dorsal/arxiv
View SchemaGeometric phases in the simple harmonic and perturbative Mathieu's oscillator systems
| Authors | JeongHyeong Park, Dae-Yup Song |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9911030 |
| URL | https://arxiv.org/abs/quant-ph/9911030 |
Abstract
Geometric phases of simple harmonic oscillator system are studied. Complete sets of "eigenfunctions" are constructed, which depend on the way of choosing classical solutions. For an eigenfunction, two different motions of the probability distribution function (pulsation of the width and oscillation of the center) contribute to the geometric phase which can be given in terms of the parameters of classical solutions. The geometric phase for a general wave function is also given. If a wave function has a parity under the inversion of space coordinate, then the geometric phase can be defined under the evolution of half of the period of classical motions. For the driven case, geometric phases are given in terms of Fourier coefficients of the external force. The oscillator systems whose classical equation of motion is Mathieu's equation are perturbatively studied, and the first term of nonvanishing geometric phase is calculated.
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"abstract": "Geometric phases of simple harmonic oscillator system are studied. Complete\nsets of \"eigenfunctions\" are constructed, which depend on the way of choosing\nclassical solutions. For an eigenfunction, two different motions of the\nprobability distribution function (pulsation of the width and oscillation of\nthe center) contribute to the geometric phase which can be given in terms of\nthe parameters of classical solutions. The geometric phase for a general wave\nfunction is also given. If a wave function has a parity under the inversion of\nspace coordinate, then the geometric phase can be defined under the evolution\nof half of the period of classical motions. For the driven case, geometric\nphases are given in terms of Fourier coefficients of the external force. The\noscillator systems whose classical equation of motion is Mathieu\u0027s equation are\nperturbatively studied, and the first term of nonvanishing geometric phase is\ncalculated.",
"arxiv_id": "quant-ph/9911030",
"authors": [
"JeongHyeong Park",
"Dae-Yup Song"
],
"categories": [
"quant-ph"
],
"title": "Geometric phases in the simple harmonic and perturbative Mathieu\u0027s oscillator systems",
"url": "https://arxiv.org/abs/quant-ph/9911030"
},
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