Numerical Investigation of Phase Space Entropy for a Quantum System in Kerr Medium Under Cavity Damping Effects

2017 ◽  
Vol 14 (8) ◽  
pp. 3953-3957
Author(s):  
Bothayna S. H Kashkari ◽  
S Abdel-Khalek
Keyword(s):  
Phase Space ◽  
Quantum System ◽  
Numerical Investigation ◽  
Kerr Medium ◽  
Damping Effects ◽  
Cavity Damping

TOPOLOGICAL ASPECTS OF THE SPECIFIC HEAT

2009 ◽  
Vol 23 (20n21) ◽  
pp. 4170-4185 ◽  
Author(s):  
C. M. SARRIS ◽  
A. N. PROTO
Keyword(s):  
Phase Space ◽  
Specific Heat ◽  
Quantum System ◽  
Uncertainty Principle ◽  
Positive Definite ◽  
Metric Tensor ◽  
Quantum Nature ◽  
Generalized Phase Space

We describe how the specific heat of a quantum system is related to a positive definite metric defined on the generalized phase space in which the dynamics and thermodynamics of the system take place. This relationship is given through the components of a second-rank covariant metric tensor, enhancing a topological nature of the specific heat. We also present two examples where it can be seen how the uncertainty principle imposes strong constraints on the values achieved by the specific heat showing its inherent quantum nature.

The Duflo non-commutative Fourier transform for the Lorentz group

2020 ◽  
Vol 17 (supp01) ◽  
pp. 2040011
Author(s):  
Giacomo Rosati
Keyword(s):  
Fourier Transform ◽  
Phase Space ◽  
Quantum System ◽  
Lie Group ◽  
Lorentz Group ◽  
Commutative Algebra ◽  
Cotangent Bundle ◽  
Irreducible Representations ◽  
Algebra Representation

For a quantum system whose phase space is the cotangent bundle of a Lie group, like for systems endowed with particular cases of curved geometry, one usually resorts to a description in terms of the irreducible representations of the Lie group, where the role of (non-commutative) phase space variables remains obscure. However, a non-commutative Fourier transform can be defined, intertwining the group and (non-commutative) algebra representation, depending on the specific quantization map. We discuss the construction of the non-commutative Fourier transform and the non-commutative algebra representation, via the Duflo quantization map, for a system whose phase space is the cotangent bundle of the Lorentz group.

Stochasticity in the Josephson map

1996 ◽  
Vol 56 (3) ◽  
pp. 493-506 ◽  
Author(s):  
Y. Nomura ◽  
Y. H. Ichikawa ◽  
A. T. Filipov
Keyword(s):  
Nonlinear Dynamics ◽  
Diffusion Coefficient ◽  
Phase Space ◽  
Characteristic Function ◽  
Numerical Investigation ◽  
Stochastic Diffusion ◽  
Standard Map ◽  
External Bias ◽  
Stochastic Parameter ◽  
Phase Space Portrait

The Josephson map describes the nonlinear dynamics of systems characterized by the standard map with a uniform external bias superposed. The intricate structures of the phase-space portrait of the Josephson map are examined here on the basis of the associated tangent map. A numerical investigation of stochastic diffusion in the Josephson map is compared with the renormalized diffusion coefficient calculated using the characteristic function. The global stochasticity of the Josephson map occurs at far smaller values of the stochastic parameter than is the case of the standard map.

An Efficient Numerical Algorithm for Constructing the Wigner Function of a Quantum System with a Polynomial Potential in Phase Space

2021 ◽  
Vol 52 (3) ◽  
pp. 438-476
Author(s):  
E. E. Perepelkin ◽  
B. I. Sadovnikov ◽  
N. G. Inozemtseva ◽  
E. V. Burlakov ◽  
R. V. Polyakova
Keyword(s):  
Phase Space ◽  
Quantum System ◽  
Wigner Function ◽  
Numerical Algorithm ◽  
Polynomial Potential

Two-level atom and quantum system entanglement and squeezing with and without classical field and damping effects

2020 ◽  
Vol 38 (3) ◽  
pp. 2817-2822
Author(s):  
E. M. Khalil ◽  
S. Abdel-Khalek ◽  
Saud Al-Awfi ◽  
M. Rasulova
Keyword(s):  
Quantum System ◽  
Classical Field ◽  
Level Atom ◽  
Damping Effects

BREAKDOWN OF LIBRATIONAL INVARIANT SURFACES

1999 ◽  
Vol 09 (05) ◽  
pp. 975-982
Author(s):  
MIQUEL ANGEL ANDREU ◽  
ALESSANDRA CELLETTI ◽  
CORRADO FALCOLINI
Keyword(s):  
Phase Space ◽  
Numerical Investigation ◽  
Invariant Tori ◽  
Three Dimensional ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
The Moon ◽  
Dimensional Phase Space ◽  
Invariant Surfaces ◽  
The Stability

A numerical investigation of the stability of invariant librational tori is presented. The method has been developed for a model describing the spin-orbit coupling in Celestial Mechanics. Periodic orbits approaching the librational torus are computed by means of Newton's method. According to Greene's criterion, their stability is strictly related to the survival of invariant tori. We consider librational tori around the main spin-orbit resonances (1:1, 3:2). Their existence provides the stability of the resonances, due to the confinement properties in the three-dimensional phase space associated to our model. The results are consistent with the actual observations of the eccentricity and of the oblateness parameter. A different behavior of the Moon and Mercury around the main resonances is evidenced, providing interesting suggestions about the different probabilities of capture in a resonance.

Some features of the geometric phase and entanglement of three-level atom under cavity damping effects

2019 ◽  
Vol 94 (11) ◽  
pp. 1691-1698
Author(s):  
S. Abdel-Khalek ◽  
Y. S. El-Saman ◽  
I. Mechai ◽  
M. Abdel-Aty
Keyword(s):  
Geometric Phase ◽  
Level Atom ◽  
Damping Effects ◽  
Cavity Damping

scholarly journals Incoherent Shock and Collapse Singularities in Non-Instantaneous Nonlinear Media

2018 ◽  
Vol 8 (12) ◽  
pp. 2559 ◽  
Author(s):  
Gang Xu ◽  
Adrien Fusaro ◽  
Josselin Garnier ◽  
Antonio Picozzi
Keyword(s):  
Phase Space ◽  
Theoretical Analysis ◽  
Collective Behavior ◽  
Optical Pulse ◽  
Random Wave ◽  
Kerr Medium ◽  
Linear Regime ◽  
Nonlinear Media ◽  
Strong Amplitude ◽  
Space Dynamics

We study the dynamics of a partially incoherent optical pulse that propagates in a slowly responding nonlinear Kerr medium. We show that irrespective of the sign of the dispersion (either normal or anomalous), the incoherent pulse as a whole exhibits a global collective behavior characterized by a dramatic narrowing and amplification in the strongly non-linear regime. The theoretical analysis based on the Vlasov formalism and the method of the characteristics applied to a reduced hydrodynamic model reveal that such a strong amplitude-incoherent pulse originates in the existence of a concurrent shock-collapse singularity (CSCS): The envelope of the intensity of the random wave exhibits a collapse singularity, while the momentum exhibits a shock singularity. The dynamic behavior of the system after the shock-collapse singularity is characterized through the analysis of the phase-space dynamics.

Sign in / Sign up

Export Citation Format

Share Document