scholarly journals Correspondences between quantum and classical orbits Berry phases and Hannay angles for harmonic oscillator system

2015 ◽  
Vol 64 (24) ◽  
pp. 240302
Author(s):  
Xin Jun-Li ◽  
Shen Jun-Xia
Keyword(s):  
Harmonic Oscillator ◽  
Oscillator System ◽  
Berry Phases ◽  
Classical Orbits

MULTI-MODE LINEAR COMPOSITE MOMENTUM REPRESENTATION AND ITS APPLICATION

2009 ◽  
Vol 23 (07) ◽  
pp. 975-988
Author(s):  
SHI-MIN XU ◽  
XING-LEI XU ◽  
JI-JIAN JIANG ◽  
HONG-QI LI ◽  
JI-SUO WANG
Keyword(s):  
Harmonic Oscillator ◽  
Unitary Transformation ◽  
Particle System ◽  
Momentum Representation ◽  
Dynamic Problems ◽  
Quantum Harmonic Oscillator ◽  
Oscillator System ◽  
Kinetic Coupling ◽  
Linear Composite ◽  
Multi Mode

A unitary transformation matrix, n linear-composite coordinate operators and n linear-composite momentum operators are constructed for an n-particle system, and the complete and orthonormal common eigenvectors of the multi-mode linear composite momentum operators are examined by virtue of the technique of integration within an ordered product of operators. The multi-mode linear composite momentum representation is proposed, and its application to a general two-mode forced quantum harmonic oscillator system with kinetic coupling is presented for solving some dynamic problems.

Coherent states and geometric phases of a generalized damped harmonic oscillator with time-dependent mass and frequency

2014 ◽  
Vol 28 (26) ◽  
pp. 1450177 ◽  
Author(s):  
I. A. Pedrosa ◽  
D. A. P. de Lima
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Classical Equation ◽  
Equation Of Motion ◽  
Time Dependent ◽  
Quantum Invariant ◽  
Dynamical Phase ◽  
Special Cases ◽  
Berry Phases ◽  
Dependent Mass

In this paper, we study the generalized harmonic oscillator with arbitrary time-dependent mass and frequency subjected to a linear velocity-dependent frictional force from classical and quantum points of view. We obtain the solution of the classical equation of motion of this system for some particular cases and derive an equation of motion that describes three different systems. Furthermore, with the help of the quantum invariant method and using quadratic invariants we solve analytically and exactly the time-dependent Schrödinger equation for this system. Afterwards, we construct coherent states for the quantized system and employ them to investigate some of the system's quantum properties such as quantum fluctuations of the coordinate and the momentum as well as the corresponding uncertainty product. In addition, we derive the geometric, dynamical and Berry phases for this nonstationary system. Finally, we evaluate the dynamical and Berry phases for three special cases and surprisingly find identical expressions for the dynamical phase and the same formulae for the Berry's phase.

Exact wave functions and nonadiabatic Berry phases of a time-dependent harmonic oscillator

1995 ◽  
Vol 52 (4) ◽  
pp. 3352-3355 ◽  
Author(s):  
Jeong-Young Ji ◽  
Jae Kwan Kim ◽  
Sang Pyo Kim ◽  
Kwang-Sup Soh
Keyword(s):  
Harmonic Oscillator ◽  
Wave Functions ◽  
Time Dependent ◽  
Berry Phases

scholarly journals Dynamics of Quantum Correlations in a Qubit-Oscillator System Interacting via a Dissipative Bath

2020 ◽  
Vol 27 (01) ◽  
pp. 2050004
Author(s):  
R. Badveli ◽  
V. Jagadish ◽  
S. Akshaya ◽  
R. Srikanth ◽  
F. Petruccione
Keyword(s):  
Harmonic Oscillator ◽  
Numerical Simulations ◽  
Dipole Interaction ◽  
Quantum Correlations ◽  
Entanglement Dynamics ◽  
Lindblad Equation ◽  
Oscillator System ◽  
Microscopic Derivation ◽  
Initial States ◽  
Classical Correlations

The entanglement dynamics in a bipartite system consisting of a qubit and a harmonic oscillator interacting only through their coupling with the same bath is studied. The considered model assumes that the qubit is coupled to the bath via the Jaynes-Cummings interaction, whilst the position of the oscillator is coupled to the position of the bath via a dipole interaction. We give a microscopic derivation of the Gorini–Kossakowski–Sudarshan–Lindblad equation for the considered model. Based on the Kossakowski matrix, we show that non-classical correlations including entanglement can be generated by the considered dynamics. We then analytically identify specific initial states for which entanglement is generated. This result is also supported by our numerical simulations.

Analytical expressions for real and complex Fano parameters in a simple classical harmonic oscillator system

2021 ◽  
Author(s):  
Seiji MIZUNO
Keyword(s):  
Harmonic Oscillator ◽  
Resonance Frequency ◽  
Real Number ◽  
Wave Phenomenon ◽  
Fano Resonance ◽  
Equation Of Motion ◽  
Coupled Oscillator ◽  
Physical Systems ◽  
Oscillator System ◽  
Analytical Expressions

Abstract We analytically study the Fano resonance in a simple coupled oscillator system. We demonstrate directly from the equation of motion that the resonance profile observed in this system is generally described by the Fano formula with a complex Fano parameter. The analytical expressions are derived for the resonance frequency, resonance width, and Fano parameter, and the conditions under which the Fano parameter becomes a real number are examined. These expressions for the simple system are also expected to be helpful for considering various other physical systems because the Fano resonance is a general wave phenomenon.

Quantum gaps and classical orbits in a rotating two-dimensional harmonic oscillator

1994 ◽  
Vol 27 (15) ◽  
pp. L553-L558 ◽  
Author(s):  
R K Bhaduri ◽  
Shuxi Li ◽  
K Tanaka ◽  
J C Waddington
Keyword(s):  
Harmonic Oscillator ◽  
Two Dimensional ◽  
Classical Orbits

LEWIS–RIESENFELD PHASES AND BERRY PHASES FOR THE HARMONIC OSCILLATOR WITH TIME-DEPENDENT FREQUENCY AND BOUNDARY CONDITIONS

2003 ◽  
Vol 17 (10) ◽  
pp. 2045-2052 ◽  
Author(s):  
LING LI ◽  
BO-ZANG LI
Keyword(s):  
Harmonic Oscillator ◽  
Invariant Theory ◽  
Berry Phase ◽  
Time Dependent ◽  
Quantum Invariant ◽  
Fixed Boundary ◽  
Dependent Frequency ◽  
Oscillating Boundary ◽  
Berry Phases ◽  
Frequency Harmonic

We use Lewis and Riesenfeld's quantum invariant theory to calculate the Lewis–Riesenfeld phases for a time-dependent frequency harmonic oscillator that is confined between a fixed boundary and a moving one. We also discuss the Berry phase for the system with a sinusoidally oscillating boundary.

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