• DOI:10.1088/0305-4470/39/1/004
• Corpus ID: 119473046

Adventures of the coupled Yang-Mills oscillators: I. Semiclassical expansion

@article{Matinyan2005AdventuresOT,
  title={Adventures of the coupled Yang-Mills oscillators: I. Semiclassical expansion},
  author={Sergei G. Matinyan and Berndt Muller},
  journal={Journal of Physics A},
  year={2005},
  volume={39},
  pages={45-59}
}

• S. Matinyan, B. Muller
• Published 25 June 2005
• Physics
• Journal of Physics A

We study the quantum mechanical motion in the x2y2 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 ( = 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 , 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 g24t3.