S G Matinyan and Y Jack Ng 2003 J. Phys. A: Math. Gen. 36 L417 doi:10.1088/0305-4470/36/25/102
S G Matinyan1,3 and Y Jack Ng2
Show affiliationsWe 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 Γ on energy shell for n = 2, it is not possible to completely disentangle the coupled oscillators (x2 y2 model) from the Higgs sector. The situation is different for n = 3 for which Γ 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.
11.15.Kc Classical and semiclassical techniques
81T13 Yang-Mills and other gauge theories (See also 53C07, 58E15)
34C15 Nonlinear oscillations, coupled oscillators
81S30 Phase space methods including Wigner distributions, etc.
Issue 25 (27 June 2003)
Received 2 January 2003, in final form 14 April 2003
Published 12 June 2003
S G Matinyan and Y Jack Ng 2003 J. Phys. A: Math. Gen. 36 L417
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