Condensed Matter Theory

Abstract:

In many integrable models static (equal time) correlation functions of local observables after a quantum quench relax to stationary values, which are described by a generalized Gibbs ensemble (GGE). Here we establish that the same holds true for dynamic (non equal time) correlation functions. More generally we show that in the absence of long-range interactions in the final Hamiltonian, the dynamics is determined by the same ensemble that describes static correlations. When the latter is a GGE the basic form of the fluctuation dissipation theorem holds, although the absorption and emission spectra are not simply related as in the thermal case. For quenches in the transverse field Ising chain (TFIC) we derive explicit expressions for the time evolution of dynamic order parameter correlators after a quench.

Abstract:

Swimming in circles occurs in a variety of situations at low Reynolds number. Here we propose a simple model for a swimmer that undergoes circular motion, generalising the model of a linear swimmer proposed by Najafi and Golestanian (Phys. Rev. E 69, 062901 (2004)). Our model consists of three solid spheres arranged in a triangular configuration, joined by two links of time-dependent length. For small strokes, we discuss the motion of the swimmer as a function of the separation angle between its links. We find that swimmers describe either clockwise or anticlockwise circular motion depending on the tilting angle in a non-trivial manner. The symmetry of the swimmer leads to a quadrupolar decay of the far flow field. We discuss the potential extensions and experimental realisation of our model.