dorsal/arxiv
View SchemaAdventures of the Coupled Yang-Mills Oscillators: I. Semiclassical Expansion
| Authors | Sergei G. Matinyan, Berndt Müller |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0506214 |
| URL | https://arxiv.org/abs/quant-ph/0506214 |
| DOI | 10.1088/0305-4470/39/1/004 |
| Journal | J.Phys. A39 (2006) 45-60 |
Abstract
We study the quantum mechanical motion in the $x^2y^2$ potentials with $n=2,3$, which arise in the spatially homogeneous limit of the Yang-Mills (YM) equations. These systems show strong stochasticity in the classical limit ($\hbar = 0$) and exhibit a quantum mechanical confinement feature. We calculate the partition function $Z(t)$ going beyond the Thomas-Fermi (TF) approximation by means of the semiclassical expansion using the Wigner-Kirkwood (WK) method. We derive a novel compact form of the differential equation for the WK function. After separating the motion in the channels of the equipotential surface from the motion in the central region, we show that the leading higher-order corrections to the TF term vanish up to eighth order in $\hbar$, if we treat the quantum motion in the hyperbolic channels correctly by adiabatic separation of the degrees of freedom. Finally, we obtain an asymptotic expansion of the partition function in terms of the parameter $g^2\hbar^4t^3$.
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"abstract": "We study the quantum mechanical motion in the $x^2y^2$ potentials with\n$n=2,3$, which arise in the spatially homogeneous limit of the Yang-Mills (YM)\nequations. These systems show strong stochasticity in the classical limit\n($\\hbar = 0$) and exhibit a quantum mechanical confinement feature. We\ncalculate the partition function $Z(t)$ going beyond the Thomas-Fermi (TF)\napproximation by means of the semiclassical expansion using the Wigner-Kirkwood\n(WK) method. We derive a novel compact form of the differential equation for\nthe WK function. After separating the motion in the channels of the\nequipotential surface from the motion in the central region, we show that the\nleading higher-order corrections to the TF term vanish up to eighth order in\n$\\hbar$, if we treat the quantum motion in the hyperbolic channels correctly by\nadiabatic separation of the degrees of freedom. Finally, we obtain an\nasymptotic expansion of the partition function in terms of the parameter\n$g^2\\hbar^4t^3$.",
"arxiv_id": "quant-ph/0506214",
"authors": [
"Sergei G. Matinyan",
"Berndt M\u00fcller"
],
"categories": [
"quant-ph",
"hep-th",
"nlin.CD"
],
"doi": "10.1088/0305-4470/39/1/004",
"journal_ref": "J.Phys. A39 (2006) 45-60",
"title": "Adventures of the Coupled Yang-Mills Oscillators: I. Semiclassical Expansion",
"url": "https://arxiv.org/abs/quant-ph/0506214"
},
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