Multikink scattering in the $ϕ^6$ model revisited

Abstract

Antikink-kink ( KK) collisions in the φ 6 model exhibit resonant scattering although the φ 6 kinks do not support any bound states to which energy could be transferred. In Phys. Rev. Lett. 107 (2011) 091602 it was conjectured that, instead, energy is transferred to a collective bound mode of the full KK configuration. Here we present further strong evidence for this conjecture.Further, we construct a collective coordinate model (CCM) for KK scattering based on this collective bound mode trapped between the KK pair which allows us to reproduce the full dynamics of KK scattering with striking accuracy. We also study kink-antikink (K K) scattering and its description by a CCM. In this case a significant role of radiation is discovered.

Spontaneous emission from excited quantum kinks

“…In higher-dimensional models, the results of such a study would be relevant to various open questions in cosmology [23]. Needless to say, additional decay channels during quantum kink-antikink collisions could have brutal phenomenological consequences for the resonance windows found in classical field theory [5,24,25].…”

“…These are large amplitude oscillations which, like the kinks themselves, are beyond the reach of perturbation theory. In the multikink sectors and the kink-antikink sector there can be unstable collective states of the combined system [4,5]. In the single kink sector, a shape mode may be excited multiple times, so that its energy is sufficient for it to escape into the meson continuum.…”

Form factors for meson-kink scattering

“…Kink-kink and kink-antikink scattering are known to be rich subjects classically [1,2,3,4,5,6,7] and quantum mechanically [8,9,10]. However the scattering of kinks with elementary mesons has received relatively little attention even classically [11,12,13] let alone in quantum field theory [14,15,16,17,18,19,20,21].…”

“…Is kink-meson scattering important? Recently the interactions of kinks with radiation has entered the spotlight [25,26,27,28,29] as it has been discovered the interactions with bulk degrees of freedom play at least as important of a role in kink dynamics as shape modes [30]. Yet, with some notable exceptions [31,32,33], so far this has largely been at the classical level, where reflectionless kinks are indeed reflectionless.…”

(Anti-)Stokes scattering on kinks

“…Certainly they play a role [6][7][8]. However it was then found [9,10] that such windows appear even in models in which the kink has no internal excitations. Thus, it has become clear that the interactions of kinks with the bulk dynamics are important [10,11].…”