scholarly journals Two-dimensional isotropic harmonic oscillator on a time-dependent sphere

2012 ◽  
Vol 45 (46) ◽  
pp. 465301 ◽  
Author(s):  
Ali Mahdifar ◽  
Behrouz Mirza ◽  
Rasoul Roknizadeh
Keyword(s):  
Harmonic Oscillator ◽  
Time Dependent ◽  
Two Dimensional ◽  
Isotropic Harmonic Oscillator

Two-dimensional isotropic harmonic oscillator approach to classical and quantum Stokes parameters

2004 ◽  
Vol 82 (10) ◽  
pp. 767-773 ◽  
Author(s):  
R D Mota ◽  
M A Xicoténcatl ◽  
V D Granados
Keyword(s):  
Harmonic Oscillator ◽  
Classical Limit ◽  
Plane Electromagnetic Wave ◽  
Stokes Parameters ◽  
Two Dimensional ◽  
Expectation Value ◽  
Isotropic Harmonic Oscillator ◽  
Pauli Matrices ◽  
Constants Of Motion ◽  
Polarization Matrix

We show that the well-known Stokes operators, defined as elements of the Jordan–Schwinger map with the Pauli matrices of two independent bosons, are equal to the constants of motion of the two-dimensional isotropic harmonic oscillator. Taking the expectation value of the Stokes operators in a two-mode coherent state, we obtain the corresponding classical Stokes parameters. We show that this classical limit of the Stokes operators, the 2 × 2 unit matrix and the Pauli matrices may be used to expand the polarization matrix. Finally, by means of the constants of motion of the classical two-dimensional isotropic harmonic oscillator, we describe the geometric properties of the polarization ellipse. Our study is restricted to the case of a monochromatic quantized-plane electromagnetic wave that propagates along the z axis.PACS Nos.: 42.50.–p, 42.25.Ja, 11.30.–j

scholarly journals Time-dependent metric for the two-dimensional, non-Hermitian coupled oscillator

2019 ◽  
Vol 35 (08) ◽  
pp. 2050041 ◽  
Author(s):  
Andreas Fring ◽  
Thomas Frith
Keyword(s):  
Harmonic Oscillator ◽  
Time Dependence ◽  
Time Dependent ◽  
Two Dimensional ◽  
Coupling Term ◽  
Coupled Oscillator ◽  
Explicit Time Dependence ◽  
Independent Model

We provide a time-dependent Dyson map and metric for the two-dimensional harmonic oscillator with a non-Hermitian ixy coupling term. This particular time-independent model exhibits spontaneously broken [Formula: see text]-symmetry and becomes unphysical in the broken regime, with the spectrum becoming partially complex. By introducing an explicit time dependence into the Dyson map, we provide a time-dependent metric that renders the model consistent across the unbroken and broken regimes.

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