Condensed Matter Theory

Abstract:

We explore the flow of a nematic liquid crystal in microfluidic channels with a rectangular cross section through experiments and numerical modeling. The flow profile and the liquid crystal orientational profile show three distinct regimes of weak, medium, and strong flow as the driving pressure is varied. These are identified by comparing polarizing optical microscopy experiments and numerical solutions of the nematofluidic equations of motion. The relative stability of the regimes is related to the de Gennes characteristic shear-flow lengths e1 and e2, together with the channel's aspect ratio w/d. Finally, we show that the liquid crystalline microfluidic flow can be fully steered from left to right of a simple microchannel by applying transverse temperature gradients. © 2013 American Physical Society.

Abstract:

We develop the theory of electronic Mach-Zehnder interferometers built from quantum Hall edge states at the Landau level filling factor ν=2, which have been investigated in a series of recent experiments and theoretical studies. We show that a detailed treatment of the dephasing and nonequlibrium transport is made possible by using bosonization combined with refermionization to study a model in which interactions between electrons are short range. In particular, this approach allows a nonperturbative treatment of electron tunneling at the quantum point contacts that act as beam splitters. We find an exact analytic expression at an arbitrary tunneling strength for the differential conductance of an interferometer with arms of equal length and obtain numerically exact results for an interferometer with unequal arms. We compare these results with previous perturbative and approximate ones and with observations. © 2013 American Physical Society.

Abstract:

We characterize in detail a wave function conceivable in fractional quantum Hall systems where a spin or equivalent degree of freedom is present. This wave function combines the properties of two previously proposed quantum Hall wave functions, namely the non-Abelian spin-singlet state and the nonunitary Gaffnian wave function. This is a spin-singlet generalization of the spin-polarized Gaffnian, which we call the "spin-singlet Gaffnian" (SSG). In this paper we present evidence demonstrating that the SSG corresponds to the ground state of a certain local Hamiltonian, which we explicitly construct, and, further, we provide a relatively simple analytic expression for the unique ground-state wave functions, which we define as the zero energy eigenstates of that local Hamiltonian. In addition, we have determined a certain nonunitary, rational conformal field theory which provides an underlying description of the SSG and we thus conclude that the SSG is ungapped in the thermodynamic limit. In order to verify our construction, we implement two recently proposed techniques for the analysis of fractional quantum Hall trial states: The "spin dressed squeezing algorithm," and the "generalized Pauli principle." © 2013 American Physical Society.

Abstract:

We present results showing how water drops, produced by ink-jet printing, spread on surfaces patterned with lattices of diamond or triangular posts. Considering post widths typically ∼7 μm and lattice spacings between 15 and 40 μm, we observe drop shapes with 3, 4 and 6-fold symmetry, depending on both the symmetry of the lattice and the shape of the posts. This is a result of the different mechanisms of interface pinning and depinning which depend on the direction of the contact line motion with respect to the post shape. Lattice Boltzmann simulations are used to describe these mechanisms in detail for triangular posts. We also follow the motion of the contact line as the drops evaporate showing that they tend to return to their original shape. To explain this we show that the easy direction for movement is the same for spreading and drying drops. We compare the behaviour of small drops with that of larger drops created by jetting several drops at the same position. We find that the contact line motion is unexpectedly insensitive to drop volume, even when a spherical cap of fluid forms above the posts. The findings are relevant to micro-fluidic applications and to the control of drop shapes in ink-jet printing. © 2013 The Royal Society of Chemistry.