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arXiv:2610.30457

Memory--Transport Competition in Physical Two-Bath Quantum Reset Dynamics

Jishad Kumar, Achilleas Lazarides, Tapio Ala-Nissila

quant-phcond-mat.stat-mechSubmitted Oct 21, 2026• Announced Oct 23, 2026• 0 citations
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Abstract

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.

Comments
15 pages, 5 figures

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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 develop an exact theory of coherence-selective stroboscopic resetting for quadratic open quantum systems within the single-particle density-matrix formalism. We focus on the survival of coherences and the associated thermodynamic cost at the stroboscopic fixed point. To this end, we introduce a one-parameter family of reset channels that continuously interpolates between complete coherence erasure and complete coherence preservation. This unifies the reset-map description, the repeated-interaction and evolving-correlation endpoint channels, and the thermodynamic cost of environmental reinitialization. For a single fermionic level coupled to a structured semi-infinite tight-binding bath, we derive the exact affine stroboscopic map, solve for its unique fixed point, and compute the retained coherence spectrum, the post-reset occupation, and the reset heat current. We find that retained coherence increases monotonically with the retention parameter, whereas the reset heat current is generically nonmonotonic and is maximized at an intermediate operating point. Thus the protocol that stores the most coherence is not the one that dissipates the most heat. Exact operating diagrams further show that coherence-optimal and coherence-per-cost-optimal protocols are both driven toward the coherence-preserving endpoint, while the heat-optimal protocol depends strongly on the reset interval. We also show that this coherence-cost geometry survives at nonzero chemical potential as a filling-biased deformation of the same fixed-point tradeoff, rather than as an independent particle-current optimization problem. These results establish coherence-selective resetting as a distinct control principle for structured-bath open quantum systems and provide an exactly solvable benchmark for memory engineering and thermodynamic optimization under repeated environmental reinitialization.
We develop an exact framework for quantum Zeno and anti-Zeno dynamics in a broad class of open systems, whose microscopic Hamiltonians are quadratic in bosonic or fermionic operators. We treat the environment through an exact stroboscopic resetting scheme acting at the level of the single-particle density matrix (SPDM). Within this framework, we consider two cases: a repeated-interaction (RI) protocol, in which the environment block is rethermalized and all system-environment coherences are erased after each step, and an evolving-correlation (EC) protocol, in which only the environment block is reset while system-environment coherences are preserved. For RI, we derive a general short-time Zeno law for the survival probability of a single-particle excitation and show that the corresponding decay rate scales linearly with the reset interval, implying Zeno freezing in the limit of infinitely frequent resets. Beyond the short-time regime, we formulate the RI dynamics directly in terms of the exact one-cycle propagator, which allows us to analyze finite-τττ anti-Zeno windows without additional approximations. For EC, we obtain a continuous-reset description in which the kept single-particle correlators obey a finite-dimensional linear differential equation. In this case the drift in the system block remains finite in the frequent-reset limit, so strict freezing is absent. We illustrate these results for a single fermionic level coupled to a semi-infinite tight-binding chain acting as a structured bath. Our results identify coherence erasure versus coherence retention as the key factor controlling the reset-induced Zeno physics.
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.
Decoherence is often modeled using Markovian master equations that predict exponential suppression of coherence and are frequently used as effective bounds on quantum behavior in complex environments. Such descriptions, however, correspond to the singular physical limit of vanishing environmental memory. Here we formulate decoherence using a general time-nonlocal decoherence functional determined solely by the environmental force correlation function, with Markovian dynamics recovered explicitly as a limiting case. For arbitrary stationary environments with finite temporal correlations, we show that the decoherence functional exhibits quadratic short-time growth that is model-independent within the finite-memory class considered. Consequently, the decoherence time defined operationally-without assuming exponential decay-scales as the square root of the environmental correlation time, independent of the detailed form of the bath correlation kernel. These results are illustrated analytically for Gaussian-correlated, soft power-law, and Ornstein-Uhlenbeck environments. In the Ornstein-Uhlenbeck case, the non-Markovian dynamics admit an exact analytical closure, yielding a closed evolution equation for the coherence. Exact numerical simulations based on a pseudomode mapping confirm the predicted scaling and show that exponential decoherence emerges only in the memoryless limit. Beyond coherence decay, we distinguish decoherence rates from observable loss of quantum signatures by analyzing purity and von Neumann entropy dynamics. We show that suppression of a specific coherence element need not coincide with irreversible entropy production. Finally, we introduce an inferred-memory perspective in which the environmental correlation time is treated as an operationally extractable parameter from dynamical data.
In resetting dynamics, a system is repeatedly coupled to and decoupled from ancillary degrees of freedom that are reinitialized between interactions. This provides a versatile route to engineer nonequilibrium steady states and constitutes a powerful and analytically transparent framework for studying nonequilibrium dynamics in quadratic fermionic models. The baseline noninteracting resetting scheme yields an affine evolution for the subsystem single-particle density matrix (SPDM), with a clear operational interpretation: a finite environment block E mediates the interaction between the subsystem S and an ideal external thermal reservoir. In this work, we develop a controlled extension of such a framework to weakly interacting systems. We introduce a Hartree mean-field treatment of density-density interactions that preserves closure of the SPDM dynamics while producing genuinely nonlinear behavior. We further construct a completely positive (CP-safe) Gaussian Lindblad embedding that reproduces the resetting dynamics in the noninteracting limit and yields a continuous-time representation of environmental thermalization when interactions are present. Our analytical results are complemented by numerical studies of a ring segmentation geometry and a minimal two-site model, revealing interaction-enabled steady states that cannot be obtained in any purely quadratic setting. Together, these results establish a general and physically consistent route for incorporating weak interactions ino resetting-based approaches to open quantum system.
We introduce a quantum stochastic resetting protocol with uniform memory, in which each resetting event returns the system to a state visited at a time chosen uniformly from its entire history. The resulting dynamics is nonunitary, non-Markovian and a direct quantum generalization of the classical preferential relocation model. Working in the energy eigenbasis, we derive the exact evolution of every density-matrix element for an arbitrary time-independent Hamiltonian and show that the Hamiltonian enters the dynamics only through the corresponding Bohr frequencies. This leads to a natural distinction between two classes of quantum systems: gapped and gapless. In \emph{gapped systems} (systems with a discrete energy spectrum), while the diagonal elements remain unchanged, the off-diagonal elements of the density matrix in the energy eigenbasis decay algebraically with a continuously varying exponent and with an amplitude that oscillates periodically in log⁡t\log tlogt. The system therefore approaches a stationary state that is independent of the resetting rate and retains a strong memory of the initial state. In \emph{gapless systems} (systems with a continuous energy spectrum), arbitrarily small Bohr frequencies prevent stationarity. Instead, the position distribution spreads on the universal (ultra-slow) scale log⁡(rt)/r\log(rt)/rlog(rt)/r, independently of the initial state and of the details of the Hamiltonian. We illustrate these results with a two-level system, a harmonic oscillator, and a free quantum particle, and contrast them with their classical counterparts.