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Physica Scripta

Magnon-Soliton Phase Shift Analysis of the Classical Continuous Heisenberg Chain

Hans C. Fogedby

Published Jan 1, 1980• 11 citations
Publisher

Abstract

Drawing from Takhtajan's solution we perform a phase shift analysis of the classical continuous Heisenberg chain.
DOI
10.1088/0031-8949/22/4/013

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The permanent profile solutions of the continuous classical Heisenberg chain is reviewed and the author expounds on the application of the inverse scattering method. Extending and amplifying the work of Takhtajan (1977) he exhibits the 'diagonal' action angle representation of the model. The spectrum of the Hamiltonian is exhausted by a magnon band and a soliton band. The magnons have no internal degrees of freedom and can be characterised by the dispersion law E=p 2 . Like the sine Gordon doublet, the solitons have internal structure, they carry a continuous angular momentum m, and are characterised by the dispersion law E=16 sin 2 (p/4)/ mod m mod , in accordance with Tjon and Wright (1977). The continuous Heisenberg chain is a completely integrable Hamiltonian system possessing an infinite number of constants of motion. The recursive procedure for the determination of the conserved integrated densities is established.