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Title: Semiclassical quantization of the one- and two-kink dark solitons
Authors: Martinez, J.C. 
Jalil, M.B.A. 
Issue Date: 1-Apr-2009
Citation: Martinez, J.C., Jalil, M.B.A. (2009-04-01). Semiclassical quantization of the one- and two-kink dark solitons. Physical Review A - Atomic, Molecular, and Optical Physics 79 (4) : -. ScholarBank@NUS Repository.
Abstract: Drawing from an analogy with a linear particle-chain model, we develop a picture of the dark optical soliton as a composite of a background and notch each enjoying a certain degree of independence. The semiclassical quantization procedure of Dashen [Phys. Rev. D 11, 3424 (1975)] is modified to allow for the separate quantization of these two entities. We apply our results to the one-kink and two-kink dark solitons. For both we find that the fluctuations about the notch can be understood as a bound state of bosons held by an attractive delta potential while the background fluctuations are seen as an ensemble of oscillators with a slightly repulsive interaction. We show that the collision effects are small for the two-kink soliton. The quantum numbers emerging from this analysis are interpreted in terms of the number of particles. Moreover, the topological character of the dark soliton also appears naturally in our description. We speculate on the possibility of fractional quantum numbers and derive the repulsive interaction of two dark solitons from the framework developed for the two-kink soliton. © 2009 The American Physical Society.
Source Title: Physical Review A - Atomic, Molecular, and Optical Physics
ISSN: 10502947
DOI: 10.1103/PhysRevA.79.043805
Appears in Collections:Staff Publications

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