Frustrated collisions and unconventional pairing on a quantum superlattice

We solve the problem of scattering and binding of two spin-1/2 fermions on a one-dimensional superlattice with a period of twice the lattice spacing analytically. We find the exact bound states and the scattering states, consisting of a generalized Bethe ansatz augmented with an extra scattering product due to "asymptotic" degeneracy. If a Bloch band is doubly occupied, the extra wave can be a bound state in the continuum corresponding to a single-particle interband transition. In all other cases, it corresponds to a quasi-momentum changing, frustrated collision.Comment: 4 pages, 2 figure

Fluctuations and response in a non-equilibrium micron-sized system

The linear response of non-equilibrium systems with Markovian dynamics satisfies a generalized fluctuation-dissipation relation derived from time symmetry and antisymmetry properties of the fluctuations. The relation involves the sum of two correlation functions of the observable of interest: one with the entropy excess and the second with the excess of dynamical activity with respect to the unperturbed process, without recourse to anything but the dynamics of the system. We illustrate this approach in the experimental determination of the linear response of the potential energy of a Brownian particle in a toroidal optical trap. The overdamped particle motion is effectively confined to a circle, undergoing a periodic potential and driven out of equilibrium by a non-conservative force. Independent direct and indirect measurements of the linear response around a non-equilibrium steady state are performed in this simple experimental system. The same ideas are applicable to the measurement of the response of more general non-equilibrium micron-sized systems immersed in Newtonian fluids either in stationary or non-stationary states and possibly including inertial degrees of freedom.Comment: 12 pages, submitted to J. Stat. Mech., revised versio