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

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.