scholarly journals Dynamics of Open Quantum Systems II, Markovian Approximation

Quantum ◽  
2022 ◽  
Vol 6 ◽  
pp. 616
Author(s):  
Marco Merkli
Keyword(s):  
Thermal Equilibrium ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Coupling Constant ◽  
Full System ◽  
Markovian Semigroup ◽  
Finite Dimensional ◽  
Markovian Dynamics ◽  
The Difference ◽  
Lindblad Master Equation

A finite-dimensional quantum system is coupled to a bath of oscillators in thermal equilibrium at temperature T>0. We show that for fixed, small values of the coupling constant λ, the true reduced dynamics of the system is approximated by the completely positive, trace preserving Markovian semigroup generated by the Davies-Lindblad generator. The difference between the true and the Markovian dynamics is O(|λ|1/4) for all times, meaning that the solution of the Gorini-Kossakowski-Sudarshan-Lindblad master equation is approximating the true dynamics to accuracy O(|λ|1/4) for all times. Our method is based on a recently obtained expansion of the full system-bath propagator. It applies to reservoirs with correlation functions decaying in time as 1/t4 or faster, which is a significant improvement relative to the previously required exponential decay.

scholarly journals COMPLEMENTARITY IN GENERIC OPEN QUANTUM SYSTEMS

2010 ◽  
Vol 24 (24) ◽  
pp. 2485-2509 ◽  
Author(s):  
SUBHASHISH BANERJEE ◽  
R. SRIKANTH
Keyword(s):  
Lower Bound ◽  
Uniform Distribution ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Atomic Systems ◽  
Information Theoretic ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
The Difference ◽  
Positive Operator Valued Measure

We develop a unified, information theoretic interpretation of the number-phase complementarity that is applicable both to finite-dimensional (atomic) and infinite-dimensional (oscillator) systems, with number treated as a discrete Hermitian observable and phase as a continuous positive operator valued measure (POVM). The relevant uncertainty principle is obtained as a lower bound on entropy excess, X, the difference between the entropy of one variable, typically the number, and the knowledge of its complementary variable, typically the phase, where knowledge of a variable is defined as its relative entropy with respect to the uniform distribution. In the case of finite-dimensional systems, a weighting of phase knowledge by a factor μ (> 1) is necessary in order to make the bound tight, essentially on account of the POVM nature of phase as defined here. Numerical and analytical evidence suggests that μ tends to 1 as the system dimension becomes infinite. We study the effect of non-dissipative and dissipative noise on these complementary variables for an oscillator as well as atomic systems.

scholarly journals Dynamics of Open Quantum Systems I, Oscillation and Decay

Quantum ◽  
2022 ◽  
Vol 6 ◽  
pp. 615 ◽  
Author(s):  
Marco Merkli
Keyword(s):  
Main Part ◽  
Open Quantum Systems ◽  
Companion Paper ◽  
Quantum Systems ◽  
Thermal Bath ◽  
Coupling Constant ◽  
Level System ◽  
Concrete Case ◽  
Finite Dimensional ◽  
Characteristic Features

We develop a framework to analyze the dynamics of a finite-dimensional quantum system S in contact with a reservoir R. The full, interacting SR dynamics is unitary. The reservoir has a stationary state but otherwise dissipative dynamics. We identify a main part of the full dynamics, which approximates it for small values of the SR coupling constant, uniformly for all times t≥0. The main part consists of explicit oscillating and decaying parts. We show that the reduced system evolution is Markovian for all times. The technical novelty is a detailed analysis of the link between the dynamics and the spectral properties of the generator of the SR dynamics, based on Mourre theory. We allow for SR interactions with little regularity, meaning that the decay of the reservoir correlation function only needs to be polynomial in time, improving on the previously required exponential decay.In this work we distill the structural and technical ingredients causing the characteristic features of oscillation and decay of the SR dynamics. In the companion paper [27] we apply the formalism to the concrete case of an N-level system linearly coupled to a spatially infinitely extended thermal bath of non-interacting Bosons.

scholarly journals On Howland time-independent formulation of CP-divisible quantum evolutions

2020 ◽  
Vol 32 (07) ◽  
pp. 2050021
Author(s):  
Krzysztof Szczygielski ◽  
Robert Alicki
Keyword(s):  
Open Quantum Systems ◽  
Standard Form ◽  
Quantum Systems ◽  
Matrix Space ◽  
Product Representation ◽  
Completely Positive ◽  
Finite Dimensional ◽  
Markovian Dynamics ◽  
Bochner Space ◽  
Densely Defined

