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Nonlinear Dynamics of Quantum Systems and Soliton Theory

Eldad Bettelheim·Alexander G. Abanov·Paul Wiegmann
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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 {\it 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 {\it 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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Eldad Bettelheim, Alexander G. Abanov, Paul Wiegmann. 2006-10-26. Nonlinear Dynamics of Quantum Systems and Soliton Theory. https://arxiv.org/abs/nlin/0605006

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