Spectral Walls at One Loop

Abstract

A spectral wall is a surface in a moduli space of classically BPS solitons where an internal excitation crosses the continuum mass threshold. It has recently been shown that spectral walls in classical field theory repel solitons whose corresponding internal excitations are excited. We investigate, for the first time, the fate of spectral walls in a quantum theory, calculating the instantaneous acceleration of a wave packet of classically BPS antikinks in the presence of an impurity. We find that, in the quantum theory, the antikinks are repelled even when the bound mode is not excited. Perhaps due to this repulsive force, the dramatic classical effects of the spectral wall are not seen in our quantum calculation.

Kink Form Factors

“…Nonetheless, for problems such as finding the energy spectrum, this light-weight method is sufficient. So far this linearized soliton sector perturbation theory has been used to calculate the two-loop masses of kink ground states [13,14], the leading corrections to the energy required to excite kink shape modes and continuum excitations [15] and the instantaneous acceleration of a kink in the presence of an impurity [16]. For this last calculation, it was necessary to consider the full position-dependence of the kink wave function.…”

Novel constructed dark, bright, and rogue waves of three models of the well-known nonlinear Schrödinger equation

“…Sneaker waves describe a stray wave that shows up on the coast. Rogue waves in the ocean are those that are taller than twice the significant wave height, which is defined as the mean of the most extraordinary third of waves in a wave record in the field of oceanography [18,19]. Due to their extremely huge size for their sea state, rogue waves aren't typically the largest waves in the ocean.…”