scholarly journals Effect of Self-Oscillation on Escape Dynamics of Classical and Quantum Open Systems

Entropy ◽  
2020 ◽  
Vol 22 (8) ◽  
pp. 839
Author(s):  
Minggen Li ◽  
Jingdong Bao
Keyword(s):  
Open System ◽  
Open Systems ◽  
Free Particle ◽  
Harmonic Oscillators ◽  
Escape Rate ◽  
Velocity Autocorrelation Function ◽  
Stat Phys ◽  
Nonmonotonic Dependence ◽  
Escape Dynamics ◽  
Quantum Open Systems

We study the effect of self-oscillation on the escape dynamics of classical and quantum open systems by employing the system-plus-environment-plus-interaction model. For a damped free particle (system) with memory kernel function expressed by Zwanzig (J. Stat. Phys. 9, 215 (1973)), which is originated from a harmonic oscillator bath (environment) of Debye type with cut-off frequency wd, ergodicity breakdown is found because the velocity autocorrelation function oscillates in cosine function for asymptotic time. The steady escape rate of such a self-oscillated system from a metastable potential exhibits nonmonotonic dependence on wd, which denotes that there is an optimal cut-off frequency makes it maximal. Comparing results in classical and quantum regimes, the steady escape rate of a quantum open system reduces to a classical one with wd decreasing gradually, and quantum fluctuation indeed enhances the steady escape rate. The effect of a finite number of uncoupled harmonic oscillators N on the escape dynamics of a classical open system is also discussed.

THE QUANTUM TRAJECTORY APPROACH TO GEOMETRIC PHASE FOR OPEN SYSTEMS

2005 ◽  
Vol 20 (22) ◽  
pp. 1635-1654 ◽  
Author(s):  
ANGELO CAROLLO
Keyword(s):  
Quantum System ◽  
Open System ◽  
Geometric Phase ◽  
Open Systems ◽  
Quantum Trajectory ◽  
Operational Method ◽  
Markovian Approximation ◽  
Physical Systems ◽  
Quantum Jump ◽  
Trajectory Approach

The quantum jump method for the calculation of geometric phase is reviewed. This is an operational method to associate a geometric phase to the evolution of a quantum system subjected to decoherence in an open system. The method is general and can be applied to many different physical systems, within the Markovian approximation. As examples, two main source of decoherence are considered: dephasing and spontaneous decay. It is shown that the geometric phase is to very large extent insensitive to the former, i.e. it is independent of the number of jumps determined by the dephasing operator.

scholarly journals Entropy and uncertainty of squeezed quantum open systems

1997 ◽  
Vol 55 (10) ◽  
pp. 5917-5935 ◽  
Author(s):  
Don Koks ◽  
Andrew Matacz ◽  
B. L. Hu
Keyword(s):  
Open Systems ◽  
Quantum Open Systems

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.

Quantum open systems

2009 ◽  
pp. 60-90
Author(s):  
Esteban A. Calzetta ◽  
Bei-Lok B. Hu
Keyword(s):  
Open Systems ◽  
Quantum Open Systems

scholarly journals Continuous monitoring of energy in quantum open systems

2019 ◽  
Vol 99 (3) ◽  
Author(s):  
G. P. Martins ◽  
N. K. Bernardes ◽  
M. F. Santos
Keyword(s):  
Continuous Monitoring ◽  
Open Systems ◽  
Quantum Open Systems

scholarly journals Asymptotic escape rates and limiting distributions for multimodal maps

2020 ◽  
pp. 1-50
Author(s):  
MARK F. DEMERS ◽  
MIKE TODD
Keyword(s):  
Variational Principle ◽  
Invariant Measure ◽  
Large Class ◽  
Open Systems ◽  
Periodic Points ◽  
Weak Condition ◽  
Escape Rate ◽  
Scaling Limits ◽  
Absolutely Continuous ◽  
Initial Distributions

We consider multimodal maps with holes and study the evolution of the open systems with respect to equilibrium states for both geometric and Hölder potentials. For small holes, we show that a large class of initial distributions share the same escape rate and converge to a unique absolutely continuous conditionally invariant measure; we also prove a variational principle connecting the escape rate to the pressure on the survivor set, with no conditions on the placement of the hole. Finally, introducing a weak condition on the centre of the hole, we prove scaling limits for the escape rate for holes centred at both periodic and non-periodic points, as the diameter of the hole goes to zero.

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