On the squeezing of coherent light coupled to a driven damped harmonic oscillator with time dependent mass and frequency

2004 ◽  
Vol 321 (5-6) ◽  
pp. 308-318 ◽  
Author(s):  
Swapan Mandal
Keyword(s):  
Harmonic Oscillator ◽  
Time Dependent ◽  
Coherent Light ◽  
Damped Harmonic Oscillator ◽  
Dependent Mass

scholarly journals Integrals of the motion and green functions for time-dependent mass harmonic oscillators

2018 ◽  
Vol 64 (1) ◽  
pp. 30
Author(s):  
Surarit Pepore
Keyword(s):  
Harmonic Oscillator ◽  
Harmonic Oscillators ◽  
Time Dependent ◽  
Green Functions ◽  
Feynman Path Integral ◽  
Feynman Path ◽  
Damped Harmonic Oscillator ◽  
System Trajectory ◽  
Dependent Mass ◽  
Motion Method

The application of the integrals of the motion of a quantum system in deriving Green function or propagator is established. The Greenfunction is shown to be the eigenfunction of the integrals of the motion which described initial points of the system trajectory in the phasespace. The explicit expressions for the Green functions of the damped harmonic oscillator, the harmonic oscillator with strongly pulsatingmass, and the harmonic oscillator with mass growing with time are obtained in co-ordinate representations. The connection between theintegrals of the motion method and other method such as Feynman path integral and Schwinger method are also discussed.

The exact evolution of the time-dependent driven damped harmonic oscillator with time-dependent mass and frequency

2002 ◽  
Vol 80 (12) ◽  
pp. 1559-1569 ◽  
Author(s):  
M Liang ◽  
B Yuan ◽  
K Zhong
Keyword(s):  
Wave Function ◽  
Harmonic Oscillator ◽  
Classical Trajectory ◽  
Wave Functions ◽  
Time Dependent ◽  
Quantization Scheme ◽  
Dynamical Phase ◽  
Damped Harmonic Oscillator ◽  
Total Phase ◽  
Dependent Mass

Under a new quantization scheme, the exact wave functions of the time-dependent driven damped harmonic oscillator with time-dependent mass and frequency are obtained. The wave functions are shape-unchanging wave packet with the center moving along the classical trajectory. The total phase of the wave function is explicitly expressed as the sum of the dynamical phase and the geometrical phase. PACS Nos.: 03.65-w, 05.40-a

On the Quantization Problem of a Driven Harmonic Oscillator with Time Dependent Mass and Frequency

2003 ◽  
Vol 17 (18) ◽  
pp. 983-990 ◽  
Author(s):  
Swapan Mandal
Keyword(s):  
Harmonic Oscillator ◽  
Time Dependent ◽  
Present Solution ◽  
Quadratic Hamiltonian ◽  
Dependent Mass ◽  
Quantization Problem

The quantization of a driven harmonic oscillator with time dependent mass and frequency (DHTDMF) is considered. We observe that the driven term has no influence on the quantization of the oscillator. It is found that the DHTDMF corresponds the general quadratic Hamiltonian. The present solution is critically compared with existing solutions of DHTDMF.

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.

scholarly journals Constructing the time independent Hamiltonian from a time dependent one

Open Physics ◽  
2007 ◽  
Vol 5 (3) ◽  
Author(s):  
Michał Dobrski
Keyword(s):  
Dynamical System ◽  
Harmonic Oscillator ◽  
Time Dependent ◽  
Damped Harmonic Oscillator ◽  
Hamiltonian Dynamical System ◽  
Equivalent Time ◽  
New Time

AbstractIn this paper we introduce a method for finding a time independent Hamiltonian of a given Hamiltonian dynamical system by canonoid transformation of canonical momenta. We find a condition that the system should satisfy to have an equivalent time independent formulation. We study the example of a damped harmonic oscillator and give the new time independent Hamiltonian for it, which has the property of tending to the standard Hamiltonian of the harmonic oscillator as damping goes to zero.

TIME-DEPENDENT BOGOLIUBOV TRANSFORMATIONS AND THE DAMPED HARMONIC OSCILLATOR

1993 ◽  
Vol 08 (21) ◽  
pp. 1999-2009
Author(s):  
P. SHANTA ◽  
S. CHATURVEDI ◽  
V. SRINIVASAN ◽  
F. MANCINI
Keyword(s):  
Harmonic Oscillator ◽  
Master Equation ◽  
Time Dependent ◽  
Damped Harmonic Oscillator ◽  
Bogoliubov Transformations ◽  
Non Equilibrium

We derive the master equation for a damped harmonic oscillator, for any α, using time-dependent Bogoliubov transformations of non-equilibrium thermofield dynamics. This investigation naturally leads us to a physically and mathematically meaningful parametrization of the Bogoliubov matrix.

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