507 research outputs found
Avalanche frontiers in dissipative abelian sandpile model as off-critical SLE(2)
Avalanche frontiers in Abelian Sandpile Model (ASM) are random simple curves
whose continuum limit is known to be a Schramm-Loewner Evolution (SLE) with
diffusivity parameter . In this paper we consider the dissipative
ASM and study the statistics of the avalanche and wave frontiers for various
rates of dissipation. We examine the scaling behavior of a number of functions
such as the correlation length, the exponent of distribution function of loop
lengths and gyration radius defined for waves and avalanches. We find that they
do scale with the rate of dissipation. Two significant length scales are
observed. For length scales much smaller than the correlation length, these
curves show properties close to the critical curves and the corresponding
diffusivity parameter is nearly the same as the critical limit. We interpret
this as the ultra violet (UV) limit where corresponding to .
For length scales much larger than the correlation length we find that the
avalanche frontiers tend to Self-Avoiding Walk, the corresponding driving
function is proportional to the Brownian motion with the diffusion parameter
corresponding to a field theory with . This is the infra
red (IR) limit. Correspondingly the central charge decreases from the IR to the
UV point.Comment: 11 Pages, 6 Figure
Abelian Gauge Theory in de Sitter Space
Quantization of spinor and vector free fields in 4-dimensional de Sitter
space-time, in the ambient space notation, has been studied in the previous
works. Various two-points functions for the above fields are presented in this
paper. The interaction between the spinor field and the vector field is then
studied by the abelian gauge theory. The U(1) gauge invariant spinor field
equation is obtained in a coordinate independent way notation and their
corresponding conserved currents are computed. The solution of the field
equation is obtained by use of the perturbation method in terms of the Green's
function. The null curvature limit is discussed in the final stage.Comment: 10 pages, typos corrected, reference adde
Dynamics of Lennard-Jones clusters: A characterization of the activation-relaxation technique
The potential energy surface (PES) of Lennard-Jones clusters is investigated
using the activation-relaxation technique (ART). This method defines events in
the configurational energy landscape as a two-step process: (a) a configuration
is first activated from a local minimum to a nearby saddle-point and (b) is
then relaxed to a new minimum. Although ART has been applied with success to a
wide range of materials such as a-Si, a-SiO2 and binary Lennard-Jones glasses,
questions remain regarding the biases of the technique. We address some of
these questions in a detailed study of ART-generated events in Lennard-Jones
(LJ) clusters, a system for which much is already known. In particular, we
study the distribution of saddle-points, the pathways between configurations,
and the reversibility of paths. We find that ART can identify all trajectories
with a first-order saddle point leaving a given minimum, is fully reversible,
and samples events following the Boltzmann weight at the saddle point.Comment: 8 pages, 7 figures in postscrip
Dust-Charge Variation Effects on Dust ion Acoustic Shock Waves in Four Component Quantum Plasma
The behavior of nonlinear quantum dust ion acoustic (QDIA) shock waves in a collisionless, unmagnetized plasma consisting of inertialess quantum electrons and positrons, classical cold ions and stationary negatively charged dust grains with dust charge variation is investigated using quantum hydrodynamic (QHD) equations. The propagation of small amplitude QDIA shock waves is governed by Burgers equation. It is shown that the dust charge variation plays an important role in the formation of such QDIA shock structures. The dependence of the shock waves amplitude and thickness on the chemical potential is investigated. The present theory is applicable to analyze the formation of nonlinear structures at quantum scales in dense astrophysical objects
Power Spectrum in Krein Space Quantization
The power spectrum of scalar field and space-time metric perturbations
produced in the process of inflation of universe, have been presented in this
paper by an alternative approach to field quantization namely, Krein space
quantization [1,2]. Auxiliary negative norm states, the modes of which do not
interact with the physical world, have been utilized in this method. Presence
of negative norm states play the role of an automatic renormalization device
for the theory.Comment: 8 pages, appear in Int. J. Theor. Phy
Watersheds are Schramm-Loewner Evolution curves
We show that in the continuum limit watersheds dividing drainage basins are
Schramm-Loewner Evolution (SLE) curves, being described by one single parameter
. Several numerical evaluations are applied to ascertain this. All
calculations are consistent with SLE, with ,
being the only known physical example of an SLE with . This lies
outside the well-known duality conjecture, bringing up new questions regarding
the existence and reversibility of dual models. Furthermore it constitutes a
strong indication for conformal invariance in random landscapes and suggests
that watersheds likely correspond to a logarithmic Conformal Field Theory (CFT)
with central charge .Comment: 5 pages and 4 figure
Fermionic One-Loop Corrections to Soliton Energies in 1+1 Dimensions
We demonstrate an unambiguous and robust method for computing fermionic
corrections to the energies of classical background field configurations. We
consider the particular case of a sequence of background field configurations
that interpolates continuously between the trivial vacuum and a widely
separated soliton/antisoliton pair in 1+1 dimensions. Working in the continuum,
we use phase shifts, the Born approximation, and Levinson's theorem to avoid
ambiguities of renormalization procedure and boundary conditions. We carry out
the calculation analytically at both ends of the interpolation and numerically
in between, and show how the relevant physical quantities vary continuously. In
the process, we elucidate properties of the fermionic phase shifts and zero
modes.Comment: 12 pages, 4 figures, uses BoxedEPS;v2: fixed numerical error in
figure dat
Atomic scale simulation of epitaxial growth: Cases of GaAs/GaAs and CdTe/GaAs
We present a kinetic Monte Carlo model describing the growth by molecular beam epitaxy (MBE) of semiconductor compounds and including a local photoemission model with reflection high-energy electron diffraction (RHEED) intensity for comparison. We investigate the cases of both homoepitaxial and heteroepitaxial growth. The valence force field approximation is used for the strain energy calculations in mismatched thin films In homoepitaxial growth of GaAs, we have study the variations of photoemission current and RHEED intensity and examined the GaAs morphology. In high lattice mismatch heteroepitaxial growth (CdTe/GaAs), we have shown the formation of grooves corresponding to (111) facets, precursor to the formation of misfit defects.We present a kinetic Monte Carlo model describing the growth by molecular beam epitaxy (MBE) of semiconductor compounds and including a local photoemission model with reflection high-energy electron diffraction (RHEED) intensity for comparison. We investigate the cases of both homoepitaxial and heteroepitaxial growth. The valence force field approximation is used for the strain energy calculations in mismatched thin films In homoepitaxial growth of GaAs, we have study the variations of photoemission current and RHEED intensity and examined the GaAs morphology. In high lattice mismatch heteroepitaxial growth (CdTe/GaAs), we have shown the formation of grooves corresponding to (111) facets, precursor to the formation of misfit defects
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