14 research outputs found
Analytical calculation of the Peierls-Nabarro pinning barrier for one-dimensional parametric double-well models
Lattice effects on the kink families of two models for one-dimensional
nonlinear Klein-Gordon systems with double-well on-site potentials are
considered. The analytical expression of the generalized Peierls-Nabarro
pinning potential is obtained and confronted with numerical simulations.Comment: RevTex, 10 pages, 4 figure
Statistical Mechanics of Double sinh-Gordon Kinks
We study the classical thermodynamics of the double sinh-Gordon (DSHG) theory
in 1+1 dimensions. This model theory has a double well potential, thus allowing
for the existence of kinks and antikinks. Though it is nonintegrable, the DSHG
model is remarkably amenable to analysis. Below we obtain exact single kink and
kink lattice solutions as well as the asymptotic kink-antikink interaction. In
the continuum limit, finding the classical partition function is equivalent to
solving for the ground state of a Schrodinger-like equation obtained via the
transfer integral method. For the DSHG model, this equation turns out to be
quasi-exactly solvable. We exploit this property to obtain exact energy
eigenvalues and wavefunctions for several temperatures both above and below the
symmetry breaking transition temperature. The availability of exact results
provides an excellent testing ground for large scale Langevin simulations. The
probability distribution function (PDF) calculated from Langevin dynamics is
found to be in striking agreement with the exact PDF obtained from the ground
state wavefunction. This validation points to the utility of a PDF-based
computation of thermodynamics utilizing Langevin methods. In addition to the
PDF, field-field and field fluctuation correlation functions were computed and
also found to be in excellent agreement with the exact results.Comment: 10 pages, 5 figures (embedded using epsfig), uses RevTeX plus macro
(included). To appear in Physica