32,394 research outputs found
Ermakov approach for the one-dimensional Helmholtz Hamiltonian
For the one-dimensional Helmholtz equation we write the corresponding
time-dependent Helmholtz Hamiltonian in order to study it as an Ermakov problem
and derive geometrical angles and phases in this contextComment: 6 pages, LaTe
Core-crust transition pressure for relativistic slowly rotating neutron stars
We study the influence of core-\textit{crust} transition pressure changes on
the general dynamical properties of neutron star configurations. First we study
the matching conditions in core-\textit{crust} transition pressure region,
where phase transitions in the equation of state causes energy density jumps.
Then using a surface \textit{crust} approximation, we can construct
configurations where the matter is described by the equation of state of the
core of the star and the core-\textit{crust} transition pressure. We will
consider neutron stars in the slow rotation limit, considering perturbation
theory up to second order in the angular velocity so that the deformation of
the star is also taken into account. The junction determines the parameters of
the star such as total mass, angular and quadrupolar momentum.Comment: 4 pages, 1 figur
Simple quantum model for light depolarization
Depolarization of quantum fields is handled through a master equation of the
Lindblad type. The specific feature of the proposed model is that it couples
dispersively the field modes to a randomly distributed atomic reservoir, much
in the classical spirit of dealing with this problem. The depolarizing dynamics
resulting from this model is analyzed for relevant states.Comment: Improved version. Accepted for publication in the Journal of the
Optical Society of America
On the Stability of Stochastic Parametrically Forced Equations with Rank One Forcing
We derive simplified formulas for analyzing the stability of stochastic
parametrically forced linear systems. This extends the results in [T. Blass and
L.A. Romero, SIAM J. Control Optim. 51(2):1099--1127, 2013] where, assuming the
stochastic excitation is small, the stability of such systems was computed
using a weighted sum of the extended power spectral density over the
eigenvalues of the unperturbed operator. In this paper, we show how to convert
this to a sum over the residues of the extended power spectral density. For
systems where the parametric forcing term is a rank one matrix, this leads to
an enormous simplification.Comment: 16 page
Discrete phase-space structure of -qubit mutually unbiased bases
We work out the phase-space structure for a system of qubits. We replace
the field of real numbers that label the axes of the continuous phase space by
the finite field \Gal{2^n} and investigate the geometrical structures
compatible with the notion of unbiasedness. These consist of bundles of
discrete curves intersecting only at the origin and satisfying certain
additional properties. We provide a simple classification of such curves and
study in detail the four- and eight-dimensional cases, analyzing also the
effect of local transformations. In this way, we provide a comprehensive
phase-space approach to the construction of mutually unbiased bases for
qubits.Comment: Title changed. Improved version. Accepted for publication in Annals
of Physic
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