239 research outputs found
Perturbative test of single parameter scaling for 1D random media
Products of random matrices associated to one-dimensional random media
satisfy a central limit theorem assuring convergence to a gaussian centered at
the Lyapunov exponent. The hypothesis of single parameter scaling states that
its variance is equal to the Lyapunov exponent. We settle discussions about its
validity for a wide class of models by proving that, away from anomalies,
single parameter scaling holds to lowest order perturbation theory in the
disorder strength. However, it is generically violated at higher order. This is
explicitely exhibited for the Anderson model.Comment: minor corrections to previous version, to appear in Annales H.
Poincar
RSB Decoupling Property of MAP Estimators
The large-system decoupling property of a MAP estimator is studied when it
estimates the i.i.d. vector from the observation
with
being chosen from a wide range of matrix ensembles, and the noise vector
being i.i.d. and Gaussian. Using the replica method, we show
that the marginal joint distribution of any two corresponding input and output
symbols converges to a deterministic distribution which describes the
input-output distribution of a single user system followed by a MAP estimator.
Under the RSB assumption, the single user system is a scalar channel with
additive noise where the noise term is given by the sum of an independent
Gaussian random variable and correlated interference terms. As the RSB
assumption reduces to RS, the interference terms vanish which results in the
formerly studied RS decoupling principle.Comment: 5 pages, presented in Information Theory Workshop 201
Weak disorder expansion for localization lengths of quasi-1D systems
A perturbative formula for the lowest Lyapunov exponent of an Anderson model on a strip is presented. It is expressed in terms of an energy-dependent doubly stochastic matrix, the size of which is proportional to the strip width. This matrix and the resulting perturbative expression for the Lyapunov exponent are evaluated numerically. Dependence on energy, strip width and disorder strength are thoroughly compared with the results obtained by the standard transfer matrix method. Good agreement is found for all energies in the band of the free operator and this even for quite large values of the disorder strength
Particle-antiparticle asymmetries from annihilations
An extensively studied mechanism to create particle-antiparticle asymmetries
is the out-of-equilibrium and CP violating decay of a heavy particle. Here we
instead examine how asymmetries can arise purely from 2 2 annihilations
rather than from the usual 1 2 decays and inverse decays. We review the
general conditions on the reaction rates that arise from S-matrix unitarity and
CPT invariance, and show how these are implemented in the context of a simple
toy model. We formulate the Boltzmann equations for this model, and present an
example solution.Comment: 5 pages, v2: added reference, v3: some changes to text in response to
comment
Baryon Number Violating Scalar Diquarks at the LHC
Baryon number violating (BNV) processes are heavily constrained by
experiments searching for nucleon decay and neutron-antineutron oscillations.
If the baryon number violation occurs via the third generation quarks, however,
we may be able to avoid the nucleon stability constraints, thus making such BNV
interactions accessible at the LHC. In this paper we study a specific class of
BNV extensions of the standard model (SM) involving diquark and leptoquark
scalars. After an introduction to these models we study one promising extension
in detail, being interested in particles with mass of O(TeV). We calculate
limits on the masses and couplings from neutron-antineutron oscillations and
dineutron decay for couplings to first and third generation quarks. We explore
the possible consequences of such a model on the matter-antimatter asymmetry.
We shall see that for models which break the global baryon minus lepton number
symmetry, (B-L), the most stringent constraints come from the need to preserve
a matter-antimatter asymmetry. That is, the BNV interaction cannot be
introduced if it would remove the matter-antimatter asymmetry independent of
baryogenesis mechanism and temperature. Finally, we examine the phenomenology
of such models at colliders such as the LHC.Comment: 10 pages, 9 figures. v2: references added, some typos corrected. v3:
some small corrections to match published version, no change in conclusion
Spectral averaging techniques for Jacobi matrices with matrix entries
A Jacobi matrix with matrix entries is a self-adjoint block tridiagonal
matrix with invertible blocks on the off-diagonals. Averaging over boundary
conditions leads to explicit formulas for the averaged spectral measure which
can potentially be useful for spectral analysis. Furthermore another variant of
spectral averaging over coupling constants for these operators is presented
Spectral averaging techniques for Jacobi matrices
Spectral averaging techniques for one-dimensional discrete Schroedinger
operators are revisited and extended. In particular, simultaneous averaging
over several parameters is discussed. Special focus is put on proving lower
bounds on the density of the averaged spectral measures. These Wegner type
estimates are used to analyze stability properties for the spectral types of
Jacobi matrices under local perturbations
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