scholarly journals On the Lyapunov–Perron reducible Markovian Master Equation

2021 ◽  
Author(s):  
Krzysztof Szczygielski
Keyword(s):  
Steady State ◽  
Master Equation ◽  
Quantum System ◽  
Projection Operator ◽  
Weak Coupling ◽  
Open Quantum System ◽  
Weak Coupling Limit ◽  
Periodic Case ◽  
Stability Of Solutions ◽  
Projection Operator Techniques

We consider an open quantum system in [Formula: see text] governed by quasiperiodic Hamiltonian with rationally independent frequencies and under the assumption of Lyapunov–Perron reducibility of the associated Schrödinger equation. We construct the Markovian Master Equation and the resulting CP-divisible evolution in the weak coupling limit regime, generalizing our previous results from the periodic case. The analysis is conducted with the application of projection operator techniques and concluded with some results regarding stability of solutions and existence of quasiperiodic global steady state.

Adiabatic Evolution of an Open Quantum System in its Instantaneous Steady State

2017 ◽  
Vol 56 (11) ◽  
pp. 3562-3571 ◽  
Author(s):  
Dongxiao Li ◽  
Songlin Wu ◽  
Hongzhi Shen ◽  
Xuexi Yi
Keyword(s):  
Steady State ◽  
Quantum System ◽  
Open Quantum System ◽  
Adiabatic Evolution ◽  
Open Quantum

Total State Dynamics in the GKSL Regime

2017 ◽  
Vol 24 (04) ◽  
pp. 1740014
Author(s):  
Nina Megier ◽  
Walter T. Strunz
Keyword(s):  
Hilbert Space ◽  
Master Equation ◽  
Open System ◽  
Density Operator ◽  
Weak Coupling ◽  
Open Quantum System ◽  
Markov Approximation ◽  
Wigner Representation ◽  
Total State ◽  
Reduced Density

We develop a framework that allows us to describe the dynamics of the total state of an open quantum system and its bosonic environment in the usual Born (weak coupling) and Markov approximation. By shifting the whole time-dependence into an unnormalized s-operator of the open system, the full dynamics is captured by an s-master equation of similar structure than the well-known Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation for the reduced dynamics. By varying the ordering parameter s (0 ≤ s ≤ 1) we obtain the partial Husimi representation (s = 0) and the partial Glauber-Sudarshan representation (s = 1) for the dynamics of the total state. For the reduced density operator the GKSL master equation can be derived easily. The case of s = 1/2, leading to a partial Wigner representation, is helpful to study the overlap of states in the total Hilbert space of system and environment.

scholarly journals Open System Model for Quantum Dynamical Maps with Classical Noise and Corresponding Master Equations

2017 ◽  
Vol 24 (04) ◽  
pp. 1740012 ◽  
Author(s):  
Chahan M. Kropf ◽  
Vyacheslav N. Shatokhin ◽  
Andreas Buchleitner
Keyword(s):  
Master Equation ◽  
Quantum System ◽  
Open System ◽  
Open Quantum System ◽  
Master Equations ◽  
Time Limit ◽  
System Model ◽  
Markov Approximation ◽  
Quantum Dynamical ◽  
Short Time

We show how random unitary dynamics arise from the coupling of an open quantum system to a static environment. Subsequently, we derive a master equation for the reduced system random unitary dynamics and study three specific cases: commuting system and interaction Hamiltonians, the short-time limit, and the Markov approximation.

scholarly journals Efficient determination of the Markovian time-evolution towards a steady-state of a complex open quantum system

2017 ◽  
Vol 220 ◽  
pp. 81-90 ◽  
Author(s):  
Thorsteinn H. Jonsson ◽  
Andrei Manolescu ◽  
Hsi-Sheng Goan ◽  
Nzar Rauf Abdullah ◽  
Anna Sitek ◽  
...  
Keyword(s):  
Steady State ◽  
Quantum System ◽  
Time Evolution ◽  
Open Quantum System ◽  
Open Quantum

Thermodynamics of Quantum Information Systems — Hamiltonian Description

2004 ◽  
Vol 11 (03) ◽  
pp. 205-217 ◽  
Author(s):  
Robert Alicki ◽  
Michał Horodecki ◽  
Paweł Horodecki ◽  
Ryszard Horodecki
Keyword(s):  
Quantum System ◽  
Weak Coupling ◽  
Heat Bath ◽  
Quantum Correlations ◽  
Weak Coupling Limit ◽  
Second Law ◽  
Hamiltonian Description ◽  
Landauer’S Principle ◽  
Thermodynamical Laws ◽  
The Cost

It is often claimed, that from a quantum system of d levels, and entropy S and heat bath of temperature T one can draw kT lnd–TS amount of work. However, the usual arguments basing on Szilard engine, are not fully rigorous. Here we prove the formula within Hamiltonian description of drawing work from a quantum system and a heat bath, at the cost of entropy of the system. We base on the derivation of thermodynamical laws and quantities in [10] within weak coupling limit. Our result provides fully physical scenario for extracting thermodynamical work form quantum correlations [4]. We also derive Landauer's principle as a consequence of the second law within the considered model.

FOKKER–PLANCK-BASED CONTROL OF A TWO-LEVEL OPEN QUANTUM SYSTEM

2013 ◽  
Vol 23 (11) ◽  
pp. 2039-2064 ◽  
Author(s):  
M. ANNUNZIATO ◽  
A. BORZI
Keyword(s):  
Master Equation ◽  
Quantum System ◽  
Open Quantum System ◽  
Planck Equation ◽  
Open Loop ◽  
Optimality System ◽  
Environment Interaction ◽  
Open Quantum ◽  
Fokker Planck Equation ◽  
Fokker Planck

The control of a two-level open quantum system subject to dissipation due to environment interaction is considered. The evolution of this system is governed by a Lindblad master equation which is augmented by a stochastic term to model the effect of time-continuous measurements. In order to control this stochastic master equation model, a Fokker–Planck control framework is investigated. Within this strategy, the control objectives are defined based on the probability density functions of the two-level stochastic process and the controls are computed as minimizers of these objectives subject to the constraints represented by the Fokker–Planck equation. This minimization problem is characterized by an optimality system including the Fokker–Planck equation and its adjoint. This optimality system is approximated by a second-order accurate, stable, conservative and positive-preserving discretization scheme. The implementation of the resulting open-loop controls is realized with a receding-horizon algorithm over a sequence of time windows. Results of numerical experiments demonstrate the effectiveness of the proposed approach.

Sign in / Sign up

Export Citation Format

Share Document