3,238 research outputs found
Spectral correlations in systems undergoing a transition from periodicity to disorder
We study the spectral statistics for extended yet finite quasi 1-d systems
which undergo a transition from periodicity to disorder. In particular we
compute the spectral two-point form factor, and the resulting expression
depends on the degree of disorder. It interpolates smoothly between the two
extreme limits -- the approach to Poissonian statistics in the (weakly)
disordered case, and the universal expressions derived for the periodic case.
The theoretical results agree very well with the spectral statistics obtained
numerically for chains of chaotic billiards and graphs.Comment: 16 pages, Late
(Broken) Gauge Symmetries and Constraints in Regge Calculus
We will examine the issue of diffeomorphism symmetry in simplicial models of
(quantum) gravity, in particular for Regge calculus. We find that for a
solution with curvature there do not exist exact gauge symmetries on the
discrete level. Furthermore we derive a canonical formulation that exactly
matches the dynamics and hence symmetries of the covariant picture. In this
canonical formulation broken symmetries lead to the replacements of constraints
by so--called pseudo constraints. These considerations should be taken into
account in attempts to connect spin foam models, based on the Regge action,
with canonical loop quantum gravity, which aims at implementing proper
constraints. We will argue that the long standing problem of finding a
consistent constraint algebra for discretized gravity theories is equivalent to
the problem of finding an action with exact diffeomorphism symmetries. Finally
we will analyze different limits in which the pseudo constraints might turn
into proper constraints. This could be helpful to infer alternative
discretization schemes in which the symmetries are not broken.Comment: 32 pages, 15 figure
Analytical results for the confinement mechanism in QCD_3
We present analytical methods for investigating the interaction of two heavy
quarks in QCD_3 using the effective action approach. Our findings result in
explicit expressions for the static potentials in QCD_3 for long and short
distances. With regard to confinement, our conclusion reflects many features
found in the more realistic world of QCD_4.Comment: 24 pages, uses REVTe
Universal spectral properties of spatially periodic quantum systems with chaotic classical dynamics
We consider a quasi one-dimensional chain of N chaotic scattering elements
with periodic boundary conditions. The classical dynamics of this system is
dominated by diffusion. The quantum theory, on the other hand, depends
crucially on whether the chain is disordered or invariant under lattice
translations. In the disordered case, the spectrum is dominated by Anderson
localization whereas in the periodic case, the spectrum is arranged in bands.
We investigate the special features in the spectral statistics for a periodic
chain. For finite N, we define spectral form factors involving correlations
both for identical and non-identical Bloch numbers. The short-time regime is
treated within the semiclassical approximation, where the spectral form factor
can be expressed in terms of a coarse-grained classical propagator which obeys
a diffusion equation with periodic boundary conditions. In the long-time
regime, the form factor decays algebraically towards an asymptotic constant. In
the limit , we derive a universal scaling function for the form
factor. The theory is supported by numerical results for quasi one-dimensional
periodic chains of coupled Sinai billiards.Comment: 33 pages, REVTeX, 13 figures (eps
Spectral Statistics in Chaotic Systems with Two Identical Connected Cells
Chaotic systems that decompose into two cells connected only by a narrow
channel exhibit characteristic deviations of their quantum spectral statistics
from the canonical random-matrix ensembles. The equilibration between the cells
introduces an additional classical time scale that is manifest also in the
spectral form factor. If the two cells are related by a spatial symmetry, the
spectrum shows doublets, reflected in the form factor as a positive peak around
the Heisenberg time. We combine a semiclassical analysis with an independent
random-matrix approach to the doublet splittings to obtain the form factor on
all time (energy) scales. Its only free parameter is the characteristic time of
exchange between the cells in units of the Heisenberg time.Comment: 37 pages, 15 figures, changed content, additional autho
Photon propagation in a cold axion background with and without magnetic field
A cold relic axion condensate resulting from vacuum misalignment in the early
universe oscillates with a frequency m, where m is the axion mass. We determine
the properties of photons propagating in a simplified version of such a
background where the sinusoidal variation is replaced by a square wave profile.
We prove that previous results that indicated that charged particles moving
fast in such a background radiate, originally derived assuming that all momenta
involved were much larger than m, hold for long wavelengths too. We also
analyze in detail how the introduction of a magnetic field changes the
properties of photon propagation in such a medium. We briefly comment on
possible astrophysical implications of these results.Comment: 17 pages, 4 figures, revised version includes an extended discussion
on physical implication
Testing the Master Constraint Programme for Loop Quantum Gravity II. Finite Dimensional Systems
This is the second paper in our series of five in which we test the Master
Constraint Programme for solving the Hamiltonian constraint in Loop Quantum
Gravity. In this work we begin with the simplest examples: Finite dimensional
models with a finite number of first or second class constraints, Abelean or
non -- Abelean, with or without structure functions.Comment: 23 pages, no figure
Optical probes of the quantum vacuum: The photon polarization tensor in external fields
The photon polarization tensor is the central building block of an effective
theory description of photon propagation in the quantum vacuum. It accounts for
the vacuum fluctuations of the underlying theory, and in the presence of
external electromagnetic fields, gives rise to such striking phenomena as
vacuum birefringence and dichroism. Standard approximations of the polarization
tensor are often restricted to on-the-light-cone dynamics in homogeneous
electromagnetic fields, and are limited to certain momentum regimes only. We
devise two different strategies to go beyond these limitations: First, we aim
at obtaining novel analytical insights into the photon polarization tensor for
homogeneous fields, while retaining its full momentum dependence. Second, we
employ wordline numerical methods to surpass the constant-field limit.Comment: 13 pages, 4 figures; typo in Eq. (5) corrected (matches journal
version
From covariant to canonical formulations of discrete gravity
Starting from an action for discretized gravity we derive a canonical
formalism that exactly reproduces the dynamics and (broken) symmetries of the
covariant formalism. For linearized Regge calculus on a flat background --
which exhibits exact gauge symmetries -- we derive local and first class
constraints for arbitrary triangulated Cauchy surfaces. These constraints have
a clear geometric interpretation and are a first step towards obtaining
anomaly--free constraint algebras for canonical lattice gravity. Taking higher
order dynamics into account the symmetries of the action are broken. This
results in consistency conditions on the background gauge parameters arising
from the lowest non--linear equations of motion. In the canonical framework the
constraints to quadratic order turn out to depend on the background gauge
parameters and are therefore pseudo constraints. These considerations are
important for connecting path integral and canonical quantizations of gravity,
in particular if one attempts a perturbative expansion.Comment: 37 pages, 5 figures (minor modifications, matches published version +
updated references
Testing the Master Constraint Programme for Loop Quantum Gravity IV. Free Field Theories
This is the fourth paper in our series of five in which we test the Master
Constraint Programme for solving the Hamiltonian constraint in Loop Quantum
Gravity. We now move on to free field theories with constraints, namely Maxwell
theory and linearized gravity. Since the Master constraint involves squares of
constraint operator valued distributions, one has to be very careful in doing
that and we will see that the full flexibility of the Master Constraint
Programme must be exploited in order to arrive at sensible results.Comment: 23 pages, no figure
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