188 research outputs found

    Adventures of the Coupled Yang-Mills Oscillators: II. YM-Higgs Quantum Mechanics

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    We continue our study of the quantum mechanical motion in the x2y2x^2y^2 potentials for n=2,3n=2,3, 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 Z(t)Z(t) beyond the Thomas-Fermi (TF) approximation by adding a harmonic (Higgs) potential and taking the limit v0v\to 0, where vv is the vacuum expectation value of the Higgs field. Using the Wigner-Kirkwood method to calculate higher-order corrections in \hbar, we show that the limit v0v\to 0 leads to power-like singularities of the type vnv^{-n}, 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

    Branching Processes and Multi-Particle Production

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    The general theory of the branching processes is used for establishing the relation between the parameters kk and nˉ\bar n of the negative binomial distribution. This relation gives the possibility to describe the overall data on multiplicity distributions in pp(ppˉ)pp (p\bar p)-collisions for energies up to 900 GeV and to make several interesting predictions for higher energies. This general approach is free from ambiguities associated with the extrapolation of the parameter kk to unity.Comment: 13 pages, (8 figures available on request), DUKE-TH-93-5

    Adventures of the Coupled Yang-Mills Oscillators: I. Semiclassical Expansion

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    We study the quantum mechanical motion in the x2y2x^2y^2 potentials with n=2,3n=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\hbar = 0) and exhibit a quantum mechanical confinement feature. We calculate the partition function Z(t)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 \hbar, 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 g24t3g^2\hbar^4t^3

    Out of equilibrium dynamics of coherent non-abelian gauge fields

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    We study out-of-equilibrium dynamics of intense non-abelian gauge fields. Generalizing the well-known Nielsen-Olesen instabilities for constant initial color-magnetic fields, we investigate the impact of temporal modulations and fluctuations in the initial conditions. This leads to a remarkable coexistence of the original Nielsen-Olesen instability and the subdominant phenomenon of parametric resonance. Taking into account that the fields may be correlated only over a limited transverse size, we model characteristic aspects of the dynamics of color flux tubes relevant in the context of heavy-ion collisions.Comment: 12 pages, 10 figures; PRD version, minor change
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