Particularly, we find that coherences are maximized when the heat current is suppressed. Although we mainly focus on analytical results in the steady state limit, numerical simulations reveal that the transient behavior of coherences contrasts the steady-state limit: large long-lived transient coherences vanish at steady state, while weak short-lived transient coherences survive, suggesting that different mechanisms are at play in these two regimes. Enhancing either the lifetime of transient coherences or their magnitude at steady state thus requires the control and optimization of different physical parameters.
We investigate a system of two interacting qubits having one of them isolated and the other coupled to a thermal reservoir. We consider two different models of system-reservoir interaction: i) a model, in which the master equation is derived taking into account the interaction between the two subsystems (qubits), ii) a naive model, in which the master equation consists of a dissipative term added to the unitary evolution term. We study the dynamics of quantities such as bipartite entanglement, quantum discord and the linear entropy of the isolated qubit for both strong and weak coupling regimes (qubit-qubit interaction) as well as for different temperatures of the reservoir. We find significant disagreements between the results obtained from the two models even in the weak coupling regime. For instance, we show that according to the phenomenological model, the isolated qubit would approach a maximally mixed state more slowly for higher temperatures (unphysical result), while the microscopic model predicts the opposite behaviour (correct result).