Real-time simulations of interacting nanostructures coupled to fermionic reservoirs can require a growing number of environmental degrees of freedom to retain long-lived correlations. We introduce tape-recorder coarse graining, which reorganizes each noninteracting lead into incoming, active, and outgoing modes. The device is propagated with the active modes, while outgoing modes are stochastically sampled and removed once their remaining integrated coupling falls below a prescribed threshold. For each outgoing-mode truncation, we derive a nonperturbative upper bound on the infidelity between the exact and truncated full device--reservoir states over any prescribed finite interval. The bound depends on the mode's remaining coupling weight and finite-interval response factors. Numerically, the active-mode count saturates in time at fixed relative threshold and grows logarithmically as the threshold is reduced. We benchmark the method on a two-site quantum point contact at zero temperature and maximal bias. For Lorentzian reservoirs, the dynamics agrees with converged HEOM calculations and the steady-state current with the Landauer--Büttiker result. For flat-band reservoirs with algebraically decaying correlations, it agrees with direct Schrödinger evolution before finite-size recurrences and reproduces the Landauer--Büttiker stationary current, while finite exponential HEOM decompositions remain unconverged. For interacting contacts, the method yields Coulomb-blockade peak splitting. In the noninteracting driven limit, it agrees with an exact Floquet Green-function calculation and reproduces coherent current suppression under periodic driving, which persists at finite Coulomb repulsion. Together, these benchmarks show that tape-recorder coarse graining enables practical long-time simulations of the full device--reservoir state in interacting fermionic transport.
Real-time simulations of interacting nanostructures coupled to fermionic reservoirs can require a growing number of environmental degrees of freedom to retain long-lived correlations. We introduce tape-recorder coarse graining, which reorganizes each noninteracting lead into incoming, active, and outgoing modes. The device is propagated with the active modes, while outgoing modes are stochastically sampled and removed once their remaining integrated coupling falls below a prescribed threshold. For each outgoing-mode truncation, we derive a nonperturbative upper bound on the infidelity between the exact and truncated full device--reservoir states over any prescribed finite interval. The bound depends on the mode's remaining coupling weight and finite-interval response factors. Numerically, the active-mode count saturates in time at fixed relative threshold and grows logarithmically as the threshold is reduced. We benchmark the method on a two-site quantum point contact at zero temperature and maximal bias. For Lorentzian reservoirs, the dynamics agrees with converged HEOM calculations and the steady-state current with the Landauer--Büttiker result. For flat-band reservoirs with algebraically decaying correlations, it agrees with direct Schrödinger evolution before finite-size recurrences and reproduces the Landauer--Büttiker stationary current, while finite exponential HEOM decompositions remain unconverged. For interacting contacts, the method yields Coulomb-blockade peak splitting. In the noninteracting driven limit, it agrees with an exact Floquet Green-function calculation and reproduces coherent current suppression under periodic driving, which persists at finite Coulomb repulsion. Together, these benchmarks show that tape-recorder coarse graining enables practical long-time simulations of the full device--reservoir state in interacting fermionic transport.
Coherence preservation and environmental renewal offer competing ways of controlling quantum memory and transport. We show that a seemingly natural protocol which exactly replaces the bath occupations while preserving arbitrary system--bath coherences need not correspond to a physical fermionic state. We instead construct a two-reservoir protocol with independent, number-conserving thermal attenuators, for which complete positivity and fermionic admissibility hold by construction. Physical attenuation necessarily modifies bath populations as well as cross correlations; the coherence control is not an independent hard-reset knob. Quadratic dynamics reduces the stroboscopic problem to an exact matrix fixed-point equation without a weak-coupling or Markov approximation. Analytically, coherence retention enhances the leading short-cycle transfer rate, including the complete-erasure limit; no general endpoint-vanishing theorem exists. An exact stationary continuity theorem forces the through-current to vanish whenever either reservoir is left entirely unrefreshed, although no analogous theorem suppresses it at complete erasure. For biased structured reservoirs, exact finite-chain calculations display distinct coherence-, current-, and signed energy-transfer operating points; a resolved high-retention boundary layer exposes strong finite-size sensitivity of the coherence peak. The model provides a microscopic, fermion-admissible benchmark for the interplay of reservoir coherence, particle transport, and energetic exchange.
