Papers by Dimitris Andresas
Physical Review E, Jun 30, 2014
We study the 1D Hamiltonian systems and their statistical behaviour, assuming the initial microca... more We study the 1D Hamiltonian systems and their statistical behaviour, 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 (2011) 315102 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.
We study the one-dimensional time-dependent Hamiltonian systems and their statistical behaviour, ... more We study the one-dimensional time-dependent Hamiltonian systems and their statistical behaviour, assuming the microcanonical ensemble of initial conditions and describing the evolution of the energy distribution in three characteristic cases: 1) parametric kick, which by definition means a discontinuous jump of a control parameter of the system, 2) linear driving, and 3) periodic driving. For the first case we specifically analyze the change of the adiabatic invariant (the canonical action) of the system under a parametric kick: A conjecture has been put forward by Papamikos and Robnik (2011) that the action at the mean energy always increases, which means, for the given statistical ensemble, that the Gibbs entropy in the mean increases (PR property). By means of a detailed rigorous 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 (e.g. has discontinuous first derivative), or if the energ...
I shall discuss the general theory of parametrically kicked systems, especially in non-linear 1D ... more I shall discuss the general theory of parametrically kicked systems, especially in non-linear 1D Hamiltonian systems. I shall present the general Papamikos-Robnik (PR) conjecture for parametrically kicked Hamilton systems, which says that for such sys-tems the adiabatic invariant (the action) for an initial microcanonical ensemble at the mean final energy always increases under a parametric kick. I shall also present many examples of the validity of the PR property, which is almost always satisfied, but can be broken in not sufficiently smooth potentials or in cases where we are in the energy range close to a separatrix in the phase space. The general conjecture, using analytical and numerical computations, is shown to hold true for important systems like homogeneous power law potentials, pendulum, Kepler system, Morse potential, Pöschl-Teller I and II potentials, cosh potential, quadratic-linear poten-tial, quadratic-quartic potential, while in three cases we demonstrate the absen...
Journal of Physics A: Mathematical and Theoretical, 2014
We study classical 1D Hamilton systems with homogeneous power law potential and their statistical... more We study classical 1D Hamilton systems with homogeneous power law potential and their statistical behaviour, assuming the microcanonical distribution of the initial conditions and describing its change under monotonically increasing timedependent function a(t) (prefactor of the potential). Using the nonlinear WKB-like method by Papamikos and Robnik J. Phys. A: Math. Theor. 44 (2012) 315102 and following a previous work by Papamikos G and Robnik M J. Phys. A: Math. Theor. 45 (2011) 015206 we specifically analyze the mean energy, the variance and the adiabatic invariant (action) of the systems for large time t → ∞ and we show that the mean energy and variance increase as powers of a(t), while the action oscillates and finally remains constant. By means of a number of detailed case studies we show that the theoretical prediction is excellent which demonstrates the usefulness of the method in such applications.
Physical Review E, 2014
We study the one-dimensional Hamiltonian systems and their statistical behavior, assuming the ini... more 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.
This book will perhaps only be under-Perhaps this book will be understood only stehen, der die Ge... more This book will perhaps only be under-Perhaps this book will be understood only stehen, der die Gedanken, die darin ausge-stood by those who have themselves already by someone who has himself already had the drückt sind-oder doch ähnliche Gedanken-thought the thoughts which are expressed in thoughts that are expressed in it-or at least schon selbst einmal gedacht hat.-Es ist also it-or similar thoughts. It is therefore not similar thoughts.-So it is not a textbook.kein Lehrbuch.-Sein Zweck wäre erreicht, a text-book. Its object would be attained if Its purpose would be achieved if it gave pleawenn es Einem, der es mit Verständnis liest there were one person who read it with under-sure to one person who read and understood Vergnügen bereitete.
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Papers by Dimitris Andresas