scholarly journals Correlated coherent states of the two-dimensional quantum oscillator with a nonstationary mode coupling

1997 ◽  
Vol 111 (2) ◽  
pp. 633-638
Author(s):  
M. E. Veisman ◽  
S. Yu. Kalmykov
Keyword(s):  
Coherent States ◽  
Mode Coupling ◽  
Quantum Oscillator ◽  
Two Dimensional

Coherent States and the Forced Quantum Oscillator

1965 ◽  
Vol 33 (7) ◽  
pp. 537-544 ◽  
Author(s):  
P. Carruthers ◽  
M. M. Nieto
Keyword(s):  
Coherent States ◽  
Quantum Oscillator

scholarly journals Mode coupling and resonance instabilities in quasi-two-dimensional dust clusters in complex plasmas

2014 ◽  
Vol 90 (3) ◽  
Author(s):  
Ke Qiao ◽  
Jie Kong ◽  
Jorge Carmona-Reyes ◽  
Lorin S. Matthews ◽  
Truell W. Hyde
Keyword(s):  
Mode Coupling ◽  
Two Dimensional ◽  
Complex Plasmas

UNIVERSAL PRANDTL NUMBER IN TWO-DIMENSIONAL KRAICHNAN-BATCHELOR TURBULENCE

2008 ◽  
Vol 22 (20) ◽  
pp. 3421-3431
Author(s):  
MALAY K. NANDY
Keyword(s):  
Prandtl Number ◽  
Mode Coupling ◽  
Perturbation Expansion ◽  
Dynamic Scaling ◽  
Two Dimensional ◽  
Turbulent Prandtl Number ◽  
Energy Regime ◽  
Self Consistent ◽  
Prandtl Numbers

We evaluate the universal turbulent Prandtl numbers in the energy and enstrophy régimes of the Kraichnan-Batchelor spectra of two-dimensional turbulence using a self-consistent mode-coupling formulation coming from a renormalized perturbation expansion coupled with dynamic scaling ideas. The turbulent Prandtl number is found to be exactly unity in the (logarithmic) enstrophy régime, where the theory is infrared marginal. In the energy régime, the theory being finite, we extract singularities coming from both ultraviolet and infrared ends by means of Laurent expansions about these poles. This yields the turbulent Prandtl number σ ≈ 0.9 in the energy régime.

Generation of Pair Coherent States in Two-dimensional Trapped Ion

2001 ◽  
Vol 18 (3) ◽  
pp. 367-369 ◽  
Author(s):  
Wang Kai-Ge ◽  
S Maniscalco ◽  
A Napoli ◽  
A Messina
Keyword(s):  
Coherent States ◽  
Two Dimensional ◽  
Trapped Ion

Phase Effect on Mode Coupling in Kelvin–Helmholtz Instability for Two-Dimensional Incompressible Fluid

2009 ◽  
Vol 52 (4) ◽  
pp. 694-696 ◽  
Author(s):  
Wang Li-Feng ◽  
Teng Ai-Ping ◽  
Ye Wen-Hua ◽  
Xue Chuang ◽  
Fan Zheng-Feng ◽  
...  
Keyword(s):  
Incompressible Fluid ◽  
Mode Coupling ◽  
Two Dimensional ◽  
Helmholtz Instability ◽  
Phase Effect

Optimized Driver Placement for Array-Driven Flat-Panel Loudspeakers

2017 ◽  
Vol 42 (1) ◽  
pp. 93-104 ◽  
Author(s):  
David A. Anderson ◽  
Michael C. Heilemann ◽  
Mark F. Bocko
Keyword(s):  
Frequency Band ◽  
Mode Coupling ◽  
Dynamic Force ◽  
Two Dimensional ◽  
Flat Panel ◽  
Piezoelectric Patch ◽  
Optimal Force ◽  
Network Method ◽  
Point Forces ◽  
Bending Modes

