Nonlinear dynamics of spin and charge in spin-Calogero model

Note: Special date and time; Monday at 11 AM
Speaker: Fabio Franchini, ICTP, Triste, Italy

When: October 5, 2009 (Mon), 11:00AM to 12:00PM (add to my calendar)

This event is part of the Condensed Matter Theory Seminar Series.

Abstract:
We study the full, nonlinear dynamics of spin and charge in the spin-Calogero model, by constructing a collective, i.e. hydrodynamic, description of the model. The latter is an integrable 1-D model of quantum spin-1/2 particles interacting through inverse-square interaction and exchange. We construct the collective Hamiltonian in a semi-classical regime where gradient corrections to the exact hydrodynamic formulation of the theory may be neglected. In this approximation, the equations of motion can be decoupled and written as to a set of independent Riemann-Hopf (or inviscid Burgers’) equations for the dressed Fermi momenta. We study the dynamics of some non-equilibrium spin-charge configurations for times smaller than the time-scale of the gradient catastrophe and we find an interesting interplay between spin and charge degrees of freedom. We also consider the limit of large coupling parameter and show that the resulting hydrodynamics for the spin sector describes the so-called Haldane-Shastry model. Finally, we show how this hydrodynamic description allows for the calculation of correlation functions that cannot be considered with conventional bosonization, such as the Emptiness Formation Probability. (http://arxiv.org/abs/0904.3762, http://arxiv.org/abs/0908.2652)