Some dynamical properties of time-dependent driven elliptical-shaped billiards are studied. It was shown that for conservative time-dependent dynamics the model exhibits Fermi acceleration [Phys. Rev. Lett. 100, 014103 (2008).] On the other hand, it was observed that damping coefficients upon collisions suppress such a phenomenon [Phys. Rev. Lett. 104, 224101 (2010)]. Here, we consider a dissipative model under the presence of in-flight dissipation due to a drag force which is assumed to be proportional to the square of the velocity of the particle. Our results reinforce that dissipation leads to a phase transition from unlimited to limited energy growth. The behavior of the average velocity is described using scaling arguments.
COBISS.SI-ID: 66907905
We consider 1D time-dependent Hamiltonian systems and their statistical properties, namely the time evolution of microcanonical distributions, whose properties are very closely related to the existence and preservation of the adiabatic invariants. We review the elements of the recent developments by Robnik and Romanovski (during 2006-2008) for the entirely general 1D time-dependent linear oscillator and try to generalize the results to the 1D nonlinear Hamilton oscillators, in particular the power-law potentials like e.g. the quartic oscillator. Furthermore, we consider the limit opposite to the adiabatic limit, namely parametrically kicked 1D Hamiltonian systems. Evenfor the linear oscillator, interesting properties are revealed: an initial kick disperses the microcanonical distribution to a spread one, but an anti-kick at an appropriate moment of time can annihilate it, kicking it back to the microcanonical distribution. The case of periodic parametric kicking is also interesting. Finally, we propose that in the parametric kicking of a general 1D Hamilton system, the average value of the adiabatic invariant always increases, which we prove for the power-law potentials. We find that the approximation of kicking is good for quite long times of the parameter variation, up to the order of not much less than one period of the oscillator. We also look at the behavior of the quartic oscillator for the case of the kick and anti-kick, and also the periodic kicking.
COBISS.SI-ID: 67549697
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.
COBISS.SI-ID: 78977281
In this paper we obtain necessary and sufficient conditions at the origin for the Lotka-Volterra complex quintic systems which are linear systems perturbed by fifth degree homogeneous polynomials. The necessity ot these conditions is derived from the first nine focus-saddle quantities and their sufficiency is proved by finding an inverse integrating factor or a first integral.
COBISS.SI-ID: 17613320
We show that the warp factor of a generic asymptotically flat black hole in five dimensions can be adjusted such that a conformal symmetry emerges. The construction preserves all near horizon properties of the black holes, such as the thermodynamic potentials and the entropy. We interpret the geometry with modified asymptotic behavior as the "bare" black hole, with the ambient flat space removed. Our warp factor subtraction generalizes hidden conformal symmetry and applies whether or not rotation is significant. We also find a relation to standard AdS/CFT correspondence by embedding the black holes in six dimensions. The asymptotic conformal symmetry guarantees a dual CFT description of the general rotating black holes.
COBISS.SI-ID: 73420033