Competition between unlimited and limited energy growth in a two-dimensional time-dependent billiard - Fregolente Mendes de Oliveira, Diego; Pöschel, Thorsten (Physics Letters A, 2013)
Some dynamical properties for a dissipative time-dependent Lorentz gas are studied. We assume that the size of the scatterers change periodically in time. We show that for some combination of the control parameters the particles come to a complete stop between the scatterers, but for some other cases, the average velocity grows unbounded. This is the first time that the unlimited energy growth is observed in a dissipative system. Finally, we study the behavior of the average velocity as a function of the number of collisions and we show that the system is scaling invariant with scaling exponents well defined. © 2013 Elsevier B.V. All rights reserved.
Keywords: Billiards; Chaos; Dissipation; Lorentz gas; Scaling

Dynamical properties for the problem of a particle in an electric field of wave packet: Low velocity and relativistic approach - Fregolente Mendes de Oliveira, Diego; Leonel, Edson D. (Physics Letters A, 2012)
We study some dynamical properties for the problem of a charged particle in an electric field considering both the low velocity and relativistic cases. The dynamics for both approaches is described in terms of a two-dimensional and nonlinear mapping. The structure of the phase spaces is mixed and we introduce a hole in the chaotic sea to let the particles to escape. By changing the size of the hole we show that the survival probability decays exponentially for both cases. Additionally, we show for the relativistic dynamics, that the introduction of dissipation changes the mixed phase space and attractors appear. We study the parameter space by using the Lyapunov exponent and the average energy over the orbit and show that the system has a very rich structure with infinite family of self-similar shrimp shaped embedded in a chaotic region. © 2012 Elsevier B.V.
Keywords: Chaos; Parameter space; Shrimps; Survival probability

In-flight and collisional dissipation as a mechanism to suppress Fermi acceleration in a breathing Lorentz gas - Fregolente Mendes de Oliveira, Diego; Leonel, Edson D. (Chaos, 2012)
Some dynamical properties for a time dependent Lorentz gas considering both the dissipative and non dissipative dynamics are studied. The model is described by using a four-dimensional nonlinear mapping. For the conservative dynamics, scaling laws are obtained for the behavior of the average velocity for an ensemble of non interacting particles and the unlimited energy growth is confirmed. For the dissipative case, four different kinds of damping forces are considered namely: (i) restitution coefficient which makes the particle experiences a loss of energy upon collisions; and in-flight dissipation given by (ii) F = -eta V-2; (iii) F = -eta V-mu with mu not equal 1 and mu not equal 2 and; (iv) F = -eta V, where eta is the dissipation parameter. Extensive numerical simulations were made and our results confirm that the unlimited energy growth, observed for the conservative dynamics, is suppressed for the dissipative case. The behaviour of the average velocity is described using scaling arguments and classes of universalities are defined. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3697392]

Influence of boundary conditions on quantum escape - Fregolente Mendes de Oliveira, Diego; Georgiou, Orestis; Gligoric, Goran; Lazarides, Achilleas; Bodyfelt, Joshua D.; Goussev, Arseni (EPL - Europhysics Letters, 2012)
It has recently been established that quantum statistics can play a crucial role in quantum escape. Here we demonstrate that boundary conditions can be equally important-moreover, in certain cases, may lead to a complete suppression of the escape. Our results are exact and hold for arbitrarily many particles. Copyright (c) EPLA, 2012

Some dynamical properties of a classical dissipative bouncing ball model with two nonlinearities - Fregolente Mendes de Oliveira, Diego; Leonel, Edson D. (Physica A-Statistical Mechanics and Its Applications, 2013)
Some dynamical properties for a bouncing ball model are studied. We show that when dissipation is introduced the structure of the phase space is changed and attractors appear. Increasing the amount of dissipation, the edges of the basins of attraction of an attracting fixed point touch the chaotic attractor. Consequently the chaotic attractor and its basin of attraction are destroyed given place to a transient described by a power law with exponent -2. The parameter-space is also studied and we show that it presents a rich structure with infinite self-similar structures of shrimp-shape. (c) 2013 Elsevier B.V. All rights reserved.
Keywords: Chaos; Fermi-map; Boundary crisis