arXiv subjects

Evgeny Polyakov

Publications and source records attributed to Evgeny Polyakov.

4 recordsLinked to original sources

arXiv2026

Long-time fermionic quantum transport with controlled full-state error using an adaptive reservoir-mode window

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-B\"uttiker result. For flat-band reservoirs with algebraically decaying correlations, it agrees with direct Schr\"odinger evolution before finite-size recurrences and reproduces the Landauer-B\"uttiker 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.

cond-mat.mes-hall↗

arXiv2025

Quantum Brownian Motion as a Classical Stochastic Process in Phase Space

We establish that the exact quantum dynamics of a Brownian particle in the Caldeira-Leggett model, with at most quadratic external potential, can be mapped, at any temperature, onto a classical, non-Markovian stochastic process in phase space. Starting from a correlated thermal equilibrium state between the particle and bath, we demonstrate that this correspondence is exact for quadratic potentials under arbitrary quantum state preparations of the particle itself. Our approach allows to consider arbitrary initial quantum states - including highly non-classical superpositions - which are incorporated via their Wigner functions, which serve as statistical weights for trajectory ensembles. Furthermore, the formalism naturally accommodates external manipulations and measurements modeled by preparation functions acting at arbitrary times, enabling the simulation of complex driven-dissipative quantum protocols. For more general, smooth potentials, we identify a natural small parameter: the density matrix becomes strongly quasidiagonal in the coordinate representation, with its off-diagonal width shrinking as the bath's spectral cutoff increases, suggesting a controlled parameter for a possible approximation.

quant-ph↗

arXiv2025

Emergence of non-Markovian Decoherent Histories in Integrable Environment: A "Tape Recorder" Model for Local Quantum Observables

We propose a new approach to coarse-grained description of quantum evolution that provides an explicit recipe to construct and evaluate multi-time decoherent histories in a controlled way, applicable to non-Markovian and integrable systems. Specifically, we study local interaction quench of a local degree of freedom (an open quantum system) within a noninteracting integrable environment. This setting allows us to identify the environmental degrees of freedom that irreversibly store records of the system's past. These modes emerge sequentially in time and define the projectors required for decoherent histories. We show numerically that the off-diagonal elements of the decoherence functional are exponentially suppressed relative to a significance threshold.

quant-ph↗

arXiv2023

Probing quantum chaos with the entropy of decoherent histories

Quantum chaos, a phenomenon that began to be studied in the last century, still does not have a rigorous understanding. By virtue of the correspondence principle, the properties of the system that lead to chaotic dynamics at the classical level must also be present in the underlying quantum system. In the classical case, the exponential divergence of nearby trajectories in time is described in terms of the Lyapunov exponent. However, in the quantum case, a similar description of chaos is, strictly speaking, impossible due to absence of trajectories. There are different approaches to remedy this situation, but the universal criterion of quantum chaos is absent. We propose the quantum chaos definition in the manner similar to the classical one using decoherent histories as a quantum analogue of trajectories. For this purpose, we consider the model of an open quantum kicked top interacting with the environment, which is a bosonic bath, and illustrate this idea. Here, the environment plays the role of a trajectory recording device. For the kicked top model at the classical level, depending on the kick strength, crossover occurs between the integrable and chaotic regimes. We show that for such a model, the production of entropy of decoherent histories is radically different in integrable and chaotic regimes. Thus, the entropy of an ensemble of quantum trajectories can be used as a signature of quantum chaos.

quant-ph↗