Quasi-periodic orbits in the scalar classical λϕ4 field theory

Belova, T. I.; Kudryavtsev, A. E.

doi:10.1016/0167-2789(88)90085-1

Cited by 50 publications

(54 citation statements)

References 7 publications

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“…Note that in Ref. [38] it was shown, however, that the escape windows can be reproduced within the collective coordinate method if the interaction with the vibrational mode of the kink is taken into account. A recent publication [29] should be mentioned here, where the vibrational modes of the kinks have been taken into account in the framework of the collective coordinate approach.…”

Section: Kink Collisions In the ϕ 6 Modelmentioning

confidence: 99%

Kink interactions in the(1+1)-dimensionalφ6model

2014

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We study kink scattering processes in the (1+1)-dimensional ϕ 6 model in the framework of the collective coordinate approximation. We find critical values of the initial velocities of the colliding kinks. These critical velocities distinguish different regimes of collisions. The exact equation of motion for the ϕ 6 model is also solved numerically with the same initial conditions.We discuss advantages and disadvantages of the collective coordinate approximation, and also outline its applicability limits. Resonance phenomena and the so-called escape windows are also observed in the kink collisions.

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Section: Kink Collisions In the ϕ 6 Modelmentioning

confidence: 99%

Kink interactions in the(1+1)-dimensionalφ6model

2014

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“…The escape of the pair kink-antikink from their mutual attraction is verified when the energy of the vibrational mode is less than the kinetic energy of the colliding kinks [9].…”

Section: Introductionmentioning

confidence: 99%

“…The former two expressions can be used to understand quantitatively how the windows centers scale with n [9], with the successive windows with even smaller thickness accumulating…”

Section: Introductionmentioning

confidence: 99%

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Kink-antikink collisions for twin models

et al. 2014

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In this work we consider kink-antikink collisions for some classes of (1, 1)-dimensional nonlinear models. We are particularly interested to investigate in which aspect the presence of a general kinetic content in the Lagrangian could be revealed in a collision process. We consider a particular class of models known as twin theories, where different models lead to same solutions for the equations of motion and same energy density profile. The theories can be distinguished in the level of linear stability of defect structure. We study a class of k-defect theories depending on a parameter M which is the twin theory of the usual φ 4 theory with standard dynamics. For M → ∞ both models are characterized by the same potential. In the regime 1/M 2 << 1, we obtain analytically the spectrum of excitations around the kink solution. It is shown that with the increasing on the parameter 1/M 2 : i) the gap between the zero-mode and the first-excited mode increases and ii) the tendency of one-bounce collision between kink-antikink increases. We numerically investigate kink-antikink scattering, looking for the influence of the parameter changing for the thickness and number of two-bounce windows, and confronting the results with our analytical findings.

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“…The static scalar equation of motion has a kink and an antikink solution φ K and φ A , 16) where z 0 is the center of the (anti-)kink. We will use λ = 2, D = 1 throughout 2 .…”

Section: Kinks and Boundariesmentioning

confidence: 99%

Particle transfer in braneworld collisions

Saffin

Tranberg

2007

J. High Energy Phys.

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We study the behaviour of fermions localized on moving kinks as these collide with either antikinks or spacetime boundaries. We numerically solve for the evolution of the scalar kinks and the bound (i.e. localized) fermion modes, and calculate the number of fermions transfered to the antikink and boundary in terms of Bogoliubov coefficients. Interpreting the boundaries as the brane on which we live, this models the ability of fermions on branes incoming from the bulk to "stick" on the world brane, even when the incoming branes bounce back into the bulk.

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Quasi-periodic orbits in the scalar classical λϕ4 field theory

Cited by 50 publications

References 7 publications

Kink interactions in the(1+1)-dimensionalφ6model

Kink interactions in the(1+1)-dimensionalφ6model

Kink-antikink collisions for twin models

Particle transfer in braneworld collisions

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