Creating kinks from particles.pdf

a r X i v : 0 8 0 3 .0 6 7 0 v 3 [ h e p - t h ] 2 5 A u g 2 0 0 8 From Particles to Kinks Sourish Dutta Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37235 D. A. Steer APC, UMR 7164, 10 rue Alice Domon et Le?onie Duquet, 75205 Paris Cedex 13, France Tanmay Vachaspati Institute for Advanced Study, Princeton, NJ 08540 CERCA, Department of Physics, Case Western Reserve University, Cleveland, OH 44106-7079 We study the creation of solitons from particles, using the λφ4 model as a prototype. We consider the scattering of small, identical, wave pulses, that are equivalent to a sequence of particles, and find that kink-antikink pairs are created for a large region in parameter space. We also find that scattering at low velocities is favorable for creating solitons that have large energy compared to the mass of a particle. A wide variety of systems, ranging from polyacetylene and Josephson junctions to high energy particle physics models, contain non-perturbative, “soliton” or “solitary wave” excitations in addition to pertubative “particle” excitations [1]. An important unsolved problem is to find ways to transition from the particle sector to the soliton sector. At a pragmatic level, we would like to develop implementable schemes that might enable solitons to be built out of particles. A transition from two energetic particles to solitons, however, is known to be exponen- tially suppressed e.g. [2] (for a review see [3]) though it may occur more readily in certain situations, such as in the background of a pre-existing kink,[4, 5]. In this paper, we will determine a class of initial condi- tions that consist of small amplitude perturbations that scatter and successfully lead to the production of a kink- antikink (“kk?”) pair in 1+1 dimensions. A trivial scheme to determine such a set of initial conditions is to time reverse the annihilation of kk?. Then the time reversed particles would assemble into an outgoing kk?. However, in any pr