Exact solutions for a soliton crystal

L.R. Dodd, Max A. Lohe

    Research output: Contribution to journalComment/debate

    Abstract

    A model field theory in one space and one time dimension for a system of fermions interacting through a scalar field with the self-energy density of the linear sigma model is considered. Exact, periodic solutions of the mean field equations for N Nf fermions on a linear lattice of N cells with Nf fermions per cell are found for arbitrarily large N. The multisoliton solutions are expressed entirely in terms of Jacobi elliptic functions and explicit expressions for the fermion energy spectrum and the energy density of the system are given. In the low-density limit the solution in a single cell reduces to the shallow or deep bag solution previously found by Campbell and Liao. Conditions for the bifurcation of the periodic, crystal solutions from solutions with a constant sigma field at high densities are derived, and comparison is made with earlier numerical work.
    Original languageEnglish
    Pages (from-to)1368-1375
    Number of pages8
    JournalJournal of Mathematical Physics
    Volume32
    Issue number5
    DOIs
    Publication statusPublished - 1991

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