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Abstract:

We study the orientational dynamics of heavy silica microrods flowing through a microfluidic channel. Comparing experiments and Brownian dynamics simulations we identify different particle orbits, in particular in-plane tumbling behavior, which cannot be explained by classical Jeffery theory, and we relate this behavior to the rotational diffusion of the rods. By constructing the full, three-dimensional, orientation distribution, we describe the rod trajectories and quantify the persistence of Jeffery orbits using temporal correlation functions of the Jeffery constant. We find that our colloidal rods lose memory of their initial configuration in about a second, corresponding to half a Jeffery period.

Abstract:

I solve a quantum chain whose Hamiltonian is comprised solely of local four-fermi operators by constructing free-fermion raising and lowering operators. The free-fermion operators are both non-local and highly non-linear in the local fermions. This construction yields the complete spectrum of the Hamiltonian and an associated classical transfer matrix. The spatially uniform system is gapless with dynamical critical exponent z=3/2, while staggering the couplings gives a more conventional free-fermion model with an Ising transition. The Hamiltonian is equivalent to that of a spin-1/2 chain with next-nearest-neighbour interactions, and has a supersymmetry generated by a sum of fermion trilinears. The supercharges are part of a large non-abelian symmetry algebra that results in exponentially large degeneracies. The model is integrable for either open or periodic boundary conditions but the free-fermion construction only works for the former, while for the latter the extended symmetry is broken and the degeneracies split.