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The Partition Function and Level Density for Yang-Mills-Higgs Quantum Mechanics | | S.G. Matinyan
; Y. Jack Ng
; | | Date: |
25 Dec 2002 | | Journal: | J.Phys. A36 (2003) L417 | | Subject: | High Energy Physics - Theory; Chaotic Dynamics | hep-th hep-ph nlin.CD quant-ph | | Affiliation: | Yerevan Physics Institute) and Y. Jack Ng (University of North Carolina | | Abstract: | We calculate the partition function $Z(t)$ and the asymptotic integrated level density $N(E)$ for Yang-Mills-Higgs Quantum Mechanics for two and three dimensions ($n = 2, 3$). Due to the infinite volume of the phase space $Gamma$ on energy shell for $n= 2$, it is not possible to disentangle completely the coupled oscillators ($x^2 y^2$-model) from the Higgs sector. The situation is different for $n = 3$ for which $Gamma$ is finite. The transition from order to chaos in these systems is expressed by the corresponding transitions in $Z(t)$ and $N(E)$, analogous to the transitions in adjacent level spacing distribution from Poisson distribution to Wigner-Dyson distribution. We also discuss a related system with quartic coupled oscillators and two dimensional quartic free oscillators for which, contrary to YMHQM, both coupling constants are dimensionless. | | Source: | arXiv, hep-th/0212304 | | Services: | Forum | Review | PDF | Favorites | |
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