1,275 research outputs found
Periodic-Orbit Theory of Anderson Localization on Graphs
We present the first quantum system where Anderson localization is completely
described within periodic-orbit theory. The model is a quantum graph analogous
to an a-periodic Kronig-Penney model in one dimension. The exact expression for
the probability to return of an initially localized state is computed in terms
of classical trajectories. It saturates to a finite value due to localization,
while the diagonal approximation decays diffusively. Our theory is based on the
identification of families of isometric orbits. The coherent periodic-orbit
sums within these families, and the summation over all families are performed
analytically using advanced combinatorial methods.Comment: 4 pages, 3 figures, RevTe
Gauge invariant perturbations around symmetry reduced sectors of general relativity: applications to cosmology
We develop a gauge invariant canonical perturbation scheme for perturbations
around symmetry reduced sectors in generally covariant theories, such as
general relativity. The central objects of investigation are gauge invariant
observables which encode the dynamics of the system. We apply this scheme to
perturbations around a homogeneous and isotropic sector (cosmology) of general
relativity. The background variables of this homogeneous and isotropic sector
are treated fully dynamically which allows us to approximate the observables to
arbitrary high order in a self--consistent and fully gauge invariant manner.
Methods to compute these observables are given. The question of backreaction
effects of inhomogeneities onto a homogeneous and isotropic background can be
addressed in this framework. We illustrate the latter by considering
homogeneous but anisotropic Bianchi--I cosmologies as perturbations around a
homogeneous and isotropic sector.Comment: 39 pages, 1 figur
Theory of 2-kicked Quantum Rotors
We examine the quantum dynamics of cold atoms subjected to {\em pairs} of
closely spaced -kicks from standing waves of light, and find behaviour
quite unlike the well-studied quantum kicked rotor (QKR). Recent experiments
[Jones et al, {\em Phys. Rev. Lett. {\bf 93}, 223002 (2004)}] identified a
regime of chaotic, anomalous classical diffusion. We show that the
corresponding quantum phase-space has a cellular structure, arising from a
unitary matrix with oscillating band-width. The corresponding eigenstates are
exponentially localized, but scale with a fractional power, , in contrast to the QKR for which . The
effect of inter-cell (and intra-cell) transport is investigated by studying the
spectral fluctuations with both periodic as well as `open' boundary conditions.Comment: 12 pages with 14 figure
Dynamical localization, measurements and quantum computing
We study numerically the effects of measurements on dynamical localization in
the kicked rotator model simulated on a quantum computer. Contrary to the
previous studies, which showed that measurements induce a diffusive probability
spreading, our results demonstrate that localization can be preserved for
repeated single-qubit measurements. We detect a transition from a localized to
a delocalized phase, depending on the system parameters and on the choice of
the measured qubit.Comment: 4 pages, 4 figures, research at Quantware MIPS Center
http://www.quantware.ups-tlse.f
Comparison of QG-Induced Dispersion with Standard Physics Effects
One of the predictions of quantum gravity phenomenology is that, in
situations where Planck-scale physics and the notion of a quantum spacetime are
relevant, field propagation will be described by a modified set of laws.
Descriptions of the underlying mechanism differ from model to model, but a
general feature is that electromagnetic waves will have non-trivial dispersion
relations. A physical phenomenon that offers the possibility of experimentally
testing these ideas in the foreseeable future is the propagation of high-energy
gamma rays from GRB's at cosmological distances. With the observation of
non-standard dispersion relations within experimental reach, it is thus
important to find out whether there are competing effects that could either
mask or be mistaken for this one. In this letter, we consider possible effects
from standard physics, due to electromagnetic interactions, classical as well
as quantum, and coupling to classical geometry. Our results indicate that, for
currently observed gamma-ray energies and estimates of cosmological parameter
values, those effects are much smaller than the quantum gravity one if the
latter is first-order in the energy; some corrections are comparable in
magnitude with the second-order quantum gravity ones, but they have a very
different energy dependence.Comment: 8 pages; Version to be published in CQG as a letter; Includes some
new comments and references, but no changes in the result
Distribution of "level velocities" in quasi 1D disordered or chaotic systems with localization
The explicit analytical expression for the distribution function of
parametric derivatives of energy levels ("level velocities") with respect to a
random change of scattering potential is derived for the chaotic quantum
systems belonging to the quasi 1D universality class (quantum kicked rotator,
"domino" billiard, disordered wire, etc.).Comment: 11 pages, REVTEX 3.
Emergent diffeomorphism invariance in a discrete loop quantum gravity model
Several approaches to the dynamics of loop quantum gravity involve
discretizing the equations of motion. The resulting discrete theories are known
to be problematic since the first class algebra of constraints of the continuum
theory becomes second class upon discretization. If one treats the second class
constraints properly, the resulting theories have very different dynamics and
number of degrees of freedom than those of the continuum theory. It is
therefore questionable how these theories could be considered a starting point
for quantization and the definition of a continuum theory through a continuum
limit. We show explicitly in a model that the {\em uniform discretizations}
approach to the quantization of constrained systems overcomes these
difficulties. We consider here a simple diffeomorphism invariant one
dimensional model and complete the quantization using {\em uniform
discretizations}. The model can be viewed as a spherically symmetric reduction
of the well known Husain--Kucha\v{r} model of diffeomorphism invariant theory.
We show that the correct quantum continuum limit can be satisfactorily
constructed for this model. This opens the possibility of treating 1+1
dimensional dynamical situations of great interest in quantum gravity taking
into account the full dynamics of the theory and preserving the space-time
covariance at a quantum level.Comment: 12 pages, Revte
Ring diagrams and electroweak phase transition in a magnetic field
Electroweak phase transition in a magnetic field is investigated within the
one-loop and ring diagram contributions to the effective potential in the
minimal Standard Model. All fundamental fermions and bosons are included with
their actual values of masses and the Higgs boson mass is considered in the
range . The effective potential is real at
sufficiently high temperature. The important role of fermions and -bosons in
symmetry behaviour is observed. It is found that the phase transition for the
field strengths G is of first order but the baryogenesis
condition is not satisfied. The comparison with the hypermagnetic field case is
done.Comment: 16 pages, Latex, changed for a mistake in the numerical par
Enhancement of vacuum polarization effects in a plasma
The dispersive effects of vacuum polarization on the propagation of a strong
circularly polarized electromagnetic wave through a cold collisional plasma are
studied analytically. It is found that, due to the singular dielectric features
of the plasma, the vacuum effects on the wave propagation in a plasma are
qualitatively different and much larger than those in pure vacuum in the regime
when the frequency of the propagating wave approaches the plasma frequency. A
possible experimental setup to detect these effects in plasma is described.Comment: 33 pages, 3 figure
Non-commutative flux representation for loop quantum gravity
The Hilbert space of loop quantum gravity is usually described in terms of
cylindrical functionals of the gauge connection, the electric fluxes acting as
non-commuting derivation operators. It has long been believed that this
non-commutativity prevents a dual flux (or triad) representation of loop
quantum gravity to exist. We show here, instead, that such a representation can
be explicitly defined, by means of a non-commutative Fourier transform defined
on the loop gravity state space. In this dual representation, flux operators
act by *-multiplication and holonomy operators act by translation. We describe
the gauge invariant dual states and discuss their geometrical meaning. Finally,
we apply the construction to the simpler case of a U(1) gauge group and compare
the resulting flux representation with the triad representation used in loop
quantum cosmology.Comment: 12 pages, matches published versio
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