title: Statistical properties of one-dimensional parametrically kicked Hamilton systems.
abstract: We study the one-dimensional Hamiltonian systems and their statistical behavior, assuming the initial microcanonical distribution and describing its change under a parametric kick, which by definition means a discontinuous jump of a control parameter of the system. Following a previous work by Papamikos and Robnik [J. Phys. A: Math. Theor. 44, 315102 (2011)], we specifically analyze the change of the adiabatic invariant (the action) of the system under a parametric kick: A conjecture has been put forward that the change of the action at the mean energy always increases, which means, for the given statistical ensemble, that the Gibbs entropy in the mean increases. By means of a detailed analysis of a great number of case studies, we show that the conjecture largely is satisfied, except if either the potential is not smooth enough or if the energy is too close to a stationary point of the potential (separatrix in the phase space). Very fast changes in a time-dependent system quite generally can be well described by such a picture and by the approximation of a parametric kick, if the change of the parameter is sufficiently fast and takes place on the time scale of less than one oscillation period. We discuss our work in the context of the statistical mechanics in the sense of Gibbs.
authors.affiliation: CAMTP-Center for Applied Mathematics and Theoretical Physics, University of Maribor, Krekova 2, SI-2000 Maribor, Slovenia, European Union.
authors.forename: Dimitris
authors.initials: D
authors.lastname: Andresas
authors.affiliation: CAMTP-Center for Applied Mathematics and Theoretical Physics, University of Maribor, Krekova 2, SI-2000 Maribor, Slovenia, European Union.
authors.forename: Benjamin
authors.initials: B
authors.lastname: Batistić
authors.affiliation: CAMTP-Center for Applied Mathematics and Theoretical Physics, University of Maribor, Krekova 2, SI-2000 Maribor, Slovenia, European Union.
authors.forename: Marko
authors.initials: M
authors.lastname: Robnik
mesh_terms: D019277:Entropy; D015233:Models, Statistical