9 research outputs found
Adventures of the Coupled Yang-Mills Oscillators: II. YM-Higgs Quantum Mechanics
We continue our study of the quantum mechanical motion in the
potentials for , which arise in the spatially homogeneous limit of the
Yang-Mills (YM) equations. In the present paper, we develop a new approach to
the calculation of the partition function beyond the Thomas-Fermi (TF)
approximation by adding a harmonic (Higgs) potential and taking the limit , where is the vacuum expectation value of the Higgs field. Using the
Wigner-Kirkwood method to calculate higher-order corrections in , we
show that the limit leads to power-like singularities of the type
, which reflect the possibility of escape of the particle along the
channels in the classical limit. We show how these singularities can be
eliminated by taking into account the quantum fluctuations dictated by the form
of the potential
Adventures of the Coupled Yang-Mills Oscillators: I. Semiclassical Expansion
We study the quantum mechanical motion in the potentials with
, which arise in the spatially homogeneous limit of the Yang-Mills (YM)
equations. These systems show strong stochasticity in the classical limit
() and exhibit a quantum mechanical confinement feature. We
calculate the partition function 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
Classical Gluon Radiation in Ultrarelativistic Nuclear Collisions: Space-Time Structure, Instabilities, and Thermalization
We investigate the space-time structure of the classical gluon field produced
in an ultrarelativistic collision between color charges. The classical solution
which was computed previously in a perturbative approach is shown to become
unstable on account of the non-Abelian self-interaction neglected in the
perturbative solution scheme. The time scale for growth of the instabilities is
found to be of the order of the distance between the colliding color charges.
We argue that these instabilities will eventually lead to thermalization of
gluons produced in an ultrarelativistic collision between heavy nuclei. The
rate of thermalization is estimated to be of order , where is the
strong coupling constant and the transverse color charge density of an
ultrarelativistic nucleus.Comment: 11 pages, REVTeX, eps-, aps-, and psfig-style files, 7 figs., figs.
2-5 in gif-format, a uucompressed version of this paper including all figures
(ca. 2.2 Mb) is available at ftp://nt1.phys.columbia.edu/pub/stabil/stab.u
Gluon Radiation and Coherent States in Ultrarelativistic Nuclear Collisions
We explore the correspondence between classical gluon radiation and quantum
radiation in a coherent state for gluons produced in ultrarelativistic nuclear
collisions. The expectation value of the invariant momentum distribution of
gluons in the coherent state is found to agree with the gluon number
distribution obtained classically from the solution of the Yang-Mills
equations. A criterion for the applicability of the coherent state formalism to
the problem of radiation in ultrarelativistic nucleus-nucleus collisions is
discussed. This criterion is found to be fulfilled for midrapidity gluons with
perturbative transverse momenta larger than about 1-2 GeV and produced in
collisions between valence partons.Comment: 15 pages, 6 figures, RevTeX (with epsf, psfig style files