1,235 research outputs found
Level Repulsion in Constrained Gaussian Random-Matrix Ensembles
Introducing sets of constraints, we define new classes of random-matrix
ensembles, the constrained Gaussian unitary (CGUE) and the deformed Gaussian
unitary (DGUE) ensembles. The latter interpolate between the GUE and the CGUE.
We derive a sufficient condition for GUE-type level repulsion to persist in the
presence of constraints. For special classes of constraints, we extend this
approach to the orthogonal and to the symplectic ensembles. A generalized
Fourier theorem relates the spectral properties of the constraining ensembles
with those of the constrained ones. We find that in the DGUEs, level repulsion
always prevails at a sufficiently short distance and may be lifted only in the
limit of strictly enforced constraints.Comment: 20 pages, no figures. New section adde
The Epstein-Glaser approach to pQFT: graphs and Hopf algebras
The paper aims at investigating perturbative quantum field theory (pQFT) in
the approach of Epstein and Glaser (EG) and, in particular, its formulation in
the language of graphs and Hopf algebras (HAs). Various HAs are encountered,
each one associated with a special combination of physical concepts such as
normalization, localization, pseudo-unitarity, causality and an associated
regularization, and renormalization. The algebraic structures, representing the
perturbative expansion of the S-matrix, are imposed on the operator-valued
distributions which are equipped with appropriate graph indices. Translation
invariance ensures the algebras to be analytically well-defined and graded
total symmetry allows to formulate bialgebras. The algebraic results are given
embedded in the physical framework, which covers the two recent EG versions by
Fredenhagen and Scharf that differ with respect to the concrete recursive
implementation of causality. Besides, the ultraviolet divergences occuring in
Feynman's representation are mathematically reasoned. As a final result, the
change of the renormalization scheme in the EG framework is modeled via a HA
which can be seen as the EG-analog of Kreimer's HA.Comment: 52 pages, 5 figure
Phase Fluctuations near the Chiral Critical Point
The Helmholtz free energy density is parametrized as a function of
temperature and baryon density near the chiral critical point of QCD. The
parametrization incorporates the expected critical exponents and amplitudes. An
expansion away from equilibrium states is achieved with Landau theory. This is
used to calculate the probability that the system is found at a density other
than the equilibrium one. Such fluctuations are predicted to be very large in
heavy ion collisions.Comment: 7 pages, 8 figures, Winter Workshop on Nuclear Dynamics 201
From Luttinger liquid to Altshuler-Aronov anomaly in multi-channel quantum wires
A crossover theory connecting Altshuler-Aronov electron-electron interaction
corrections and Luttinger liquid behavior in quasi-1D disordered conductors has
been formulated. Based on an interacting non-linear sigma model, we compute the
tunneling density of states and the interaction correction to the conductivity,
covering the full crossover.Comment: 15 pages, 3 figures, revised version, accepted by PR
Helfrich-Canham bending energy as a constrained non-linear sigma model
The Helfrich-Canham bending energy is identified with a non-linear sigma
model for a unit vector. The identification, however, is dependent on one
additional constraint: that the unit vector be constrained to lie orthogonal to
the surface. The presence of this constraint adds a source to the divergence of
the stress tensor for this vector so that it is not conserved. The stress
tensor which is conserved is identified and its conservation shown to reproduce
the correct shape equation.Comment: 5 page
Fermions and Loops on Graphs. II. Monomer-Dimer Model as Series of Determinants
We continue the discussion of the fermion models on graphs that started in
the first paper of the series. Here we introduce a Graphical Gauge Model (GGM)
and show that : (a) it can be stated as an average/sum of a determinant defined
on the graph over (binary) gauge field; (b) it is equivalent
to the Monomer-Dimer (MD) model on the graph; (c) the partition function of the
model allows an explicit expression in terms of a series over disjoint directed
cycles, where each term is a product of local contributions along the cycle and
the determinant of a matrix defined on the remainder of the graph (excluding
the cycle). We also establish a relation between the MD model on the graph and
the determinant series, discussed in the first paper, however, considered using
simple non-Belief-Propagation choice of the gauge. We conclude with a
discussion of possible analytic and algorithmic consequences of these results,
as well as related questions and challenges.Comment: 11 pages, 2 figures; misprints correcte
Lattice QCD without topology barriers
As the continuum limit is approached, lattice QCD simulations tend to get
trapped in the topological charge sectors of field space and may consequently
give biased results in practice. We propose to bypass this problem by imposing
open (Neumann) boundary conditions on the gauge field in the time direction.
The topological charge can then flow in and out of the lattice, while many
properties of the theory (the hadron spectrum, for example) are not affected.
Extensive simulations of the SU(3) gauge theory, using the HMC and the closely
related SMD algorithm, confirm the absence of topology barriers if these
boundary conditions are chosen. Moreover, the calculated autocorrelation times
are found to scale approximately like the square of the inverse lattice
spacing, thus supporting the conjecture that the HMC algorithm is in the
universality class of the Langevin equation.Comment: Plain TeX source, 26 pages, 4 figures include
Field theoretical analysis of adsorption of polymer chains at surfaces: Critical exponents and Scaling
The process of adsorption on a planar repulsive, "marginal" and attractive
wall of long-flexible polymer chains with excluded volume interactions is
investigated. The performed scaling analysis is based on formal analogy between
the polymer adsorption problem and the equivalent problem of critical phenomena
in the semi-infinite n-vector model (in the limit ) with a
planar boundary. The whole set of surface critical exponents characterizing the
process of adsorption of long-flexible polymer chains at the surface is
obtained. The polymer linear dimensions parallel and perpendicular to the
surface and the corresponding partition functions as well as the behavior of
monomer density profiles and the fraction of adsorbed monomers at the surface
and in the interior are studied on the basis of renormalization group field
theoretical approach directly in d=3 dimensions up to two-loop order for the
semi-infinite n-vector model. The obtained field- theoretical
results at fixed dimensions d=3 are in good agreement with recent Monte Carlo
calculations. Besides, we have performed the scaling analysis of
center-adsorbed star polymer chains with arms of the same length and we
have obtained the set of critical exponents for such system at fixed d=3
dimensions up to two-loop order.Comment: 22 pages, 12 figures, 4 table
From quantum to classical dynamics: The relativistic model in the framework of the real-time functional renormalization group
We investigate the transition from unitary to dissipative dynamics in the
relativistic vector model with the
interaction using the nonperturbative functional renormalization group in the
real-time formalism. In thermal equilibrium, the theory is characterized by two
scales, the interaction range for coherent scattering of particles and the mean
free path determined by the rate of incoherent collisions with excitations in
the thermal medium. Their competition determines the renormalization group flow
and the effective dynamics of the model. Here we quantify the dynamic
properties of the model in terms of the scale-dependent dynamic critical
exponent in the limit of large temperatures and in
spatial dimensions. We contrast our results to the behavior expected at
vanishing temperature and address the question of the appropriate dynamic
universality class for the given microscopic theory.Comment: 32 pages, 12 captioned figures; revised and extended version accepted
for publication in PR
Nonlinear wave-packet dynamics in a disordered medium
In this article we develop an effective theory of pulse propagation in a
nonlinear and disordered medium. The theory is formulated in terms of a
nonlinear diffusion equation. Despite its apparent simplicity this equation
describes novel phenomena which we refer to as "locked explosion" and
"diffusive" collapse. In this sense the equation can serve as a paradigmatic
model, that can be applied to such distinct physical systems as laser beams
propagating in disordered photonic crystals or Bose-Einstein condensates
expanding in a disordered environment
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