arXiv subjects

Evgeny A. Polyakov

Publications and source records attributed to Evgeny A. Polyakov.

8 recordsLinked to original sources

arXiv2023

Beyond The Fermi's Golden Rule: Discrete-Time Decoherence Of Quantum Mesoscopic Devices Due To Bandlimited Quantum Noise

We are at the midst of second quantum revolution where the mesoscopic quantum devies are actively employed for technological purposes. Despite this fact, the description of their real-time dynamics beyond the Fermi's golden rule remains a formiddable theoretical problem. This is due to the rapid spread of entanglement within the degrees of freedom of the surrounding environment. This is accompanied with a quantum noise (QN) acting on the mesoscopic device. In this work we propose a possible way out: to exploit the fact that this QN is usually bandlimited. This is because its spectral density is often contained in peaks of localized modes and resonances, and may be constrained by bandgaps. Inspired by the Kotelnikov sampling theorem from the theory of classical bandlimited signals, we put forward and explore the idea that when the QN spectral density has effective bandwidth $B$, the quantum noise becomes a discrete-time process, with an elementary time step $τ\propto B^{-1}$. After each time step $τ$, one new QN degree of freedom (DoF) gets coupled to the device for the first time, and one new QN DoF get irreversibly decoupled. Only a bounded number of QN DoFs are significantly coupled at any time moment. We call these DoFs the \textit{Kotelnikov modes}. As a result, the real-time dissipative quantum motion has a natural structure of a discrete-time matrix product state, with a bounded bond dimension. This yields a microscopically derived collision model. The temporal entanglement entropy appears to be bounded (area-law scaling) in the frame of Kotelnikov modes. The irreversibly decoupled modes can be traced out as soon as they occur during the real-time evolution. This leads to a novel\textit{bandlimited} input-output formalism and to quantum jump Monte Carlo simulation techniques for real-time motion of open quantum systems. We illustrate this idea on a spin-boson model.

quant-ph↗

arXiv2022

Real-Time Motion of Open Quantum Systems: Structure of Entanglement, Renormalization Group, and Trajectories

In this work we provide a complete description of the lifecycle of entanglement during the real-time motion of open quantum systems. The quantum environment can have arbitrary (e.g. structured) spectral density. The entanglement can be seen constructively as a Lego: its bricks are the modes of the environment. These bricks are connected to each other via operator transforms. The central result is that each infinitesimal time interval one new (incoming) mode of the environment gets coupled (entangled) to the open system, and one new (outgoing) mode gets irreversibly decoupled (disentangled from future). Moreover, each moment of time, only a few relevant modes (3 - 4 in the considered cases) are non-negligibly coupled to the future quantum motion. These relevant mode change (flow, or renormalize) with time. As a result, the temporal entanglement has the structure of a matrix-product operator. This allows us to pose a number of questions and to answer them in this work: what is the intrinsic quantum complexity of a real time motion; does this complexity saturate with time, or grows without bounds; how to do the real-time renormalization group in a justified way; how the classical Brownian stochastic trajectories emerge from the quantum evolution; how to construct the few-mode representations of non-Markovian environments. We provide illustrative simulations of the spin-boson model for various spectral densities of the environment: semicircle, subohmic, Ohmic, and superohmic.

quant-ph↗

arXiv2019

Non-Markovian Quantum State Diffusion in a Fermionic Bath

We present a stochastic approach for the description of the quantum dynamics of open system in a fermionic environment (bath). The full quantum evolution as provided by the Schrodinger equation is reformulated exactly as a probabilistic average over the so-called dressed quantum trajectories. The latter are defined as follows. The fermionic environment can be represented as a fermi sea whose "surface" is covered by the ripples of quantum fluctuations. If we consider these fluctuations in the basis of the particle-hole coherent states, then these fluctuations produce a classical particle-hole noise.The probability distribution of this noise is provided by the generalized particle-hole Husimi function of the vacuum. Then we define the dressed quantum trajectory as the evolution of the open system and the bath which is conditioned on a particular particle-hole noise sample. The resulting description resembles the non-Markovian quantum state diffusion for the bosonic bath. Therefore, we expect that our fermionic approach will share its favourable propeties like the possibility to carry out Monte-Carlo simulations of non-Markovian quantum dynamics on long times.

cond-mat.str-el↗

arXiv2018

Dressed Quantum Trajectories: Novel Approach to the non-Markovian Dynamics of Open Quantum Systems on a Wide Time Scale

