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

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.

EFFECT OF PHASE FLUCTUATIONS OF LASER ON OPTICAL FORCES IN A TWO-LEVEL ATOM

2000 ◽  
Vol 14 (17n18) ◽  
pp. 631-637 ◽  
Author(s):  
S. V. LAWANDE ◽  
P. V. PANAT
Keyword(s):  
Angular Momentum ◽  
Steady State ◽  
Master Equation ◽  
Gaussian Beam ◽  
Laser Field ◽  
Density Operator ◽  
Bessel Beam ◽  
Optical Forces ◽  
Phase Fluctuations ◽  
Level Atom

An effect of phase fluctuations of a driving laser field on dissipative and dipolar forces of two-level atom is considered. The phase fluctuations are treated by a phase diffusion model where phase fluctuations follow Wiener–Levy process. An exact master equation for the relevant density operator is obtained and solved in the steady state. Optical forces are calculated. The effect of phase fluctuations on angular momentum imparted by a Laguerre–Gaussian beam and an ideal Bessel beam to the atom is investigated.

SOLVING THE MASTER EQUATION FOR AN ATTENUATED OR AMPLIFIED NONLINEAR OSCILLATOR VIA A SUPEROPERATOR METHOD

2002 ◽  
Vol 16 (15n16) ◽  
pp. 595-600 ◽  
Author(s):  
HUAI-XIN LU ◽  
ZENG-BING CHEN ◽  
YONG-DE ZHANG
Keyword(s):  
Master Equation ◽  
Time Evolution ◽  
Explicit Solution ◽  
Density Operator ◽  
Nonlinear Oscillator ◽  
Initial State

Using the decomposition theorm of superoperators, an explicit solution of the master equation for an attenuated or amplified nonlinear oscillator is presented. It is found that the time evolution of the density operator can be easily obtained from an arbitary initial state using this method.

Exact solution of degenerate and nondegenerate optical parametric oscillator coupled with a squeezed thermal bath

2018 ◽  
Vol 32 (21) ◽  
pp. 1850247
Author(s):  
B. M. Villegas-Martínez ◽  
H. M. Moya-Cessa ◽  
F. Soto-Eguibar
Keyword(s):  
Exact Solution ◽  
Master Equation ◽  
Optical Parametric Oscillator ◽  
Density Operator ◽  
Parametric Oscillator ◽  
Thermal Bath ◽  
Optical Parametric ◽  
Formal Solutions

We solve exactly the master equation of the degenerate and nondegenerate parametric oscillator in the presence of a squeezed reservoir. We show that the formal solutions of both systems can be obtained in terms of the density operator by applying squeeze transformations and using the superoperators formalism.

scholarly journals Hyperpolarization and the physical boundary of Liouville space

2021 ◽  
Vol 2 (1) ◽  
pp. 395-407
Author(s):  
Malcolm H. Levitt ◽  
Christian Bengs
Keyword(s):  
Master Equation ◽  
Density Operator ◽  
Spin Dynamics ◽  
Physical Region ◽  
State Density ◽  
Von Neumann Entropy ◽  
Von Neumann ◽  
Liouville Space ◽  
Density Operators ◽  
Physical Boundary

Abstract. The quantum state of a spin ensemble is described by a density operator, which corresponds to a point in the Liouville space of orthogonal spin operators. Valid density operators are confined to a particular region of Liouville space, which we call the physical region and which is bounded by multidimensional figures called simplexes. Each vertex of a simplex corresponds to a pure-state density operator. We provide examples for spins I=1/2, I=1, I=3/2 and for coupled pairs of spins-1/2. We use the von Neumann entropy as a criterion for hyperpolarization. It is shown that the inhomogeneous master equation for spin dynamics leads to non-physical results in some cases, a problem that may be avoided by using the Lindbladian master equation.

scholarly journals AN APPROXIMATE SOLUTION OF THE JAYNES–CUMMINGS MODEL WITH DISSIPATION

2011 ◽  
Vol 08 (08) ◽  
pp. 1799-1814 ◽  
Author(s):  
KAZUYUKI FUJII ◽  
TATSUO SUZUKI
Keyword(s):  
Approximate Solution ◽  
Master Equation ◽  
Density Operator ◽  
General Setting

In this paper we treat the Jaynes–Cummings model with dissipation and give an approximate solution to the master equation for the density operator under the general setting by making use of the Zassenhaus expansion.

GENERALIZED MASTER EQUATION FOR NON-EXTENSIVE REACTION-DIFFUSION SYSTEMS

2007 ◽  
Vol 21 (02n03) ◽  
pp. 103-108 ◽  
Author(s):  
JUNLIN WU ◽  
HUAIJUN CHEN
Keyword(s):  
Distribution Function ◽  
Master Equation ◽  
Probability Distribution Function ◽  
Density Operator ◽  
Reaction Diffusion ◽  
Phenomenological Theory ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
New Equation ◽  
Generalized Master Equation

Based on the theory of non-equilibrium statistics and density operator equation, the generalized master equation satisfied by characteristic function for the non-extensive reaction-diffusion systems affected by pressure is derived by calculating the time variation of probability distribution function, where the pressure of the non-extensive systems is given in the framework of Tsallis statistics. This new equation not only depends on the non-extensive parameter but also has more nonlinear terms as compared with the master equation in the phenomenological theory and thus has more generality.

scholarly journals AN APPROXIMATE SOLUTION OF THE JAYNES–CUMMINGS MODEL WITH DISSIPATION II: ANOTHER APPROACH

2012 ◽  
Vol 09 (04) ◽  
pp. 1250036 ◽  
Author(s):  
KAZUYUKI FUJII ◽  
TATSUO SUZUKI
Keyword(s):  
Approximate Solution ◽  
Master Equation ◽  
Infinite Series ◽  
Density Operator ◽  
General Setting ◽  
Preceding Paper ◽  
Compact Form ◽  
Initial Condition

In the preceding paper (arXiv: 1103.0329 [quant-ph]) we treated the Jaynes–Cummings model with dissipation and gave an approximate solution to the master equation for the density operator under the general setting by making use of the Zassenhaus expansion. However, to obtain a compact form of the approximate solution (which is in general complicated infinite series) is very hard when an initial condition is given. To overcome this difficulty we develop another approach and obtain a compact approximate solution when some initial condition is given.

Sign in / Sign up

Export Citation Format

Share Document