25,026 research outputs found
On the energy momentum dispersion in the lattice regularization
For a free scalar boson field and for U(1) gauge theory finite volume
(infrared) and other corrections to the energy-momentum dispersion in the
lattice regularization are investigated calculating energy eigenstates from the
fall off behavior of two-point correlation functions. For small lattices the
squared dispersion energy defined by is in both cases
negative ( is the Euclidean space-time dimension and the
energy of momentum eigenstates). Observation of has
been an accepted method to demonstrate the existence of a massless photon
() in 4D lattice gauge theory, which we supplement here by a study of
its finite size corrections. A surprise from the lattice regularization of the
free field is that infrared corrections do {\it not} eliminate a difference
between the groundstate energy and the mass parameter of the free
scalar lattice action. Instead, the relation is
derived independently of the spatial lattice size.Comment: 9 pages, 2 figures. Parts of the paper have been rewritten and
expanded to clarify the result
The probability distribution of a trapped Brownian particle in plane shear flows
We investigate the statistical properties of an over-damped Brownian particle
that is trapped by a harmonic potential and simultaneously exposed to a linear
shear flow or to a plane Poiseuille flow. Its probability distribution is
determined via the corresponding Smoluchowski equation, which is solved
analytically for a linear shear flow. In the case of a plane Poiseuille flow,
analytical approximations for the distribution are obtained by a perturbation
analysis and they are substantiated by numerical results. There is a good
agreement between the two approaches for a wide range of parameters.Comment: 5 pages, 4 figur
The unreasonable effectiveness of equilibrium-like theory for interpreting non-equilibrium experiments
There has been great interest in applying the results of statistical
mechanics to single molecule experiements. Recent work has highlighted
so-called non-equilibrium work-energy relations and Fluctuation Theorems which
take on an equilibrium-like (time independent) form. Here I give a very simple
heuristic example where an equilibrium result (the barometric law for colloidal
particles) arises from theory describing the {\em thermodynamically}
non-equilibrium phenomenon of a single colloidal particle falling through
solution due to gravity. This simple result arises from the fact that the
particle, even while falling, is in {\em mechanical} equilibrium (gravitational
force equal the viscous drag force) at every instant. The results are
generalized by appeal to the central limit theorem. The resulting time
independent equations that hold for thermodynamically non-equilibrium (and even
non-stationary) processes offer great possibilities for rapid determination of
thermodynamic parameters from single molecule experiments.Comment: 6 page
Multicanonical Study of the 3D Ising Spin Glass
We simulated the Edwards-Anderson Ising spin glass model in three dimensions
via the recently proposed multicanonical ensemble. Physical quantities such as
energy density, specific heat and entropy are evaluated at all temperatures. We
studied their finite size scaling, as well as the zero temperature limit to
explore the ground state properties.Comment: FSU-SCRI-92-121; 7 pages; sorry, no figures include
Multicanonical Recursions
The problem of calculating multicanonical parameters recursively is
discussed. I describe in detail a computational implementation which has worked
reasonably well in practice.Comment: 23 pages, latex, 4 postscript figures included (uuencoded
Z-compressed .tar file created by uufiles), figure file corrected
Computing Masses from Effective Transfer Matrices
We study the use of effective transfer matrices for the numerical computation
of masses (or correlation lengths) in lattice spin models. The effective
transfer matrix has a strongly reduced number of components. Its definition is
motivated by a renormalization group transformation of the full model onto a
1-dimensional spin model. The matrix elements of the effective transfer matrix
can be determined by Monte Carlo simulation. We show that the mass gap can be
recovered exactly from the spectrum of the effective transfer matrix. As a
first step towards application we performed a Monte Carlo study for the
2-dimensional Ising model. For the simulations in the broken phase we employed
a multimagnetical demon algorithm. The results for the tunnelling correlation
length are particularly encouraging.Comment: (revised version: a few references added) LaTeX file, 25 pages, 6
PostScript figures, (revised version: a few references added
Multi-variable translation equation which arises from homothety
In many regular cases, there exists a (properly defined) limit of iterations
of a function in several real variables, and this limit satisfies the
functional equation (1-z)f(x)=f(f(xz)(1-z)/z); here z is a scalar and x is a
vector. This is a special case of a well-known translation equation. In this
paper we present a complete solution to this functional equation in case f is a
continuous function on a single point compactification of a 2-dimensional real
vector space. It appears that, up to conjugation by a homogeneous continuous
function, there are exactly four solutions. Further, in a 1-dimensional case we
present a solution with no regularity assumptions on f.Comment: 15 page
Particles held by springs in a linear shear flow exhibit oscillatory motion
The dynamics of small spheres, which are held by linear springs in a low
Reynolds number shear flow at neighboring locations is investigated. The flow
elongates the beads and the interplay of the shear gradient with the nonlinear
behavior of the hydrodynamic interaction among the spheres causes in a large
range of parameters a bifurcation to a surprising oscillatory bead motion. The
parameter ranges, wherein this bifurcation is either super- or subcritical, are
determined.Comment: 4 pages, 5 figure
Multi-Overlap Simulations for Transitions between Reference Configurations
We introduce a new procedure to construct weight factors, which flatten the
probability density of the overlap with respect to some pre-defined reference
configuration. This allows one to overcome free energy barriers in the overlap
variable. Subsequently, we generalize the approach to deal with the overlaps
with respect to two reference configurations so that transitions between them
are induced. We illustrate our approach by simulations of the brainpeptide
Met-enkephalin with the ECEPP/2 energy function using the global-energy-minimum
and the second lowest-energy states as reference configurations. The free
energy is obtained as functions of the dihedral and the root-mean-square
distances from these two configurations. The latter allows one to identify the
transition state and to estimate its associated free energy barrier.Comment: 12 pages, (RevTeX), 14 figures, Phys. Rev. E, submitte
Testing Error Correcting Codes by Multicanonical Sampling of Rare Events
The idea of rare event sampling is applied to the estimation of the
performance of error-correcting codes. The essence of the idea is importance
sampling of the pattern of noises in the channel by Multicanonical Monte Carlo,
which enables efficient estimation of tails of the distribution of bit error
rate. The idea is successfully tested with a convolutional code
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