We present a method for investigating the steady-state transport properties of one-dimensional correlated quantum systems. Using a procedure based on our analysis of finite-size effects in a related classical model (LC line) we show that stationary currents can be obtained from transient currents in finite systems driven out of equilibrium. The nonequilibrium dynamics of correlated quantum systems is calculated using the time-evolving block decimation method. To demonstrate our method we determine the full I-V characteristic of the spinless fermion model with nearest-neighbor hopping tH and interaction VH using two different setups to generate currents (turning on/off a potential bias). Our numerical results agree with exact results for noninteracting fermions (VH=0). For interacting fermions we find that in the linear regime $eV\ensuremath{\ll}4{t}_{\text{H}}$ the current I is independent from the setup and our numerical data agree with the predictions of the Luttinger liquid theory combined with the Bethe Ansatz solution. For larger potentials V the steady-state current depends on the current-generating setup and as V increases we find a negative differential conductance with one setup while the currents saturate at finite values in the other one. Both effects are due to finite renormalized bandwidths.
We extend the recently developed causal superfermion approach to the real-time diagrammatic transport theory to time-dependent decay problems. Its usefulness is illustrated for the Anderson model of a quantum dot with tunneling rates depending on spin due to ferromagnetic electrodes and/or spin polarization of the tunnel junction. This approach naturally leads to an exact result for one of the time-dependent decay modes for any value of the Coulomb interaction compatible with the wideband limit. We generalize these results to multilevel Anderson models and indicate constraints they impose on renormalization-group schemes in order to recover the exact noninteracting limit.(i) We first set up a second quantization scheme in the space of density operators constructing ``causal'' field superoperators using the fundamental physical principles of causality/probability conservation and fermion-parity superselection (univalence). The time-dependent perturbation series for the time evolution is renormalized by explicitly performing the wideband limit on the superoperator level. As a result, the occurrence of destruction and creation superoperators are shown to be tightly linked to the physical short- and long-time reservoir correlations, respectively. This effective theory takes as a reference a damped local system, which may also provide an interesting starting point for numerical calculations of memory kernels in real time. (ii) A remarkable feature of this approach is the natural appearance of a fermion-parity protected decay mode which can be measured using a setup proposed earlier [Phys. Rev. B 85, 075301 (2012)]. This mode can be calculated exactly in the fully Markovian, infinite-temperature limit by leading-order perturbation theory, but surprisingly persists unaltered for finite temperature, for any interaction and tunneling spin polarization. (iii) Finally, we show how a Liouville-space analog of the Pauli principle directly leads to an exact expression in the noninteracting limit for the time evolution, extending previous works by starting from an arbitrary initial mixed state including spin and pairing coherences and two-particle correlations stored on the quantum dot. This exact result is obtained already in finite-order renormalized perturbation theory, which surprisingly is not quadratic but quartic in the field superoperators, despite the absence of Coulomb interaction. The latter fact we relate to the time evolution of the two-particle component of the mixed state, which is just the fermion-parity operator, a cornerstone of the formalism. We illustrate how the super-Pauli-principle also simplifies problems with nonzero Coulomb interaction.
Structured baths can reshape transport fluctuations in mesoscopic quantum devices, yet a predictive criterion for when this enhances precision has been lacking. We propose a route towards such precision advantages by utilizing bath memory in coherent fermionic transport through a noninteracting quantum-dot chain. Using the Landauer-Büttiker formalism, we derive a dual impedance-matching condition that synchronizes the conductor mode splitting, boundary dissipation, and bath bandwidth, and sustains constructive multimode interference across the transmission window. The analytical predictions for the optimal bath bandwidths show excellent agreement with exact nonequilibrium Green's function calculations of the transport for Lorentzian, Gaussian, and Newns spectral densities. The prescription yields an optimal bath bandwidth at which the current Fano factor is minimized and the thermodynamic and kinetic precision coefficients are simultaneously enhanced beyond their Markovian limits. The alignment of the optimal precision regime with the experimentally accessible current Fano factor minimum thus provides a practical strategy for designing precision-enhanced transport in mesoscopic platforms such as semiconductor quantum-dot arrays and ultracold fermionic channels.
Extended reservoirs provide a framework for capturing macroscopic, continuum environments, such as metallic electrodes driving a current through a nanoscale contact, impurity, or material. We examine the application of this approach to periodically driven systems, specifically in the context of quantum transport. As with nonequilibrium steady states in time-independent scenarios, the current displays a Kramers' turnover including the formation of a plateau region that captures the physical, continuum limit response. We demonstrate that a simple stability criteria identifies an appropriate relaxation rate to target this physical plateau. Using this approach, we study quantum transport through a periodically driven tilted lattice coupled to two metallic reservoirs held at a finite bias and temperature. We use this model to benchmark the extended reservoir approach and assess the stability criteria. The approach recovers well-understood physical behavior in the limit of weak system-reservoir coupling. Extended reservoirs enable addressing strong coupling and nonlinear response as well, where we analyze how transport responds to the dynamics inside the driven lattice. These results set the foundations for the use of extended reservoir approach for periodically driven, quantum systems, such as many-body Floquet states.
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).