Nonlinear Dynamics of Quantum Systems and Soliton Theory
Eldad Bettelheim, Alexander G. Abanov, Paul Wiegmann
Abstract
We show that space-time evolution of one-dimensional fermionic systems is described by nonlinear equations of soliton theory. We identify a space-time 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 to apply the apparatus of soliton theory to the study of non-linear 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.
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