Statistical properties of a dissipative kicked system: critical exponents and scaling invariance

Abstract

A new universal {\it empirical} function that depends on a single critical exponent (acceleration exponent) is proposed to describe the scaling behavior in a dissipative kicked rotator. The scaling formalism is used to describe two regimes of dissipation: (i) strong dissipation and (ii) weak dissipation. For case (i) the model exhibits a route to chaos known as period doubling and the Feigenbaum constant along the bifurcations is obtained. When weak dissipation is considered the average action as well as its standard deviation are described using scaling arguments with critical exponents. The universal {\it empirical} function describes remarkably well a phase transition from limited to unlimited growth of the average action.

References in corpus (6)

• Corrugated waveguide under scaling investigation
• Fermi acceleration and suppression of Fermi acceleration in a time-dependent Lorentz Gas
• Chaotic dynamics of the elliptical stadium billiard in the full parameter space
• In-flight dissipation as a mechanism to suppress Fermi acceleration
• Boundary crisis and suppression of Fermi acceleration in a dissipative two dimensional non-integrable time-dependent billiard
• Chaotic dynamics of a Bose-Einstein condensate coupled to a qubit

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