A new approach to the theory and simulation of the non-Markovian dynamics of open quantum systems is presented. It is based on identification of a parameter which is uniformly small on wide time intervals: the occupation of the virtual cloud of quanta. By "virtual" we denote those bath excitations which were emitted by the system, but eventually will be reabsorbed before any measurement of the bath state. A favourable property of the virtual cloud is that the number of its quanta is expected to saturate on long times, since physically this cloud is a (retarded) polarization of the bath around the system. Therefore, the joint state of open system and of virtual cloud (the dressed state) can be accurately represented in a truncated basis of Fock states, on a wide time scale. At the same time, there can be arbitrarily large number of observable quanta, especially if the open system is under driving. However, by employing a Monte Carlo sampling of the measurement outcomes of the bath, we can simulate the dynamics of the observable quantum field. In this work we consider the measurement with respect to the coherent states, which yields the Husimi function as the positive (quasi)probability distribution of the outcomes. The evolution of dressed state which corresponds to a particular fixed outcome is called the dressed qauntum trajectory. Therefore, the Monte Carlo sampling of these trajectories yields a stochastic simulation method with promising convergence properties on wide time scales.

quant-ph↗

arXiv2017

Stochastic Wave-Function Simulation of Irreversible Emission Processes for Open Quantum Systems in a Non-Markovian Environment

When conducting the numerical simulation of quantum transport, the main obstacle is a rapid growth of the dimension of entangled Hilbert subspace. The Quantum Monte Carlo simulation techniques, while being capable of treating the problems of high dimension, are hindered by the so-called "sign problem". In the quantum transport, we have fundamental asymmetry between the processes of emission and absorption of environment excitations: the emitted excitations are rapidly and irreversibly scattered away. Whereas only a small part of these excitations is absorbed back by the open subsystem, thus exercising the non-Markovian self-action of the subsystem onto itself. We were able to devise a method for the exact simulation of the dominant quantum emission processes, while taking into account the small backaction effects in an approximate self-consistent way. Such an approach allows us to efficiently conduct simulations of real-time dynamics of small quantum subsystems immersed in non-Markovian bath for large times, reaching the quasistationary regime. As an example we calculate the spatial quench dynamics of Kondo cloud for a bozonized Kodno impurity model.

cond-mat.quant-gas↗

arXiv2017

Stochastic dressed wavefunction: a numerically exact solver for bosonic impurity model dynamics within wide time interval

In the dynamics of driven impurity models, there is a fundamental asymmetry between the processes of emission and absorption of environment excitations: most of the emitted excitations are rapidly and irreversibly scattered away, and only a small amount of them is reabsorbed back. We propose to use a stochastic simulation of the irreversible quantum emission processes in real-time dynamics, while taking into account the reabsorbed virtual excitations by the bath discretization. The resulting method delivers a fast convergence with respect to the number of bath sites, on a wide time interval, without the sign problem.

cond-mat.str-el↗

arXiv2016

Analytically continued physical states in the path-integral: a sign-problem-free Quantum Monte Carlo simulation of Bell states dynamics

The derivation of path integrals is reconsidered. It is shown that the expression for the discretized action is not unique, and the path integration domain can be deformed so that at least Gaussian path integrals become probabillistic. This leads to a practical algorithm of sign-problem-free Monte Carlo sampling from the Gaussian path integrals. Moreover, the dynamical influence of Gaussian quantum system (the bath) on any other quantum system can be exactly represented as interaction with classical non-Markovian noise. We discuss the relation of these findings to the Bell's theorem and the Feynman's conjecture on the exponential complexity of the classical simulation of quantum systems. In Feynman's path integral we have quasiprobability distributions for trajectories, and in analitycally continued path integrals we have probability distributions for quasitrajectories.

quant-ph↗

arXiv2016

Grassmann phase-space methods for fermions: uncovering classical probability structure

The phase-space description of bosonic quantum systems has numerous applications in such fields as quantum optics, trapped ultracold atoms, and transport phenomena. Extension of this description to the case of fermionic systems leads to formal Grassmann phase-space quasiprobability distributions and master equations. The latter are usually considered as not possessing probabillistic interpretation and as not directly computationally accessible. Here, we describe how to construct $c$-number interpretations of Grassmann phase space representations and their master equations. As a specific example, the Grassmann $B$ representation is considered. We disscuss how to introduce $c$-number probability distributions on Grassmann algebra and how to integrate them. A measure of size and proximity is defined for Grassmann numbers, and the Grassmann derivatives are introduced which are based on infinitesimal variations of function arguments. An example of $c$-number interpretation of formal Grassmann equations is presented.

quant-ph↗