Phase Space Research Papers - Academia.edu (original) (raw)

We propose a theory of deterministic chaos for discrete systems, based on their representations in binary state spaces $ \Omega $, homeomorphic to the space of symbolic dynamics. This formalism is applied to neural networks and cellular... more

We propose a theory of deterministic chaos for discrete systems, based on their representations in binary state spaces $ \Omega $, homeomorphic to the space of symbolic dynamics. This formalism is applied to neural networks and cellular automata; it is found that such systems cannot be viewed as chaotic when one uses the Hamming distance as the metric for the

Two time theory is derived via localization of the global Sp(2) [or Osp(1/2), Osp(N/2), Sp(2N),...] symmetry in phase space in order to give a self contained introduction to two time theory. Then it is shown that from the two-times... more

Two time theory is derived via localization of the global Sp(2) [or Osp(1/2), Osp(N/2), Sp(2N),...] symmetry in phase space in order to give a self contained introduction to two time theory. Then it is shown that from the two-times physics point of view theories of point particles on many known black hole backgrounds are Sp(2) gauge duals of one another and of course also gauge dual to all other equal dimensional gauges from earlier two time related publications (hydrogen atom, ...). We reproduce the free (quantum) relativistic particle on 1+1 dimensional black hole backgrounds and 2+1 dimensional BTZ ones. Other 2+1 black holes and n+1 ones are touched on but explicitely found only as cross sections of complicated (n+1)+1 backgrounds. Further we give near horizon solutions (e.g. n+1 Robertson-Bertotti). Since two time physics can reproduce these backgrounds all particle actions have hidden symmetries that have not been noticed before.

There's been a recent surge of interest in the study of low-dimensional packed elastic manifolds. In fact, the simple act of crumpling a piece of paper does require the simultaneous interaction of many fascinating mechanisms. These... more

There's been a recent surge of interest in the study of low-dimensional packed elastic manifolds. In fact, the simple act of crumpling a piece of paper does require the simultaneous interaction of many fascinating mechanisms. These include energy condensation from large length scales to small singular structures, topological self-avoidance and complex phase space landscapes reminiscent of frustration in the context

Drawing inspiration from Dirac's work on functions of non commuting observables, we develop a fresh approach to phase space descriptions of operators and the Wigner distribution in quantum mechanics. The construction presented here is... more

Drawing inspiration from Dirac's work on functions of non commuting observables, we develop a fresh approach to phase space descriptions of operators and the Wigner distribution in quantum mechanics. The construction presented here is marked by its economy, naturalness and more importantly, by its potential for extensions and generalisations to situations where the underlying configuration space is non Cartesian.

We study a model of Brownian particles which are pumped with energy by means of a non-linear friction function, for which different types are discussed. A suitable expression for a non-linear, velocity-dependent friction function is... more

We study a model of Brownian particles which are pumped with energy by means of a non-linear friction function, for which different types are discussed. A suitable expression for a non-linear, velocity-dependent friction function is derived by considering an internal energy depot of the Brownian particles. In this case, the friction function describes the pumping of energy in the range of small velocities, while in the range of large velocities the known limit of dissipative friction is reached. In order to investigate the influence of additional energy supply, we discuss the velocity distribution function for different cases. Analytical solutions of the corresponding Fokker-Planck equation in 2d are presented and compared with computer simulations. Different to the case of passive Brownian motion, we find several new features of the dynamics, such as the formation of limit cycles in the four-dimensional phase-space, a large mean squared displacement which increases quadratically with the energy supply, or non-equilibrium velocity distributions with crater-like form. Further, we point to some generalizations and possible applications of the model.

The EEG (Electroencephalogram) signal indicates the electrical activity of the brain. They are highly random in nature and may contain useful information about the brain state. However, it is very difficult to get useful information from... more

The EEG (Electroencephalogram) signal indicates the electrical activity of the brain. They are highly random in nature and may contain useful information about the brain state. However, it is very difficult to get useful information from these signals directly in the time domain just by observing them. They are basically non-linear and nonstationary in nature. Hence, important features can be

Motivated by the interpretation of the Ooguri-Strominger-Vafa conjecture as a holographic correspondence in the mini-superspace approximation, we study the radial quantization of stationary, spherically symmetric black holes in four... more

Motivated by the interpretation of the Ooguri-Strominger-Vafa conjecture as a holographic correspondence in the mini-superspace approximation, we study the radial quantization of stationary, spherically symmetric black holes in four dimensions. A key ingredient is the classical equivalence between the radial evolution equation and geodesic motion of a fiducial particle on the moduli space M^*_3 of the three-dimensional theory after reduction along the time direction. In the case of N=2 supergravity, M^*_3 is a para-quaternionic-Kahler manifold; in this case, we show that BPS black holes correspond to a particular class of geodesics which lift holomorphically to the twistor space Z of M^*_3, and identify Z as the BPS phase space. We give a natural quantization of the BPS phase space in terms of the sheaf cohomology of Z, and compute the exact wave function of a BPS black hole with fixed electric and magnetic charges in this framework. We comment on the relation to the topological string amplitude, extensions to N>2 supergravity theories, and applications to automorphic black hole partition functions.

There is a great deal of justified concern about continuity through scientific theory change. Our thesis is that, particularly in physics, such continuity can be appropriately captured at the level of conceptual frameworks (the level... more

There is a great deal of justified concern about continuity through scientific theory change. Our thesis is that, particularly in physics, such continuity can be appropriately captured at the level of conceptual frameworks (the level above the theories themselves) using conceptual space models. Indeed, we contend that the conceptual spaces of three of our most important physical theories—Classical Mechanics (CM), Special Relativity Theory (SRT), and Quantum Mechanics (QM)—have already been so modelled as phase-spaces. Working with their phase-space formulations, one can trace the conceptual changes and continuities in transitioning from CM to QM, and from CM to SRT. By offering a revised severity-ordering of changes that conceptual frameworks can undergo, we provide reasons to doubt the commonly held view that SRT is conceptually closer to CM than QM is.

We study the existence of periodic trajectories for nonautonomous differential equations and inclusions remaining in a prescribed compact subset of an extended phase space. These sets of constraints are nonconvex right-continuous tubes... more

We study the existence of periodic trajectories for nonautonomous differential equations and inclusions remaining in a prescribed compact subset of an extended phase space. These sets of constraints are nonconvex right-continuous tubes not satisfying the viability tangential condition on the whole boundary. We find sufficient conditions for existence of viable periodic trajectories studying properties of the exit subset of the tube. A new approximation approach for continuous multivalued maps is presented. 1.