Classical dynamics of the Abelian Higgs model from the critical point and beyond

Abstract

We present two different families of solutions of the U(1)-Higgs model in a (1 + 1) dimensional setting leading to a localization of the gauge field. First we consider a uniform background (the usual vacuum), which corresponds to the fully higgsed-superconducting phase. Then we study the case of a non-uniform background in the form of a domain wall which could be relevantly close to the critical point of the associated spontaneous symmetry breaking. For both cases we obtain approximate analytical nodeless and nodal solutions for the gauge field resulting as bound states of an effective Pöschl-Teller potential created by the scalar field. The two scenaria differ only in the scale of the characteristic localization length. Numerical simulations confirm the validity of the obtained analytical solutions. Additionally we demonstrate how a kink may be used as a mediator driving the dynamics from the critical point and beyond.

Scattering of the φ8 kinks with power-law asymptotics

“…Today, the study of the properties of topological defects is a vast and very fast developing area. Interactions of kinks with each other and with impurities have been studied [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43]; see also results for branes [44], bubble-like structures [45,46], interactions of breathers [47], and so on [48][49][50][51][52][53][54]. Many interesting and important results have been obtained in the (1+1)dimensional models with polynomial potentials: ϕ 4 , ϕ 6 , ϕ 8 , and so on [55][56][57][58][59][60][61][63][64][65][66][67][68][69][70]].…”

“…and so on [48][49][50][51][52][53][54]. Many interesting and important results have been obtained in the (1+1)dimensional models with polynomial potentials: ϕ 4 , ϕ 6 , ϕ 8 , and so on [55][56][57][58][59][60][61][63][64][65][66][67][68][69][70]].…”

Amplitude Higgs Mode and Admittance in Superconductors with a Moving Condensate

“…The AM in the superconductors resembles gapful Higgs modes in field theories that can be interpreted as Higgs bosons [6]. The similarity of quantum field theory and cosmology to superconductivity and other ordered phases in condensed matter has intensively been discussed previously [7][8][9][10] and the attempts to probe the AM in superconductors was stimulated to a large extent by this similarity.…”

“…The dashed line [38][39][40] corresponds to the real part of the first term in Eq. (10) [described by I (1) 0 in Eq. ( 45) of Supplemental Material].…”

“…The peak in panel (a) corresponds to the second term in Eq. (10) [described by δI (1) in Eq. ( 48) of Supplemental Material].…”