scholarly journals On noncommutative energy spectra in two-dimensional coupling harmonic oscillator

2021 ◽  
Vol 70 (20) ◽  
pp. 200301-200301
Author(s):  
Gou Li-Dan ◽  
2018 ◽  
Vol 2 (1) ◽  
Author(s):  
Yu-ichiro Matsushita ◽  
Hirofumi Nishi ◽  
Jun-ichi Iwata ◽  
Taichi Kosugi ◽  
Atsushi Oshiyama

Mathematics ◽  
2018 ◽  
Vol 6 (10) ◽  
pp. 180 ◽  
Author(s):  
Laure Gouba

The system of a two-dimensional damped harmonic oscillator is revisited in the extended phase space. It is an old problem that has already been addressed by many authors that we present here with some fresh points of view and carry on a whole discussion. We show that the system is singular. The classical Hamiltonian is proportional to the first-class constraint. We pursue with the Dirac’s canonical quantization procedure by fixing the gauge and provide a reduced phase space description of the system. As a result, the quantum system is simply modeled by the original quantum Hamiltonian.


1986 ◽  
Vol 163 ◽  
pp. 227-256 ◽  
Author(s):  
F. O. Thomas ◽  
V. W. Goldschmidt

An experimental study of the developing structural characteristics of a two-dimensional jet in an extremely quiet environment was performed. The jet, at an exit Reynolds number of 6000 and with fluctuation intensity under 0.2% at the mouth, was operated within a large anechoic room. Measurements of energy spectra, fluctuation phase angles and two-dimensionality led to the inference of structural patterns in the flow. These patterns are initially characterized by relatively strong symmetric modes exhibiting limited two-dimensionality and oriented parallel to the mouth of the jet. Subsequent downstream evolution led to the formation of an antisymmetric pattern beyond the jet potential core and the associated development of extended structures possessing a definite large lateral inclination. The results of this work suggest a developing large-scale structural pattern more complicated than previously supposed.


2000 ◽  
Vol 61 (6) ◽  
pp. 6572-6577 ◽  
Author(s):  
Norbert Schorghofer

2001 ◽  
Vol 203 ◽  
pp. 555-557
Author(s):  
P. K. Browning ◽  
G. E. Vekstein

We investigate the acceleration of charged particles in the framework of collisionless reconnection. A steady reconnection scenario is considered, with a two dimensional X-point magnetic field geometry having also a uniform field component transverse to the plane of the X-point field, and an inductive electric field generating an inflow of particles. Test particle trajectories are studied, and the energy spectra of the accelerated particles are determined.


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