Mott states under the influence of fermion-boson conversion: invasion of superfluidity

I study the influence of fermion-boson conversion near Feshbach resonances on Mott states of Cooper pairs and demonstrate possible invasion of superfluidity. The quantum dynamics of Fermi-Bose gases is studied using both an effective coupled $U(1)\otimes U(1)$ quantum rotor Hamiltonian and a coupled XXZ $\otimes$ XXZ spin Hamiltonian. I also point out two distinct branches of collective modes in superfluid states, one of which involves anti-symmetric phase oscillations in fermionic and bosonic channels and is {\em always} gapped because of fermion-boson conversion.Comment: 5 pages; typos correcte

Data-based stochastic model reduction for the Kuramoto--Sivashinsky equation

The problem of constructing data-based, predictive, reduced models for the Kuramoto-Sivashinsky equation is considered, under circumstances where one has observation data only for a small subset of the dynamical variables. Accurate prediction is achieved by developing a discrete-time stochastic reduced system, based on a NARMAX (Nonlinear Autoregressive Moving Average with eXogenous input) representation. The practical issue, with the NARMAX representation as with any other, is to identify an efficient structure, i.e., one with a small number of terms and coefficients. This is accomplished here by estimating coefficients for an approximate inertial form. The broader significance of the results is discussed.Comment: 23 page, 7 figure