Solitons on the Boundaries of Microscopic Systems

Sierk Pötting, Pierre Meystre, Ewan M. Wright

Tarik Yefsah, Martin W. Zwierlein

6 Li atoms following a one-sided phase imprint. Via tomographic imaging, we observe the formation of a planar dark soliton, and its subsequent snaking and decay into a vortex ring. The latter eventually breaks at the boundary of the superuid, nally leaving behind a single, remnant solitonic vortex. The nodal surface is directly imaged and reveals its decay into a vortex ring via a puncture of the initial soliton plane. At intermediate stages we nd evidence for more exotic structures resembling -solitons. The observed evolution of the nodal surface represents dynamics that occurs at the length scale of the interparticle spacing, thus providing new experimental input for microscopic theories of strongly correlated fermions.

Irina Bariakhtar, Alexander Nazarenko

Richard J. Szabo

Fermion number fractionization in quantum field theory on a finite interval is studied for a (1 + 1) dimensional fermion-soliton system with explicit charge conjugation symmetry breaking. The effects of boundary conditions on the fractional fermion number and the connection with the corresponding open space problem are investigated. It is argued that the open space fractional charges can be correctly reproduced from the finite interval results only through a careful definition of what is meant by the soliton charge. This definition of the charge distinguishes between the fermionic and boundary induced charges in the system, and isolates the soliton from possibly other charged topological objects in the system. It therefore gives a true measure of the localized fractional fermion number induced on the soliton of interest. It is then rigorously proven that the corresponding charge fluctuations vanish, and hence that the induced fractional charge on the soliton is a quantum observable.

Giacomo Mauro D’Ariano, Mario Rasetti

Eldad Bettelheim, Alexander G. Abanov, Paul B. Wiegmann

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.