17,199 research outputs found
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 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 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 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 100 GeV more aged pulsars could be the main contributors.Comment: Accepted for publication in Journal of High Energy Astrophysics
(2015
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