Identification of semiclassical chaos in two-dimensional PT-symmetric systems

2003 ◽  
Vol 81 (6) ◽  
pp. 835-846 ◽  
Author(s):  
Asiri Nanayakkara ◽  
Chula Abayaratne
Keyword(s):  
Phase Space ◽  
Complex Systems ◽  
Quantum Level ◽  
Two Dimensional ◽  
Level Spacing ◽  
Chaotic Motions ◽  
Complex Phase ◽  
Wigner Distributions ◽  
Symmetric Complex ◽  
Symmetric Systems

Identification of regular and chaotic motions of two-dimensional PT-symmetric complex systems was investigated. New definitions have been introduced to study properties of trajectories in complex phase space. Projections of these trajectories on complex x- and y-planes, Lyapunov exponents, and surfaces of section have been used for identifying regular and irregular (chaotic) motions in complex phase space. Quantum level spacing distributions of these systems have also been calculated for finding out the connection between regular and irregular states with standard distributions such as Poisson and Wigner distributions. It has been found that the PT-symmetric complex systems behave in the same way as the real systems. PACS No.: 05.45.Ac

scholarly journals Negative heat capacity for a Klein–Gordon oscillator in non-commutative complex phase space

2017 ◽  
Vol 14 (10) ◽  
pp. 1750141 ◽  
Author(s):  
Slimane Zaim ◽  
Hakim Guelmamene ◽  
Yazid Delenda
Keyword(s):  
Magnetic Field ◽  
Heat Capacity ◽  
Thermal Properties ◽  
Phase Space ◽  
Energy Levels ◽  
Two Dimensional ◽  
Complex Phase ◽  
First Order ◽  
Klein Gordon

We obtain exact solutions to the two-dimensional (2D) Klein–Gordon oscillator in a non-commutative (NC) complex phase space to first order in the non-commutativity parameter. We derive the exact NC energy levels and show that the energy levels split to [Formula: see text] levels. We find that the non-commutativity plays the role of a magnetic field interacting automatically with the spin of a particle induced by the non-commutativity of complex phase space. The effect of the non-commutativity parameter on the thermal properties is discussed. It is found that the dependence of the heat capacity [Formula: see text] on the NC parameter gives rise to a negative quantity. Phenomenologically, this effectively confirms the presence of the effects of self-gravitation induced by the non-commutativity of complex phase space.

Complex dynamical invariants for two-dimensional nonhermitian Hamiltonian systems

2012 ◽  
Vol 90 (2) ◽  
pp. 151-157 ◽  
Author(s):  
J.S. Virdi ◽  
F. Chand ◽  
C.N. Kumar ◽  
S.C. Mishra
Keyword(s):  
Phase Space ◽  
Hamiltonian Systems ◽  
General Result ◽  
Two Dimensional ◽  
Complex Phase ◽  
Quartic Potential ◽  
Dynamical Invariants ◽  
Extended Complex ◽  
Space Approach

Keeping in view the importance of dynamical invariants, attempts have been made to investigate complex invariants for two-dimensional Hamiltonian systems within the framework of the extended complex phase space approach. The rationalization method has been used to derive an invariant of a general nonhermitian quartic potential. Invariants for three specific potentials are also obtained from the general result.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

scholarly journals Optical Thouless conductance and level-spacing statistics in two-dimensional Anderson localizing systems

2019 ◽  
Vol 100 (6) ◽  
Author(s):  
Sandip Mondal ◽  
Randhir Kumar ◽  
Martin Kamp ◽  
Sushil Mujumdar
Keyword(s):  
Two Dimensional ◽  
Level Spacing

scholarly journals Tunneling mechanism due to chaos in a complex phase space

2001 ◽  
Vol 64 (2) ◽  
Author(s):  
T. Onishi ◽  
A. Shudo ◽  
K. S. Ikeda ◽  
K. Takahashi
Keyword(s):  
Phase Space ◽  
Complex Phase ◽  
Tunneling Mechanism

scholarly journals Dirac’s Method for the Two-Dimensional Damped Harmonic Oscillator in the Extended Phase Space

Mathematics ◽  
2018 ◽  
Vol 6 (10) ◽  
pp. 180 ◽  
Author(s):  
Laure Gouba
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator ◽  
Canonical Quantization ◽  
Extended Phase Space ◽  
Two Dimensional ◽  
Class Constraint ◽  
Extended Phase ◽  
Damped Harmonic Oscillator ◽  
Points Of View ◽  
Space Description

The system of a two-dimensional damped harmonic oscillator is revisited in the extended phase space. It is an old problem that has already been addressed by many authors that we present here with some fresh points of view and carry on a whole discussion. We show that the system is singular. The classical Hamiltonian is proportional to the first-class constraint. We pursue with the Dirac’s canonical quantization procedure by fixing the gauge and provide a reduced phase space description of the system. As a result, the quantum system is simply modeled by the original quantum Hamiltonian.

scholarly journals Bifurcations of a Controlled Two-Bar Linkage Motion with Considering Viscous Frictions

2011 ◽  
Vol 18 (1-2) ◽  
pp. 365-375 ◽  
Author(s):  
Qingkai Han ◽  
Xueyan Zhao ◽  
Xingxiu Li ◽  
Bangchun Wen
Keyword(s):  
Phase Space ◽  
Lyapunov Exponents ◽  
Time Domain ◽  
Shooting Method ◽  
Viscous Friction ◽  
Dynamical Model ◽  
Chaotic Motions ◽  
Amplitude Spectra ◽  
Set Up ◽  
Joint Motions

In this paper, we investigate the joint viscous friction effects on the motions of a two-bar linkage under controlling of OPCL. The dynamical model of the two-bar linkage with an OPCL controller is firstly set up with considering the two joints' viscous frictions. Thereafter, the motion bifurcations of the two-bar linkage along the values of joint viscous frictions are obtained using shooting method. Then, single-periodic, multiple-periodic, quasi-periodic and chaotic motions of link rotating angles are simulated with given different viscous friction values, and they are illustrated in time domain waveforms, phase space portraits, amplitude spectra and Poincare mapping graphs, respectively. Additionally, for the chaotic case, Lyapunov exponents and hypothesis possibilities of the two joint motions are also estimated.

scholarly journals Effects of Vegetation and Topography on the Boundary Layer Structure above the Amazon Forest

2020 ◽  
Vol 77 (8) ◽  
pp. 2941-2957
Author(s):  
Marcelo Chamecki ◽  
Livia S. Freire ◽  
Nelson L. Dias ◽  
Bicheng Chen ◽  
Cléo Quaresma Dias-Junior ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Phase Space ◽  
Vertical Structure ◽  
Layer Structure ◽  
Roughness Sublayer ◽  
Large Contribution ◽  
Amazon Forest ◽  
Two Dimensional ◽  
Dimensional Phase Space ◽  
Field Campaigns

Abstract Observational data from two field campaigns in the Amazon forest were used to study the vertical structure of turbulence above the forest. The analysis was performed using the reduced turbulent kinetic energy (TKE) budget and its associated two-dimensional phase space. Results revealed the existence of two regions within the roughness sublayer in which the TKE budget cannot be explained by the canonical flat-terrain TKE budgets in the canopy roughness sublayer or in the lower portion of the convective ABL. Data analysis also suggested that deviations from horizontal homogeneity have a large contribution to the TKE budget. Results from LES of a model canopy over idealized topography presented similar features, leading to the conclusion that flow distortions caused by topography are responsible for the observed features in the TKE budget. These results support the conclusion that the boundary layer above the Amazon forest is strongly impacted by the gentle topography underneath.

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