scholarly journals Exact wave function of dual-coupled two-dimensional harmonic oscillators with time-dependent and anisotropic mass and frequency

2010 ◽  
Vol 59 (2) ◽  
pp. 759
Author(s):  
Ling Rui-Liang ◽  
Feng Jin-Fu ◽  
Hu Yun
Keyword(s):  
Wave Function ◽  
Harmonic Oscillators ◽  
Time Dependent ◽  
Two Dimensional ◽  
Exact Wave Function

Coupled harmonic oscillators and their application in the dynamics of entanglement and the nonadiabatic Berry phases

2021 ◽  
Author(s):  
A. Abidi ◽  
A. Trabelsi ◽  
S. Krichene
Keyword(s):  
Wave Function ◽  
Coupling Parameter ◽  
Angular Frequency ◽  
Harmonic Oscillators ◽  
Time Dependent ◽  
Logarithmic Scale ◽  
Initial State ◽  
Coupled Harmonic Oscillators ◽  
Berry Phases ◽  
Time Dependance

In the dynamic description of physical systems, the two coupled harmonic oscillators time-dependent mass, angular frequency and coupling parameter are recognized as a good working example. We present in this work an analytical treatment with a numerical evaluation of the entanglement and the nonadiabatic Berry phases in the vacuum state. On the basis of an exact resolution of the wave function solution of the time-dependent Schr¨odinger’s equation (T DSE) using the Heisenberg picture approach, we derive the wave function of the two coupled harmonic oscillators. At the logarithmic scale, we derive the entanglement entropies and the temperature. We discuss the existence of the cyclical initial state (CIS) based on an instant Hamiltonian and we obtain the corresponding nonadiabatic Berry phases through a period T. Moreover, we extend the result to case of N coupled harmonic oscillators. We use the numerical calculation to follow the dynamic evolution of the entanglement in comparison to the time dependance of the nonadiabatic Berry phases and the time dependance of the temperature. For two coupled harmonic oscillators with time-independent mass and angular frequency, the nonadiabatic Berry phases present a very slight oscillations with the equivalent period as the period of the entanglement. A second model is composed of two coupled harmonic oscillators with angular frequency which change initially as well as lately. Here in, the entanglement and the temperature exhibit the same oscillatory behavior with exponential increase in temperature.

scholarly journals LIE SYSTEMS AND INTEGRABILITY CONDITIONS FOR t-DEPENDENT FREQUENCY HARMONIC OSCILLATORS

2010 ◽  
Vol 07 (02) ◽  
pp. 289-310 ◽  
Author(s):  
JOSÉ F. CARIÑENA ◽  
JAVIER DE LUCAS ◽  
MANUEL F. RAÑADA
Keyword(s):  
General Solution ◽  
Lie Group ◽  
Harmonic Oscillators ◽  
Time Dependent ◽  
Two Dimensional ◽  
One Dimensional ◽  
Dependent Frequency ◽  
Integrability Conditions ◽  
Lie Systems ◽  
Frequency Harmonic

Time-dependent frequency harmonic oscillators (TDFHOs) are studied through the theory of Lie systems. We show that they are related to a certain kind of equation in the Lie group SL(2, ℝ). Some integrability conditions appear as conditions to be able to transform such equations into simpler ones in a very specific way. As a particular application of our results we find t-dependent constants of the motion for certain one-dimensional TDFHOs and the general solution for a two-dimensional TDFHO. Our approach provides a unifying framework which allows us to apply our developments to all Lie systems associated with equations in SL(2, ℝ) and to generalize our methods to study any Lie system.

BEHAVIOR OF DYNAMICAL SYSTEMS SUBJECTED TO CONTINUOUS AND DISCONTINUOUS FORCING: APPLICATION TO LAMINAR CHAOTIC MIXING

1996 ◽  
Vol 06 (12b) ◽  
pp. 2627-2634 ◽  
Author(s):  
A.T. PÉREZ ◽  
R. CHACÓN ◽  
A. CASTELLANOS
Keyword(s):  
Wave Function ◽  
Dynamical Systems ◽  
Time Dependent ◽  
Chaotic Mixing ◽  
Mixing Efficiency ◽  
Unperturbed System ◽  
Dimensional System ◽  
Two Dimensional ◽  
Two Dimensional System ◽  
Time Periodic

This paper studies the effect of continuous and discontinuous time dependent forcings onto dynamical systems. We compare these different forcings in the context of laminar chaotic mixing. It is shown that the response of a Hamiltonian two-dimensional system to a time periodic sinusoidal forcing differs qualitatively and quantitatively from the response to a square wave function of the same frequency. Consequently, the mixing efficiency of both types of forcings are different. Also a periodic function of the same shape as that of the velocity of the unperturbed system is tested as a forcing, its mixing efficiency being intermediate.

Exact wave function of a harmonic plus an inverse harmonic potential with time-dependent mass and frequency

1998 ◽  
Vol 58 (2) ◽  
pp. 1574-1577 ◽  
Author(s):  
Chung-In Um ◽  
Shang-Moon Shin ◽  
Kyu-Hwang Yeon ◽  
Thomas F. George
Keyword(s):  
Wave Function ◽  
Time Dependent ◽  
Harmonic Potential ◽  
Exact Wave Function ◽  
Dependent Mass

scholarly journals Integrable unsteady motion with an application to ocean eddies

1998 ◽  
Vol 5 (3) ◽  
pp. 145-151
Author(s):  
A. D. Kirwan, Jr. ◽  
B. L. Lipphardt, Jr.
Keyword(s):  
Potential Vorticity ◽  
Particle Motion ◽  
Gulf Stream ◽  
Incompressible Flows ◽  
Unsteady Motion ◽  
Ring System ◽  
Time Dependent ◽  
Two Dimensional ◽  
Ocean Eddies ◽  
Multilayered Systems

Abstract. Application of the Brown-Samelson theorem, which shows that particle motion is integrable in a class of vorticity-conserving, two-dimensional incompressible flows, is extended here to a class of explicit time dependent dynamically balanced flows in multilayered systems. Particle motion for nonsteady two-dimensional flows with discontinuities in the vorticity or potential vorticity fields (modon solutions) is shown to be integrable. An example of a two-layer modon solution constrained by observations of a Gulf Stream ring system is discussed.

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