Chirikov analysis

Chirikov analysis quantitatively reveals the coupling responsible for the resonant energy transfer. Equation (13) can be transformed to action-angle coordinates via Eqs. (5) and (6), with the result... 

How close do the frequencies have to be to permit complete energy transfer as in Fig. lb The answer is defined by the resonance width, which can be determined by the Chirikov analysis. Similarly, Chirikov analysis can be used to predict the time scale for the energy exchange between the modes (48). Hence, nonlinear resonance analysis gives a very complete picture of the periodic exchange of energy between two modes, as shown in Fig. lb. 

As is well known (Chirikov, 1979 Izrailev, 1990), the phase-space evolution of the norelativistic classical kicked rotor is described by nonrelativistic standard map. The analysis of this map shows that the motion of the nonrelativistic kicked rotor is accompanied by unlimited diffusion in the energy and momentum. However, this diffusion is suppressed in the quantum case (Casati et.al., 1979 Izrailev, 1990). Such a suppression of diffusive growth of the energy can be observed when one considers the (classical) relativistic extention of the classical standard map (Nomura et.al., 1992) which was obtained recently by considering the motion of the relativistic electron in the field of an electrostatic wave packet. The relativistic generalization of the standard map is obtained recently (Nomura et.al., 1992)... 

Abstract. Classical regular and chaotic dynamics of the particle bound in the Coulomb plus linear potential under the influence of time-periodical perturbations is treated using resonace analysis. Critical value of the external field at which chaotization will occur is evaluated analytically based on the Chirikov criterion of stochasticity. 

In this paper we consider the QCD counterpart of this problem. Namely, we address the problem of regular and chaotic motion in periodically driven quarkonium. Using resonance analysis based on the Chirikov criterion of stochasticity we estimate critical values of the external field strength at which quarkonium motion enters into chaotic regime. 

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