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

Publication ,  Journal Article
Matinyan, SG; Müller, B
Published in: Journal of Physics A: Mathematical and General
January 6, 2006

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 (ℏ ≤ 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 ℏ, 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 2ℏ4t3. © 2006 IOP Publishing Ltd.

Duke Scholars

Published In

Journal of Physics A: Mathematical and General

DOI

ISSN

0305-4470

Publication Date

January 6, 2006

Volume

39

Issue

1

Start / End Page

45 / 59

Related Subject Headings

  • Mathematical Physics
  • 02 Physical Sciences
  • 01 Mathematical Sciences
 

Citation

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Matinyan, S. G., & Müller, B. (2006). Adventures of the coupled Yang-Mills oscillators: I. Semiclassical expansion. Journal of Physics A: Mathematical and General, 39(1), 45–59. https://doi.org/10.1088/0305-4470/39/1/004
Matinyan, S. G., and B. Müller. “Adventures of the coupled Yang-Mills oscillators: I. Semiclassical expansion.” Journal of Physics A: Mathematical and General 39, no. 1 (January 6, 2006): 45–59. https://doi.org/10.1088/0305-4470/39/1/004.
Matinyan SG, Müller B. Adventures of the coupled Yang-Mills oscillators: I. Semiclassical expansion. Journal of Physics A: Mathematical and General. 2006 Jan 6;39(1):45–59.
Matinyan, S. G., and B. Müller. “Adventures of the coupled Yang-Mills oscillators: I. Semiclassical expansion.” Journal of Physics A: Mathematical and General, vol. 39, no. 1, Jan. 2006, pp. 45–59. Scopus, doi:10.1088/0305-4470/39/1/004.
Matinyan SG, Müller B. Adventures of the coupled Yang-Mills oscillators: I. Semiclassical expansion. Journal of Physics A: Mathematical and General. 2006 Jan 6;39(1):45–59.

Published In

Journal of Physics A: Mathematical and General

DOI

ISSN

0305-4470

Publication Date

January 6, 2006

Volume

39

Issue

1

Start / End Page

45 / 59

Related Subject Headings

  • Mathematical Physics
  • 02 Physical Sciences
  • 01 Mathematical Sciences