When driven by a potential bias between two finite reservoirs, the particle current across a quantum system evolves from an initial loading through a coherent, followed by a metastable phase, and ultimately fades away upon equilibration. We formulate a theory which fully accounts for the associated, distinct time scales, and identifies the parameter dependence of the decay rate which ultimately controls the convergence towards equilibrium. Our formalism guarantees total particle number conservation and fundamental consistency between macroscopic and internal currents flowing in the system. We furthermore establish a clear imprint of the fermionic or bosonic particle character on the resulting conductance.
When driven by a potential bias between two finite reservoirs, the particle current across a quantum system evolves from an initial loading through a coherent, followed by a metastable phase, and ultimately fades away upon equilibration. We formulate a theory which fully accounts for the associated, distinct time scales, and identifies the parameter dependence of the decay rate which ultimately controls the convergence towards equilibrium. Our formalism guarantees total particle number conservation and fundamental consistency between macroscopic and internal currents flowing in the system. We furthermore establish a clear imprint of the fermionic or bosonic particle character on the resulting conductance.
We present a formalism to study many-particle quantum transport across a lattice locally connected to two finite, nonstationary (bosonic or fermionic) reservoirs, both of which are in a thermal state. We show that, for conserved total particle number, a system of nonlinear quantum-classical master equations describes the concurrent many-particle time evolution on the lattice and in the reservoirs. The finiteness of the reservoirs makes a macroscopic current emerge, which decreases exponentially in time and asymptotically drives the many-particle configuration into an equilibrium state where the particle flow ceases. We analytically derive the timescale of this equilibration process, and, furthermore, investigate the imprint of many-particle interferences on the transport process.
We analyze the equilibration process between two either fermionic or bosonic reservoirs containing ultracold atoms with a fixed total number of particles that are weakly connected via a few-level quantum system. We allow for both the temperatures and particle densities of the reservoirs to evolve in time. Subsequently, linearizing the resulting equations enables us to characterize the equilibration process and its time scales in terms of equilibrium reservoir properties and linear-response transport coefficients. Additionally, we investigate the use of such a device as particle transistor or particle capacitor and analyze its efficiency.
Nonequilibrium energy transport serves as one of fundamental problems in quantum thermodynamics and quantum technologies. Driven quantum master equation in the dressed picture provides an efficient way of investigating nonequilibrium energy flow in general driven-dissipative quantum systems, where the systems are simultaneously driven by the finite thermodynamic bias and coherent driving field. The validity and general applicability of driven quantum master equation is confirmed by comparing with Floquet master equation, by analyzing energy currents in generic spin and boson models. The additional driving phase reserved in system-reservoir interactions, will apparently modify microscopic energy exchange processes. The steady-state energy currents are dramatically enhanced, in particular near the resonant regimes. In contrast, the traditional dressed master equation yields distinct behaviors of the energy currents. We hope that the driven quantum master equation may provide an efficient utility for the control of quantum transport and thermodynamic performances in driven-dissipative nanodevices.
We present a generic, compact formula for the current flowing in interacting and noninteracting systems which are driven out of equilibrium by biased reservoirs described by Lindblad jump operators. We show that, in the limit of high temperature and chemical potential, our formula is equivalent to the well-known Meir-Wingreen formula, which describes the current flowing through a system connected to fermionic baths, therefore bridging the gap between the two formalisms. Our formulation gives a systematic way to address the transport properties of correlated systems strongly driven out of equilibrium. As an illustration, we provide explicit calculations of the current in three cases : (i) a single-site impurity, (ii) a free-fermionic chain, and (iii) a fermionic chain with loss and gain terms along the chain. In this last case, we find that the current across the system has the same behavior for loss or gain terms and depends on the loss/gain rate in a nonmonotonic way.
Open-system simulations of quantum transport provide a platform for the study of true steady states, Floquet states, and the role of temperature, time dynamics, and fluctuations, among other physical processes. They are rapidly gaining traction, especially techniques that revolve around "extended reservoirs," a collection of a finite number of degrees of freedom with relaxation that maintains a bias or temperature gradient, and have appeared under various guises (e.g., the extended or mesoscopic reservoir, auxiliary master equation, and driven Liouville-von Neumann approaches). Yet, there are still a number of open questions regarding the behavior and convergence of these techniques. Here, we derive general analytical solutions, and associated asymptotic analyses, for the steady-state current driven by finite reservoirs with proportional coupling to the system/junction. In doing so, we present a simplified and unified derivation of the non-interacting and many-body steady-state currents through arbitrary junctions, including outside of proportional coupling. We conjecture that the analytic solution for proportional coupling is the most general of its form for isomodal relaxation (i.e., relaxing proportional coupling will remove the ability to find compact, general analytical expressions for finite reservoirs). These results should be of broad utility in diagnosing the behavior and implementation of extended reservoir and related approaches, including the convergence to the Landauer limit (for non-interacting systems) and the Meir-Wingreen formula (for many-body systems).
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.