21,408 research outputs found
Propagation and perfect transmission in three-waveguide axially varying couplers
We study a class of three-waveguide axially varying structures whose dynamics
are described by the su(3) algebra. Their analytic propagator can be found
based on the corresponding Lie group generators. In particular, we show that
the field propagator corresponding to three-waveguide structures that have
arbitrarily varying coupling coefficients and identical refractive indices is
associated with the orbital angular momentum algebra. The conditions necessary
to achieve perfect transmission from the first to the last waveguide element
are obtained and particular cases are elucidated analytically.Comment: 5 pages, 4 figure
Physical consequences of PNP and the DMRG-annealing conjecture
Computational complexity theory contains a corpus of theorems and conjectures
regarding the time a Turing machine will need to solve certain types of
problems as a function of the input size. Nature {\em need not} be a Turing
machine and, thus, these theorems do not apply directly to it. But {\em
classical simulations} of physical processes are programs running on Turing
machines and, as such, are subject to them. In this work, computational
complexity theory is applied to classical simulations of systems performing an
adiabatic quantum computation (AQC), based on an annealed extension of the
density matrix renormalization group (DMRG). We conjecture that the
computational time required for those classical simulations is controlled
solely by the {\em maximal entanglement} found during the process. Thus, lower
bounds on the growth of entanglement with the system size can be provided. In
some cases, quantum phase transitions can be predicted to take place in certain
inhomogeneous systems. Concretely, physical conclusions are drawn from the
assumption that the complexity classes {\bf P} and {\bf NP} differ. As a
by-product, an alternative measure of entanglement is proposed which, via
Chebyshev's inequality, allows to establish strict bounds on the required
computational time.Comment: Accepted for publication in JSTA
A single structured light beam as an atomic cloud splitter
We propose a scheme to split a cloud of cold non-interacting neutral atoms
based on their dipole interaction with a single structured light beam which
exhibits parabolic cylindrical symmetry. Using semiclassical numerical
simulations, we establish a direct relationship between the general properties
of the light beam and the relevant geometric and kinematic properties acquired
by the atomic cloud as its passes through the beam.Comment: 10 pages, 5 figure
Ermakov-Lewis symmetry in photonic lattices
We present a class of waveguide arrays that is the classical analog of a
quantum harmonic oscillator where the mass and frequency depend on the
propagation distance. In these photonic lattices refractive indices and second
neighbor couplings define the mass and frequency of the analog quantum
oscillator, while first neighbor couplings are a free parameter to adjust the
model. The quantum model conserves the Ermakov-Lewis invariant, thus the
photonic crystal also posses this symmetry.Comment: 8 pages, 3 figure
Variational approach for walking solitons in birefringent fibres
We use the variational method to obtain approximate analytical expressions
for the stationary pulselike solutions in birefringent fibers when differences
in both phase velocities and group velocities between the two components and
rapidly oscillating terms are taken into account. After checking the validity
of the approximation we study how the soliton pulse shape depends on its
velocity and nonlinear propagation constant. By numerically solving the
propagation equation we have found that most of these stationary solutions are
stable.Comment: LaTeX2e, uses graphicx package, 23 pages with 8 figure
The group of strong Galois objects associated to a cocommutative Hopf quasigroup
Let H be a cocommutative faithfully flat Hopf quasigroup in a strict
symmetric monoidal category with equalizers. In this paper we introduce the
notion of (strong) Galois H-object and we prove that the set of isomorphism
classes of (strong) Galois H-objects is a (group) monoid which coincides, in
the Hopf algebra setting, with the Galois group of H-Galois objects introduced
by Chase and Sweedler
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