Information-theoretic and Wigner-function approaches to the nonclassical state dynamics for the variable-frequency harmonic oscillator

1993 ◽  
Vol 70 (4) ◽  
pp. 434-436 ◽  
Author(s):  
J. Aliaga ◽  
G. Crespo ◽  
A. N. Proto
Keyword(s):  
Harmonic Oscillator ◽  
Wigner Function ◽  
Variable Frequency ◽  
Nonclassical State ◽  
Information Theoretic ◽  
Frequency Harmonic

Variable Frequency Harmonic Oscillator in an Electromagnetic Field

2004 ◽  
Vol 41 (1) ◽  
pp. 45-47 ◽  
Author(s):  
Huang Bo-Wen ◽  
Wang Jing-Shan ◽  
Gu Zhi-Yu ◽  
Qian Shang-Wu
Keyword(s):  
Electromagnetic Field ◽  
Harmonic Oscillator ◽  
Variable Frequency ◽  
Frequency Harmonic

scholarly journals Extended Wigner function for the harmonic oscillator in the phase space

2020 ◽  
Vol 19 ◽  
pp. 103546
Author(s):  
E.E. Perepelkin ◽  
B.I. Sadovnikov ◽  
N.G. Inozemtseva ◽  
E.V. Burlakov
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator ◽  
Wigner Function

On the generalization of moyal equation for an arbitrary linear quantization

2021 ◽  
Vol 24 (01) ◽  
pp. 2150003
Author(s):  
Leonid A. Borisov ◽  
Yuriy N. Orlov
Keyword(s):  
Characteristic Function ◽  
Harmonic Oscillator ◽  
Linear Combination ◽  
Stationary Solution ◽  
Wigner Function ◽  
Inverse Operator ◽  
Stationary Solutions ◽  
Weyl Quantization ◽  
Quantization Rule ◽  
Arbitrary Linear Combination

For an arbitrary linear combination of quantizations, the kernel of the inverse operator is constructed. An equation for the evolution of the Wigner function for an arbitrary linear quantization is derived and it is shown that only for Weyl quantization this equation does not contain a source of quasi-probability. Stationary solutions for the Wigner function of a harmonic oscillator are constructed, depending on the characteristic function of the quantization rule. In the general case of Hermitian linear quantization these solutions are real but not positive. We found the representation of Weyl quantization in the form of the limit of a sequence of linear Hermitian quantizations, such that for each element of this sequence the stationary solution of the Moyal equation is positive.

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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