Evidence for the Unbinding of the $ϕ^4$ Kink's Shape Mode

Evslin, Jarah

doi:10.48550/arxiv.2104.14387

Cited by 2 publications

(2 citation statements)

References 24 publications

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“…Finally, one may also ask about the importance of spectral walls in quantum theory where the vibrational modes can play a significant role, see e.g. [41]- [46].…”

Section: Discussionmentioning

confidence: 99%

Spectral walls in multifield kink dynamics

Adam,

Oles,

Romanczukiewicz

et al. 2021

Preprint

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We show that spectral walls are common phenomena in the dynamics of kinks in (1+1) dimensions. They occur in models based on two or more scalar fields with a nonempty Bogomol'nyi-Prasam-Sommerfield (BPS) sector, hosting two zero modes, where they are one of the main factors governing the soliton dynamics. We also show that spectral walls appear as singularities of the dynamical vibrational moduli space. I. INTRODUCTIONDespite their prevalence in many physical systems, there is no satisfactory understanding of interactions of topological solitons in generic, non-integrable models. Even in the φ 4 model in (1+1) dimensions, which is probably the simplest, prototypic theory with topological kinks, there is no quantitative explanation of the involved, chaotic pattern of final state formation in kinkantikink collisions, like soliton annihilation or their backscattering after several bounces, although a significant role of the normal modes has been conjectured [1]. There are, in fact, three qualitatively distinct ways in which solitons can interact. First of all, depending on their topological charge and relative orientation, solitons attract or repel each other, deforming their shapes. Secondly, most solitons carry internal degrees of freedom (DoF), i.e., normal modes, which can be easily excited during collisions. The transfer of energy from the kinetic to the internal DoF can further complicate the soliton dynamics. Finally, solitons couple to radiation which also may lead to the appearance of important phenomena (like, e.g., negative radiation pressure). All these factors contribute to the fascinating complexity of solitonic interactions.A common strategy which may provide further insight into the complicated dynamics of solitonic collisions is to reduce the full field theory (a system of partial differential equations with infinitely many DoF) to a mechanical like system with a finite number of DoF, which evolve via ordinary differential equations [2]. These reduced effective DoF, called moduli, span a subset of field configurations which should capture the main aspects of the dynamics. Of course, one of the main issues is to identify the proper moduli. A natural and simply guess is to consider the lightest

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“…Finally, one may also ask about the importance of spectral walls in quantum theory where the vibrational modes can play a significant role, see e.g. [41]- [46].…”

Section: Discussionmentioning

confidence: 99%

Spectral walls in multifield kink dynamics

Adam,

Oles,

Romanczukiewicz

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…For example, in the context of (3+1)dimensional Skyrmions, it may improve the vibrational quantization procedure [41]. This is, of course, related to the question of possible quantum corrections to kink dynamics, recently reconsidered by Evslin [42]. Quantum corrections can contribute to shape mode dynamics, and therefore presumably to the dynamics of Derrick modes at any order.…”

Section: Discussionmentioning

confidence: 99%

Relativistic Moduli Space for Kink Collisions

Adam,

Manton,

Oles

et al. 2021

Preprint

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The moduli space approximation to kink dynamics permits a relativistic generalization if the Derrick scaling parameter is used as a collective coordinate. We develop a perturbative approach to the resulting relativistic moduli space by expanding the Derrick scaling parameter about unity and treating the higher-order Derrick modes as new degrees of freedom. This approach allows us to resolve apparent (coordinate) singularities order-by-order, and systematically incorporates relativistic corrections perturbatively in multi-soliton scattering. It gives an excellent description of kink-antikink collisions in φ 4 field theory already at first order.

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Evidence for the Unbinding of the $ϕ^4$ Kink's Shape Mode

Cited by 2 publications

References 24 publications

Spectral walls in multifield kink dynamics

Spectral walls in multifield kink dynamics

Relativistic Moduli Space for Kink Collisions

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