We extend Howland time-independent formalism to the case of completely positive and trace preserving dynamics of finite-dimensional open quantum systems governed by periodic, time-dependent Lindbladian in Weak Coupling Limit, expanding our result from previous papers. We propose the Bochner space of periodic, square integrable matrix-valued functions, as well as its tensor product representation, as the generalized space of states within the time-independent formalism. We examine some densely defined operators on this space, together with their Fourier-like expansions and address some problems related to their convergence by employing general results on Banach space-valued Fourier series, such as the generalized Carleson–Hunt theorem. We formulate Markovian dynamics in the generalized space of states by constructing appropriate time-independent Lindbladian in standard (Lindblad–Gorini–Kossakowski–Sudarshan) form, as well as one-parameter semigroup of bounded evolution maps. We show their similarity with Markovian generators and dynamical maps defined on matrix space, i.e. the generator still possesses a standard form (extended by closed perturbation) and the resulting semigroup is also completely positive, trace preserving and a contraction.

scholarly journals Perturbation Analysis of Quantum Reset Models

2021 ◽  
Vol 183 (1) ◽  
Author(s):  
Géraldine Haack ◽  
Alain Joye
Keyword(s):  
Steady State ◽  
Perturbation Analysis ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Markov Semigroup ◽  
Coupling Constant ◽  
Coupling Term ◽  
Open Quantum ◽  
Effective Dynamics ◽  
A Chain

AbstractThis paper is devoted to the analysis of Lindblad operators of Quantum Reset Models, describing the effective dynamics of tri-partite quantum systems subject to stochastic resets. We consider a chain of three independent subsystems, coupled by a Hamiltonian term. The two subsystems at each end of the chain are driven, independently from each other, by a reset Lindbladian, while the center system is driven by a Hamiltonian. Under generic assumptions on the coupling term, we prove the existence of a unique steady state for the perturbed reset Lindbladian, analytic in the coupling constant. We further analyze the large times dynamics of the corresponding CPTP Markov semigroup that describes the approach to the steady state. We illustrate these results with concrete examples corresponding to realistic open quantum systems.

scholarly journals Shortcuts to Adiabaticity in Driven Open Quantum Systems: Balanced Gain and Loss and Non-Markovian Evolution

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 336 ◽  
Author(s):  
Sahar Alipour ◽  
Aurelia Chenu ◽  
Ali T. Rezakhani ◽  
Adolfo del Campo
Keyword(s):  
Open Quantum Systems ◽  
Quantum Systems ◽  
Quantum Oscillator ◽  
Quantum Processes ◽  
Open Quantum ◽  
Markovian Dynamics ◽  
Shortcuts To Adiabaticity ◽  
Speed Up ◽  
Gain And Loss ◽  
Universal Scheme

A universal scheme is introduced to speed up the dynamics of a driven open quantum system along a prescribed trajectory of interest. This framework generalizes counterdiabatic driving to open quantum processes. Shortcuts to adiabaticity designed in this fashion can be implemented in two alternative physical scenarios: one characterized by the presence of balanced gain and loss, the other involves non-Markovian dynamics with time-dependent Lindblad operators. As an illustration, we engineer superadiabatic cooling, heating, and isothermal strokes for a two-level system, and provide a protocol for the fast thermalization of a quantum oscillator.

scholarly journals Tomograms for open quantum systems: In(finite) dimensional optical and spin systems

2016 ◽  
Vol 366 ◽  
pp. 148-167 ◽  
Author(s):  
Kishore Thapliyal ◽  
Subhashish Banerjee ◽  
Anirban Pathak
Keyword(s):  
Open Quantum Systems ◽  
Quantum Systems ◽  
Spin Systems ◽  
Open Quantum ◽  
Finite Dimensional

scholarly journals Colloquium: Non-Markovian dynamics in open quantum systems

2016 ◽  
Vol 88 (2) ◽  
Author(s):  
Heinz-Peter Breuer ◽  
Elsi-Mari Laine ◽  
Jyrki Piilo ◽  
Bassano Vacchini
Keyword(s):  
Open Quantum Systems ◽  
Quantum Systems ◽  
Open Quantum ◽  
Markovian Dynamics

Dynamic Correlations in Open Quantum Systems: The Dephasing Model

2020 ◽  
Vol 27 (02) ◽  
pp. 2050007
Author(s):  
Vasyl’ Ignatyuk
Keyword(s):  
Kinetic Energy ◽  
Open Quantum Systems ◽  
Kinetic Equations ◽  
Quantum Systems ◽  
Quantum Master Equation ◽  
Coupling Constant ◽  
Open Quantum ◽  
Dynamic Correlations ◽  
Exactly Solvable ◽  
Analytical Result

We study the dynamical correlations in open quantum systems on an example of an exactly solvable dephasing model. The system of non-Markovian kinetic equations for the generalized coherence and quasi-temperature is derived up to the 2-nd order in the coupling constant using the generalized quantum master equation [20]. Numerical and analytical solutions of the kinetic equations are obtained. The analytical result shows a redistribution of the real and imaginary parts of the coherence as compared to the exact one. We give a physical interpretation to the quasi-temperature, relating it to the nonequilibrium kinetic energy of the environment.

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