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.

Finite Temperature Dynamics of the Total State in an Open System Model

2005 ◽  
Vol 12 (01) ◽  
pp. 65-80 ◽  
Author(s):  
Walter T. Strunz
Keyword(s):  
Open System ◽  
Finite Temperature ◽  
Density Operator ◽  
Point Of View ◽  
System Model ◽  
Markov Approximation ◽  
Zero Temperature ◽  
Stochastic Schrödinger Equation ◽  
Total State ◽  
Reduced Density

We determine the dynamics of the total state of a system and environment for an open system model, at finite temperature. Based on a partial Husimi representation, our framework describes the full dynamics very efficiently through equations in the Hilbert space of the open system only. We briefly review the zero-temperature case and present the corresponding new finite temperature theory, within the usual Born-Markov approximation. As we will show, from a reduced point of view, our approach amounts to the derivation of a stochastic Schrödinger equation description of the dynamics. We show how the reduced density operator evolves according to the expected (finite temperature) master equation of Lindblad form.

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.

PATH INTEGRAL DERIVATION OF AN EXACT MASTER EQUATION

1995 ◽  
Vol 09 (02) ◽  
pp. 87-94 ◽  
Author(s):  
S. V. LAWANDE ◽  
Q. V. LAWANDE
Keyword(s):  
Density Matrix ◽  
Harmonic Oscillator ◽  
Master Equation ◽  
Path Integral ◽  
Open System ◽  
Coherent States ◽  
Reduced Density Matrix ◽  
Feynman Propagator ◽  
Reduced Density

The Feynman propagator in coherent states representation is obtained for a system of a single harmonic oscillator coupled to a reservoir of N oscillators. Using this propagator, an exact master equation is obtained for the evolution of the reduced density matrix for the open system of the oscillator.

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.

Aspects of the weak-coupling theory of open systems

1983 ◽  
Vol 61 (11) ◽  
pp. 1479-1485 ◽  
Author(s):  
I. D. Cox ◽  
W. E. Hagston ◽  
B. J. Holmes
Keyword(s):  
Perturbation Theory ◽  
Open System ◽  
Weak Coupling ◽  
Open Systems ◽  
Higher Order ◽  
Projection Operators ◽  
Coupling Theory ◽  
Weak Coupling Theory ◽  
Damping Theory ◽  
Insight Into

Damping theory of an open system S is usually formulated in terms of projection operators which introduce nonuniqueness into the analysis. An insight into the nature of the approximations that arise from this aspect of the formalism is revealed by considering systems of varying complexity. This leads to the conclusion that the results of higher order perturbation theory approximations may not be meaningful.

scholarly journals Positivity violations of the density operator in the Caldeira-Leggett master equation

2019 ◽  
Vol 73 (3) ◽  
Author(s):  
Gábor Homa ◽  
József Zsolt Bernád ◽  
László Lisztes
Keyword(s):  
Master Equation ◽  
Density Operator

scholarly journals Husimi–Wigner representation of chaotic eigenstates

2008 ◽  
Vol 464 (2094) ◽  
pp. 1503-1524 ◽  
Author(s):  
Fabricio Toscano ◽  
Anatole Kenfack ◽  
Andre R.R Carvalho ◽  
Jan M Rost ◽  
Alfredo M Ozorio de Almeida
Keyword(s):  
Hilbert Space ◽  
Coherent State ◽  
Pure State ◽  
Degrees Of Freedom ◽  
Factor Space ◽  
Wigner Functions ◽  
Higher Dimensional ◽  
Wigner Representation ◽  
Quantum Point ◽  
The Individual

Just as a coherent state may be considered as a quantum point, its restriction to a factor space of the full Hilbert space can be interpreted as a quantum plane. The overlap of such a factor coherent state with a full pure state is akin to a quantum section. It defines a reduced pure state in the cofactor Hilbert space. Physically, this factorization corresponds to the description of interacting components of a quantum system with many degrees of freedom and the sections could be generated by conceivable partial measurements. The collection of all the Wigner functions corresponding to a full set of parallel quantum sections defines the Husimi–Wigner representation. It occupies an intermediate ground between the drastic suppression of non-classical features, characteristic of Husimi functions, and the daunting complexity of higher dimensional Wigner functions. After analysing these features for simpler states, we exploit this new representation as a probe of numerically computed eigenstates of a chaotic Hamiltonian. Though less regular, the individual two-dimensional Wigner functions resemble those of semiclassically quantized states.

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