How to Count Kinks: From the Continuum to the Lattice and Back

We present lattice simulations of nonequilibrium quantum fields in Minkowskian space-time. Starting from a non-thermal initial state, the real-time quantum ensemble in 3+1 dimensions is constructed by a stochastic process in an additional (5th) ``Langevin-time''. For the example of a self-interacting scalar field we show how to resolve apparent unstable Langevin dynamics, and compare our quantum results with those obtained in classical field theory. Such a direct simulation m...

A ri proof of the effective potential (lattice corrections included) deduced by Trullinger and Sasaki is given. Using asymptotic methods from the theory of differential equations depending on a large parameter, the lattice corrections to the kink and kink-kink contributions to the free energy are calculated. The results are in complete agreement with a first order correction to the energy of the static kink.

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 solvi...

In this paper we use 1D quantum mechanical systems with Higgs-like interaction potential to study the emergence of topological objects at finite temperature. Two different model systems are studied, the standard double-well potential model and a newly introduced discrete kink model. Using Monte-Carlo simulations as well as analytic methods, we demonstrate how kinks become abundant at low temperatures. These results may shed useful insights on how topological phenomena may occ...

The study of nonlinear phenomena in systems with many degrees of freedom often relies on complex numerical simulations. In trying to model realistic situations, these systems may be coupled to an external environment which drives their dynamics. For nonlinear field theories coupled to thermal (or quantum) baths, discrete lattice formulations must be dealt with extreme care if the results of the simulations are to be interpreted in the continuum limit. Using techniques from re...

In this thesis, we study interactions between topological defects in two-dimensional spacetimes. These defects are called kinks. They are solutions of scalar field theories with localized energy which propagate without losing its shape. In order to understand the resonance phenomenon exhibited by those models, we built a toy model where the kink's vibrational mode turns into a quasinormal mode. This causes the suppression of resonance windows and, consequently, its fractal st...

Motivated by bubble nucleation in first order phase transitions, we question the validity of the effective potential for inhomogeneous configurations. In an attempt to get some insight into the importance of derivative terms, we analyze a simple model, a kink in (1+1) dimensions and zero temperature. We evaluate the energy shift from the quantum fluctuations about the non-uniform background ({\it i.e.}, the effective action) and compare it to the energy from the effective pot...

By means of dynamical mean field theory calculations, it was recently discovered that kinks generically arise in strongly correlated systems, even in the absence of external bosonic degrees of freedoms such as phonons. However, the physical mechanism behind these kinks remained unclear. On the basis of the perturbative and numerical renormalization group theory, we herewith identify these kinks as the effective Kondo energy scale of the interacting lattice system which is sho...

The q-state Potts model in two dimensions exhibits a first-order transition for q>4. As q->4+ the correlation length at this transition diverges. We argue that this limit defines a massive integrable quantum field theory whose lowest excitations are kinks connecting 4+1 degenerate ground states. We construct the S-matrix of this theory and the two-particle form factors, and hence estimate a number of universal amplitude ratios. These are in very good agreement with the result...

In the paper, we make use of Manton's analytical method to investigate the force between kink and the anti-kink with large distance in $1+1$ dimensional field theory. The related potential has infinite order corrections of exponential pattern, and coefficients for each order are determined. These coefficients can also be obtained by solving the equation of the fluctuation around the vacuum. At the lowest order, the kink lattice represents the Toda lattice. With higher order c...