Integrability of a Coupled Harmonic Oscillator in Extended Complex Phase Space

2015 ◽  
Vol 4 (1) ◽  
pp. 35-48
Author(s):  
Ram Mehar Singh
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator ◽  
Complex Phase ◽  
Extended Complex ◽  
Coupled Harmonic Oscillator

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.

Classical invariants for non-Hermitian anharmonic potentials

2020 ◽  
Vol 98 (11) ◽  
pp. 1004-1008
Author(s):  
Ram Mehar Singh ◽  
S.B. Bhardwaj ◽  
Kushal Sharma ◽  
Anand Malik ◽  
Fakir Chand
Keyword(s):  
Phase Space ◽  
Dynamical Systems ◽  
Hamiltonian Systems ◽  
One Dimension ◽  
Complex Dynamical Systems ◽  
Complex Phase ◽  
Extended Complex ◽  
Space Approach

Keeping in view the importance of complex dynamical systems, we investigate the classical invariants for some non-Hermitian anharmonic potentials in one dimension. For this purpose, the rationalization method is employed under the elegance of the extended complex phase space approach. The invariants obtained are expected to play an important role in studying complex Hamiltonian systems at the classical as well as quantum levels.

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

Scale transformations in phase space and stretched states of a harmonic oscillator

2017 ◽  
Vol 192 (1) ◽  
pp. 1080-1096 ◽  
Author(s):  
V. A. Andreev ◽  
D. M. Davidović ◽  
L. D. Davidović ◽  
Milena D. Davidović ◽  
Miloš D. Davidović
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator ◽  
Scale Transformations

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.

One-Dimensional Harmonic Oscillator in Quantum Phase Space

2011 ◽  
Vol 110-116 ◽  
pp. 3750-3754
Author(s):  
Jun Lu ◽  
Xue Mei Wang ◽  
Ping Wu
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator ◽  
Quantum Phase ◽  
Space Representation ◽  
Wave Mechanics ◽  
One Dimensional ◽  
Matrix Mechanics ◽  
The Matrix ◽  
Quantum Wave ◽  
The One

Within the framework of the quantum phase space representation established by Torres-Vega and Frederick, we solve the rigorous solutions of the stationary Schrödinger equations for the one-dimensional harmonic oscillator by means of the quantum wave-mechanics method. The result shows that the wave mechanics and the matrix mechanics are equivalent in phase space, just as in position or momentum space.

Decoherence of Driven Coupled Harmonic Oscillator

2016 ◽  
Vol 01 (01) ◽  
Author(s):  
Kenfack Sadem Christian ◽  
Nguimeya GP ◽  
Talla PK ◽  
Fotue AJ ◽  
Fobasso MFC ◽  
...  
Keyword(s):  
Harmonic Oscillator ◽  
Coupled Harmonic Oscillator
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