dorsal/arxiv
View SchemaNonadiabatic geometric phase for the cyclic evolution of a time-dependent Hamiltonian system
| Authors | Jie Liu, Bambi Hu, Baowen Li |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9806076 |
| URL | https://arxiv.org/abs/quant-ph/9806076 |
| DOI | 10.1103/PhysRevA.58.3448 |
Abstract
The geometric phases of the cyclic states of a generalized harmonic oscillator with nonadiabatic time-periodic parameters are discussed in the framework of squeezed state. It is shown that the cyclic and quasicyclic squeezed states correspond to the periodic and quasiperiodic solutions of an effective Hamiltonian defined on an extended phase space, respectively. The geometric phase of the cyclic squeezed state is found to be a phase-space area swept out by a periodic orbit. Furthermore, a class of cyclic states are expressed as a superposition of an infinte number of squeezed states. Their geometric phases are found to be independent of $\hbar$, and equal to $-(n+1/2)$ times the classical nonadiabatic Hannay angle.
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"abstract": "The geometric phases of the cyclic states of a generalized harmonic\noscillator with nonadiabatic time-periodic parameters are discussed in the\nframework of squeezed state. It is shown that the cyclic and quasicyclic\nsqueezed states correspond to the periodic and quasiperiodic solutions of an\neffective Hamiltonian defined on an extended phase space, respectively. The\ngeometric phase of the cyclic squeezed state is found to be a phase-space area\nswept out by a periodic orbit. Furthermore, a class of cyclic states are\nexpressed as a superposition of an infinte number of squeezed states. Their\ngeometric phases are found to be independent of $\\hbar$, and equal to\n$-(n+1/2)$ times the classical nonadiabatic Hannay angle.",
"arxiv_id": "quant-ph/9806076",
"authors": [
"Jie Liu",
"Bambi Hu",
"Baowen Li"
],
"categories": [
"quant-ph",
"chao-dyn",
"cond-mat",
"nlin.CD"
],
"doi": "10.1103/PhysRevA.58.3448",
"title": "Nonadiabatic geometric phase for the cyclic evolution of a time-dependent Hamiltonian system",
"url": "https://arxiv.org/abs/quant-ph/9806076"
},
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