8 research outputs found
Measuring the Hausdorff Dimension of Quantum Mechanical Paths
We measure the propagator length in imaginary time quantum mechanics by Monte
Carlo simulation on a lattice and extract the Hausdorff dimension . We
find that all local potentials fall into the same universality class giving
like the free motion. A velocity dependent action () in the path integral (e.g. electrons moving in
solids, or Brueckner's theory of nuclear matter) yields if and if . We discuss the
relevance of fractal pathes in solid state physics and in , in particular
for the Wilson loop in .Comment: uuencoded and compressed shell archive file. 8 pages with 7 figure
Chern-Simons term in the 4-dimensional SU(2) Higgs Model
Using Seiberg's definition for the geometric charge in SU(2) lattice gauge
theory, we have managed to apply it also to the Chern-Simons term. We checked
the periodic structure and determined the Chern-Simons density on small
lattices and with L=4,\, 6,\mbox{ and }8 near the
critical region in the SU(2) Higgs model. The data indicate that tunneling is
increased at high temperature.Comment: 7 pages plus 4 PS figure
A Lower Bound on in the O(4) Model on Anisotropic Lattices
Results of an investigation of the spin model at finite temperature
using anisotropic lattices are presented. In both the large approximation
and numerical simulations using the Wolff cluster algorithm we find that the
ratio of the symmetry restoration temperature to the Higgs mass
is independent of the anisotropy . From the numerical
simulations we obtain a lower bound of at a value for the Higgs mass , which is lowered
further by about at . Requiring certain timelike
correlation functions to coincide with their spacelike counterparts, quantum
and scaling corrections to the anisotropy are determined and are found to be
small, i.e., the anisotropy is found to be close to the ratio of spacelike and
timelike lattice spacings.Comment: 16 pages with 4 ps figures included. LaTeX file. BI-TP 92/27,
FSU-SCRI-92-101, HLRZ-92-40, TIFR/TH/92-4
Vacuum Tunneling and Periodic Structure in Lattice Higgs Models
Using a geometric definition for the lattice Chern-Simons term in even
dimensions, we have studied the distribution of Chern-Simons numbers for the
2d-U(1) and the 4d-SU(2) lattice Higgs models. The periodic structure of the
distributions is preserved in our lattice formulation and has been examined in
detail. In both cases the finite size effects visible in the distribution of
Chern-Simons numbers are well accounted for by the Haar measure. Moreover, we
find that grows with the spatial volume. We also
find numerical evidence that tunneling in 4d is increased at high temperature.
(PS-File including Figures available via E-mail: [email protected])Comment: 25 pages, 5 figures, LaTeX (+ PicLaTeX) file, HLRZ-93-08 and BI-TP
93/0
Fluctuations of Chern-Simons numbers in the SU(2) Higgs model
Karsch F, Laursen ML, Neuhaus T, Plache B. Fluctuations of Chern-Simons numbers in the SU(2) Higgs model. International journal of modern physics, C. 1993;4(06):1195-1204.We investigate vacuum transitions in lattice higgs models at finite temperature. The 2 dimensional U(1) Higgs model is used as a toy model. In the 4 dimensional SU(2) Higgs model the region of the phase transition and temperatures above it are considered. The couplings (beta, kappa, lambda) = (2.25, 0.27, 0.5) and (8.0, 0.12996, 0.0017235) correspond to masses in lattice units (a(sigma) m(H), a(sigma) m(W)) of (0.02, 0.05) and (0.2, 0.2), respectively. The algorithm is described and a parallelized version is proposed. Taking the influence of the finite lattice into account we discuss temperature effects. We compare our results with perturbative estimates and claim that they link low and high temperature approximations
A Study of symmetry restoration at finite temperature in the O(4) model using anisotropic lattices
Gavai RV, Heller UM, Karsch F, Plache B, Neuhaus T. A Study of symmetry restoration at finite temperature in the O(4) model using anisotropic lattices. Nucl.Phys.Proc.Suppl. 1992;26:539-541
Thermal Fluctuations of Chern-Simons Numbers in the Lattice SU(2) Higgs Model
We study the temperature dependence of the Chern-Simons number fluctuations
in the SU(2) Higgs Model on Euclidean lattices with spatial sizes up to 20^3.
Temperatures well above the Higgs phase transition are achieved on
anisotropic lattices. Numerical results are compared to perturbative results on
finite lattices as well as in continuum perturbation theory. We find
qualitative agreement with perturbative estimates and see at high temperatures
a tendency towards static configurations. Up to temperatures we
find indication that tunneling between vacuums with different Chern-Simons
numbers are still exponentially suppressed. (Full PostScript file available via
Email from [email protected] )Comment: 18 pages latex, (+piclatex+epsf (for 6 figures)), HLRZ-93-39 BI-TP
93/2