Nonlinear dynamics of quantum systems and soliton theory

E. Bettelheim*, A. G. Abanov, P. Wiegmann

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


We show that spacetime evolution of one-dimensional fermionic systems is described by nonlinear equations of soliton theory. We identify a spacetime dependence of a matrix element of fermionic systems related to the orthogonality catastrophe or boundary states with the τ-function of the modified KP-hierarchy. The established relation allows us to apply the apparatus of soliton theory to the study of nonlinear aspects of quantum dynamics. We also describe a bosonization in momentum space-a representation of a fermion operator by a Bose field in the presence of a boundary state.

Original languageAmerican English
Pages (from-to)F193-F207
JournalJournal of Physics A: Mathematical and Theoretical
Issue number8
StatePublished - 23 Feb 2007
Externally publishedYes


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