Abstract The recently demonstrated ‘modal crossover network’ method for flat panel loudspeaker tuning employs an array of force drivers to selectively excite one or more panel bending modes from a spectrum of panel bending modes. A regularly spaced grid of drivers is a logical configuration for a two-dimensional driver array, and although this can be effective for exciting multiple panel modes it will not necessarily exhibit strong coupling to all of the modes within a given band of frequencies. In this paper a method is described to find optimal force driver array layouts to enable control of all the panel bending modes within a given frequency band. The optimization is carried out both for dynamic force actuators, treated as point forces, and for piezoelectric patch actuators. The optimized array layouts achieve similar maximum mode coupling efficiencies in comparison with regularly spaced driver arrays; however, in the optimized arrays all of the modes within a specified frequency band may be independently addressed, which is important for achieving a desired loudspeaker frequency response. Experiments on flat panel loudspeakers with optimized force actuator array layouts show that each of the panel modes within a selected frequency band may be addressed independently and that the inter-modal crosstalk is typically −30 dB or less with non-ideal drivers.

Probabilistic aspects of the SU(2)-harmonic oscillator

2000 ◽  
Vol 37 (1) ◽  
pp. 306-314
Author(s):  
Shunlong Luo
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Probability Distributions ◽  
Quantum Probability ◽  
Dimensional Sphere ◽  
Large Radius ◽  
Two Dimensional ◽  
Bargmann Transform ◽  
Gaussian Distributions ◽  
Binomial Distributions

In the framework of quantum probability, we present a simple geometrical mechanism which gives rise to binomial distributions, Gaussian distributions, Poisson distributions, and their interrelation. More specifically, by virtue of coherent states and a toy analogue of the Bargmann transform, we calculate the probability distributions of the position observable and the Hamiltonian arising in the representation of the classic group SU(2). This representation may be viewed as a constrained harmonic oscillator with a two-dimensional sphere as the phase space. It turns out that both the position observable and the Hamiltonian have binomial distributions, but with different asymptotic behaviours: with large radius and high spin limit, the former tends to the Gaussian while the latter tends to the Poisson.

Coherent states for Smorodinsky-Winternitz potentials

Open Physics ◽  
2009 ◽  
Vol 7 (4) ◽  
Author(s):  
Nuri Ünal
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Wave Packets ◽  
Harmonic Oscillators ◽  
Polar Coordinates ◽  
Two Dimensional ◽  
Cartesian Coordinates ◽  
Physical Time ◽  
First Case

AbstractIn this study, we construct the coherent states for a particle in the Smorodinsky-Winternitz potentials, which are the generalizations of the two-dimensional harmonic oscillator problem. In the first case, we find the non-spreading wave packets by transforming the system into four oscillators in Cartesian, and also polar, coordinates. In the second case, the coherent states are constructed in Cartesian coordinates by transforming the system into three non-isotropic harmonic oscillators. All of these states evolve in physical-time. We also show that in parametric-time, the second case can be transformed to the first one with vanishing eigenvalues.

Mode-coupling instability of two-dimensional plasma crystals

2009 ◽  
Vol 16 (8) ◽  
pp. 083706 ◽  
Author(s):  
S. K. Zhdanov ◽  
A. V. Ivlev ◽  
G. E. Morfill
Keyword(s):  
Mode Coupling ◽  
Two Dimensional ◽  
Plasma Crystals ◽  
Mode Coupling Instability

Probabilistic aspects of the SU(2)-harmonic oscillator

2000 ◽  
Vol 37 (01) ◽  
pp. 306-314
Author(s):  
Shunlong Luo
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Probability Distributions ◽  
Quantum Probability ◽  
Dimensional Sphere ◽  
Large Radius ◽  
Two Dimensional ◽  
Bargmann Transform ◽  
Gaussian Distributions ◽  
Binomial Distributions

In the framework of quantum probability, we present a simple geometrical mechanism which gives rise to binomial distributions, Gaussian distributions, Poisson distributions, and their interrelation. More specifically, by virtue of coherent states and a toy analogue of the Bargmann transform, we calculate the probability distributions of the position observable and the Hamiltonian arising in the representation of the classic group SU(2). This representation may be viewed as a constrained harmonic oscillator with a two-dimensional sphere as the phase space. It turns out that both the position observable and the Hamiltonian have binomial distributions, but with different asymptotic behaviours: with large radius and high spin limit, the former tends to the Gaussian while the latter tends to the Poisson.

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