Symmetry Reduction of Quasi-Free States

Given a group-invariant quasi-free state on the algebra of canonical commutation relations (CCR), we show how group averaging techniques can be used to obtain a symmetry reduced CCR algebra and reduced quasi-free state. When the group is compact this method of symmetry reduction leads to standard results which can be obtained using other methods. When the group is non-compact the group averaging prescription relies upon technically favorable conditions which we delineate. As an example, we consider symmetry reduction of the usual vacuum state for a Klein-Gordon field on Minkowski spacetime by a non-compact subgroup of the Poincar\'e group consisting of a 1-parameter family of boosts, a 1-parameter family of spatial translations and a set of discrete translations. We show that the symmetry reduced CCR algebra and vacuum state correspond to that used by each of Berger, Husain, and Pierri for the polarized Gowdy ${\bf T}^3$ quantum gravity model.Comment: 18 page

IFSM representation of Brownian motion with applications to simulation

Several methods are currently available to simulate paths of the Brownian motion. In particular, paths of the BM can be simulated using the properties of the increments of the process like in the Euler scheme, or as the limit of a random walk or via L2 decomposition like the Kac-Siegert/Karnounen-Loeve series. In this paper we first propose a IFSM (Iterated Function Systems with Maps) operator whose fixed point is the trajectory of the BM. We then use this representation of the process to simulate its trajectories. The resulting simulated trajectories are self-affine, continuous and fractal by construction. This fact produces more realistic trajectories than other schemes in the sense that their geometry is closer to the one of the true BM's trajectories. The IFSM trajectory of the BM can then be used to generate more realistic solutions of stochastic differential equations

Quantum mechanics in finite dimensional Hilbert space

The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with the infinite dimensional case. The construction of an unbiased basis for state determination is discussed.Comment: 14 pages, no figure

Non-local transport and the Hall viscosity of 2D hydrodynamic electron liquids

In a fluid subject to a magnetic field the viscous stress tensor has a dissipationless antisymmetric component controlled by the so-called Hall viscosity. We here propose an all-electrical scheme that allows a determination of the Hall viscosity of a two-dimensional electron liquid in a solid-state device.Comment: 12 pages, 4 figure

Model-Based Control Using Koopman Operators

This paper explores the application of Koopman operator theory to the control of robotic systems. The operator is introduced as a method to generate data-driven models that have utility for model-based control methods. We then motivate the use of the Koopman operator towards augmenting model-based control. Specifically, we illustrate how the operator can be used to obtain a linearizable data-driven model for an unknown dynamical process that is useful for model-based control synthesis. Simulated results show that with increasing complexity in the choice of the basis functions, a closed-loop controller is able to invert and stabilize a cart- and VTOL-pendulum systems. Furthermore, the specification of the basis function are shown to be of importance when generating a Koopman operator for specific robotic systems. Experimental results with the Sphero SPRK robot explore the utility of the Koopman operator in a reduced state representation setting where increased complexity in the basis function improve open- and closed-loop controller performance in various terrains, including sand.Comment: 8 page

Possible Contribution to Electron and Positron Fluxes from Pulsars and their Nebulae

The AMS-02 experiment confirms the excess of positrons in cosmic rays (CRs) for energy above 10 GeV with respect to the secondary production of positrons in the interstellar medium. This is interpreted as evidence of the existence of a primary source of these particles. Possible candidates are dark matter or astrophysical sources. In this work we discuss the possible contribution due to pulsars and their nebulae. Our key assumption is that the primary spectrum of electrons and positrons at the source is the same of the well known photon spectrum observed from gamma-rays telescopes. Using a diffusion model in the Galaxy we propagate the source spectra up to the Solar System. We compare our results with the recent experiments and with the LIS modelComment: To appear in the Proceedings of the 14th ICATPP Conference, Villa Olmo 23-27 September 201

Electron hydrodynamics dilemma: whirlpools or no whirlpools

In highly viscous electron systems such as, for example, high quality graphene above liquid nitrogen temperature, a linear response to applied electric current becomes essentially nonlocal, which can give rise to a number of new and counterintuitive phenomena including negative nonlocal resistance and current whirlpools. It has also been shown that, although both effects originate from high electron viscosity, a negative voltage drop does not principally require current backflow. In this work, we study the role of geometry on viscous flow and show that confinement effects and relative positions of injector and collector contacts play a pivotal role in the occurrence of whirlpools. Certain geometries may exhibit backflow at arbitrarily small values of the electron viscosity, whereas others require a specific threshold value for whirlpools to emerge

Pulsar Wind Nebulae as a source of the observed electron and positron excess at high energy: the case of Vela-X

We investigate, in terms of production from pulsars and their nebulae, the cosmic ray positron and electron fluxes above $\sim10$ GeV, observed by the AMS-02 experiment up to 1 TeV. We concentrate on the Vela-X case. Starting from the gamma-ray photon spectrum of the source, generated via synchrotron and inverse Compton processes, we estimated the electron and positron injection spectra. Several features are fixed from observations of Vela-X and unknown parameters are borrowed from the Crab nebula. The particle spectra produced in the pulsar wind nebula are then propagated up to the Solar System, using a diffusion model. Differently from previous works, the omnidirectional intensity excess for electrons and positrons is obtained as a difference between the AMS-02 data and the corresponding local interstellar spectrum. An equal amount of electron and positron excess is observed and we interpreted this excess (above $\sim$100 GeV in the AMS-02 data) as a supply coming from Vela-X. The particle contribution is consistent with models predicting the gamma-ray emission at the source. The input of a few more young pulsars is also allowed, while below $\sim$100 GeV more aged pulsars could be the main contributors.Comment: Accepted for publication in Journal of High Energy Astrophysics (2015