scholarly journals Numerical study of the phase space of modulated exponentially coupled harmonic oscillators

2007 ◽  
Vol 17 (4) ◽  
pp. 041109
Author(s):  
A. F. Isakovic
Keyword(s):  
Phase Space ◽  
Numerical Study ◽  
Harmonic Oscillators ◽  
Coupled Harmonic Oscillators

THE EIGENVALUES OF TWO MODES COUPLED HARMONIC OSCILLATORS IN NONCOMMUTATIVE PHASE-SPACE

2011 ◽  
Vol 26 (09) ◽  
pp. 1561-1567 ◽  
Author(s):  
XIN-FENG DIAO ◽  
CHAO-YUN LONG ◽  
GUANG-JIE GUO ◽  
ZHENG-WEN LONG
Keyword(s):  
Phase Space ◽  
Coordinate Transformation ◽  
Algebraic Method ◽  
Harmonic Oscillators ◽  
Noncommutative Phase Space ◽  
Coupled Harmonic Oscillators

The Hamiltonian of two modes coupled harmonic oscillators in noncommutative phase-space can be expressed in the standard quadric form by introducing a coordinate transformation. As a result, the coupling items are eliminated and the Hamiltonian can be simplified to the two modes independent harmonic oscillators. Then, the corresponding energy spectrums are obtained with an algebraic method.

DEFORMATION QUANTIZATION FOR COUPLED HARMONIC OSCILLATORS ON A GENERAL NONCOMMUTATIVE SPACE

2008 ◽  
Vol 23 (06) ◽  
pp. 445-456 ◽  
Author(s):  
BINGSHENG LIN ◽  
SICONG JING ◽  
TAIHUA HENG
Keyword(s):  
Phase Space ◽  
Deformation Quantization ◽  
Harmonic Oscillators ◽  
Energy Spectra ◽  
Noncommutative Space ◽  
Wigner Functions ◽  
Noncommutative Phase Space ◽  
Classical Systems ◽  
Coupled Harmonic Oscillators ◽  
Special Cases

Deformation quantization is a powerful tool to quantize some classical systems especially in noncommutative space. In this work we first show that for a class of special Hamiltonian one can easily find relevant time evolution functions and Wigner functions, which are intrinsic important quantities in the deformation quantization theory. Then based on this observation we investigate a two-coupled harmonic oscillators system on the general noncommutative phase space by requiring both spatial and momentum coordinates do not commute each other. We derive all the Wigner functions and the corresponding energy spectra for this system, and consider several interesting special cases, which lead to some significant results.

scholarly journals Berry Phase for Time-Dependent Coupled Harmonic Oscillators in the Noncommutative Phase Space via Path Integral Techniques

2020 ◽  
pp. 58-70
Author(s):  
Leila Khiari ◽  
Tahar Boudjedaa ◽  
Abdenacer Makhlouf ◽  
Mohammed Tayeb Meftah
Keyword(s):  
Phase Space ◽  
Path Integral ◽  
Adiabatic Approximation ◽  
Berry Phase ◽  
Quadratic System ◽  
Harmonic Oscillators ◽  
Time Dependent ◽  
Noncommutative Phase Space ◽  
Integral Formalism ◽  
Coupled Harmonic Oscillators

The purpose of this paper is the description of Berry’s phase, in the Euclidean Path Integral formalism, for 2D quadratic system: two time dependent coupled harmonic oscillators. This treatment is achieved by using the adiabatic approximation in the commutative and noncommutative phase space

Adaptive cluster synchronisation of coupled harmonic oscillators with multiple leaders

2013 ◽  
Vol 7 (5) ◽  
pp. 765-772 ◽  
Author(s):  
Housheng Su ◽  
Hongwei Wang ◽  
Michael Z. Q. Chen ◽  
Najl V. Valeyev ◽  
Xiaofan Wang
Keyword(s):  
Harmonic Oscillators ◽  
Coupled Harmonic Oscillators ◽  
Multiple Leaders

scholarly journals Group synchronization of diffusively coupled harmonic oscillators

Kybernetika ◽  
2016 ◽  
pp. 629-647 ◽  
Author(s):  
Liyun Zhao ◽  
Jun Liu ◽  
Lan Xiang ◽  
Jin Zhou
Keyword(s):  
Harmonic Oscillators ◽  
Coupled Harmonic Oscillators ◽  
Group Synchronization
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