Analytic expressions for the steady-state current with finite extended reservoirs

Abstract

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 maintain 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).

14 pages

References in corpus (26)

• Perspective: Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM)
• Physical approaches to DNA sequencing and detection
• Non-perturbative treatment of non-Markovian dynamics of open quantum systems
• Real-time simulations of nonequilibrium transport in the single-impurity Anderson model
• Nonequilibrium Dynamical Mean Field Theory: an auxiliary Quantum Master Equation approach
• Influence of the environment and probes on rapid DNA sequencing via transverse electronic transport
• Super-fermion representation of the Lindblad master equation for the electron transport problem
• Approach to steady state transport in nanoscale conductors
• Transport properties and Kondo correlations in nanostructures: the time-dependent DMRG method applied to quantum dots coupled to Wilson chains
• Exact open quantum system dynamics using the Hierarchy of Pure States (HOPS)
• Microscopic Current Dynamics in Nanoscale Junctions
• Strong enhancement of transport by interaction on contact links
• Weak coupling approximations in non-Markovian Transport
• Stochastic jump processes for non-Markovian quantum dynamics
• Derivation of nonlinear single-particle equations via many-body Lindblad superoperators: A density-matrix approach
• Driving denaturation: Nanoscale thermal transport as a probe of DNA melting
• Systematic Perturbation Theory for Dynamical Coarse-Graining
• Comment on "Characterization of the tunneling conductance across DNA bases"
• Hierarchical quantum master equation approach to current fluctuations in nonequilibrium charge transport through nanosystems
• Decoherence due to contacts in ballistic nanostructures
• Tunable Thermal Switching via DNA-Based Nano Devices
• Time-dependent transport in open systems based on quantum master equations
• Relaxation-limited electronic currents in extended reservoir simulations
• Relaxation Dynamics of Meso-Reservoirs
• Finite representations of continuum environments
• Optimal in situ electromechanical sensing of molecular species

Cited by in corpus (11)

• Quantum thermodynamics with fast driving and strong coupling via the mesoscopic leads approach
• Performance of Reservoir Discretizations in Quantum Transport Simulations
• Accumulative reservoir construction: Bridging continuously relaxed and periodically refreshed extended reservoirs
• Entropy production in the mesoscopic-leads formulation of quantum thermodynamics
• Impact of dephasing on non-equilibrium steady-state transport in fermionic chains with long-range hopping
• Transport in a periodically driven tilted lattice via the extended reservoir approach: Stability criterion for recovering the continuum limit
• Spectral Density Modulation and Universal Markovian Closure of Fermionic Environments
• Thermoelectric cooling of a finite reservoir coupled to a quantum dot
• The confluence of fractured resonances at points of dynamical, many--body flare
• Dual current anomalies and quantum transport within extended reservoir simulations
• Approaching the scaling limit of transport through lattices with dephasing