Noether's Theorem Invariants for a Time-Dependent Damped Harmonic Oscillator with a Force Quadratic in Velocity

1989 ◽  
Vol 10 (7) ◽  
pp. 615-619 ◽  
Author(s):  
Zhi-Yu Gu ◽  
Shang-Wu Qian
Keyword(s):  
Harmonic Oscillator ◽  
Time Dependent ◽  
Noether’S Theorem ◽  
Noether's Theorem ◽  
Damped Harmonic Oscillator

On Noether's theorem for the invariant of the time-dependent harmonic oscillator

2009 ◽  
Vol 30 (6) ◽  
pp. 1337-1343 ◽  
Author(s):  
Sumiyoshi Abe ◽  
Yuichi Itto ◽  
Mamoru Matsunaga
Keyword(s):  
Harmonic Oscillator ◽  
Time Dependent ◽  
Noether’S Theorem ◽  
Noether's Theorem

scholarly journals LINEAR TIME-DEPENDENT INVARIANTS FOR SCALAR FIELDS AND NOETHER’S THEOREM

1994 ◽  
Vol 09 (19) ◽  
pp. 1785-1790 ◽  
Author(s):  
O. CASTAÑOS ◽  
R. LÓPEZ-PEÑA ◽  
V.I. MAN’KO
Keyword(s):  
Scalar Field ◽  
Infinite Number ◽  
Linear Time ◽  
Scalar Fields ◽  
Time Dependent ◽  
Noether’S Theorem ◽  
Noether's Theorem

The infinite number of time-dependent linear in field and conjugated momenta invariants is derived for the scalar field using the Noether’s theorem procedure.

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.

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.

scholarly journals Noether's theorem and time-dependent quantum invariants

1994 ◽  
Vol 27 (5) ◽  
pp. 1751-1770 ◽  
Author(s):  
O Castanos ◽  
R Lopez-Pena ◽  
V I Man'ko
Keyword(s):  
Time Dependent ◽  
Noether’S Theorem ◽  
Quantum Invariants ◽  
Noether's Theorem
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