Zero- and one-dimensional magnetic traps for quasi-particles

We investigate the possibility of trapping quasi-particles possessing spin degree of freedom in hybrid structures. The hybrid system we are considering here is composed of a semi-magnetic quantum well placed a few nanometers below a ferromagnetic micromagnet. We are interested in two different micromagnet shapes: cylindrical (micro-disk) and rectangular geometry. We show that in the case of a micro-disk, the spin object is localized in all three directions and therefore zero-dimensional states are created, and in the case of an elongated rectangular micromagnet, the quasi-particles can move freely in one direction, hence one-dimensional states are formed. After calculating profiles of the magnetic field produced by the micromagnets, we analyze in detail the possible light absorption spectrum for different micromagnet thicknesses, and different distances between the micromagnet and the semimagnetic quantum well. We find that the discrete spectrum of the localized states can be detected via spatially-resolved low temperature optical measurement.Comment: 15 pages, 9 figure

Patterns and localized structures in bistable semiconductor resonators

We report experiments on spatial switching dynamics and steady state structures of passive nonlinear semiconductor resonators of large Fresnel number. Extended patterns and switching front dynamics are observed and investigated. Evidence of localization of structures is given.Comment: 5 pages with 9 figure

Brane Tilings and Specular Duality

We study a new duality which pairs 4d N=1 supersymmetric quiver gauge theories. They are represented by brane tilings and are worldvolume theories of D3 branes at Calabi-Yau 3-fold singularities. The new duality identifies theories which have the same combined mesonic and baryonic moduli space, otherwise called the master space. We obtain the associated Hilbert series which encodes both the generators and defining relations of the moduli space. We illustrate our findings with a set of brane tilings that have reflexive toric diagrams.Comment: 42 pages, 16 figures, 5 table

Few smooth d-polytopes with n lattice points

We prove that, for fixed n there exist only finitely many embeddings of Q-factorial toric varieties X into P^n that are induced by a complete linear system. The proof is based on a combinatorial result that for fixed nonnegative integers d and n, there are only finitely many smooth d-polytopes with n lattice points. We also enumerate all smooth 3-polytopes with at most 12 lattice points. In fact, it is sufficient to bound the singularities and the number of lattice points on edges to prove finiteness.Comment: 20+2 pages; major revision: new author, new structure, new result

Dynamical density functional theory for dense atomic liquids

Starting from Newton's equations of motion, we derive a dynamical density functional theory (DDFT) applicable to atomic liquids. The theory has the feature that it requires as input the Helmholtz free energy functional from equilibrium density functional theory. This means that, given a reliable equilibrium free energy functional, the correct equilibrium fluid density profile is guaranteed. We show that when the isothermal compressibility is small, the DDFT generates the correct value for the speed of sound in a dense liquid. We also interpret the theory as a dynamical equation for a coarse grained fluid density and show that the theory can be used (making further approximations) to derive the standard mode coupling theory that is used to describe the glass transition. The present theory should provide a useful starting point for describing the dynamics of inhomogeneous atomic fluids.Comment: 14 pages, accepted for publication in J. Phys.: Condens. Matte

Temperature Evolution Law of Imperfect Relativistic Fluids

The first-order general relativistic theory of a generic dissipative (heat-conducting, viscous, particle-creating) fluid is rediscussed from a unified covariant frame-independent point of view. By generalizing some previous works in the literature, we derive a formula for the temperature variation rate, which is valid both in Eckart's (particle) and in the Landau-Lifshitz (energy) frames. Particular attention is paid to the case of gravitational particle creation and its possible cross-effect with the bulk viscosity mechanism.Comment: 14 pages, no figure, revte

A Guide to Localized Frames and Applications to Galerkin-like Representations of Operators

This chapter offers a detailed survey on intrinsically localized frames and the corresponding matrix representation of operators. We re-investigate the properties of localized frames and the associated Banach spaces in full detail. We investigate the representation of operators using localized frames in a Galerkin-type scheme. We show how the boundedness and the invertibility of matrices and operators are linked and give some sufficient and necessary conditions for the boundedness of operators between the associated Banach spaces.Comment: 32 page

Topological Defects and Interactions in Nematic Emulsions

Inverse nematic emulsions in which surfactant-coated water droplets are dispersed in a nematic host fluid have distinctive properties that set them apart from dispersions of two isotropic fluids or of nematic droplets in an isotropic fluid. We present a comprehensive theoretical study of the distortions produced in the nematic host by the dispersed droplets and of solvent mediated dipolar interactions between droplets that lead to their experimentally observed chaining. A single droplet in a nematic host acts like a macroscopic hedgehog defect. Global boundary conditions force the nucleation of compensating topological defects in the nematic host. Using variational techniques, we show that in the lowest energy configuration, a single water droplet draws a single hedgehog out of the nematic host to form a tightly bound dipole. Configurations in which the water droplet is encircled by a disclination ring have higher energy. The droplet-dipole induces distortions in the nematic host that lead to an effective dipole-dipole interaction between droplets and hence to chaining.Comment: 17 double column pages prepared by RevTex, 15 eps figures included in text, 2 gif figures for Fig. 1

Calabi-Yau Fourfolds with Flux and Supersymmetry Breaking

In Calabi-Yau fourfold compactifications of M-theory with flux, we investigate the possibility of partial supersymmetry breaking in the three-dimensional effective theory. To this end, we place the effective theory in the framework of general N=2 gauged supergravities, in the special case where only translational symmetries are gauged. This allows us to extract supersymmetry-breaking conditions, and interpret them as conditions on the 4-form flux and Calabi-Yau geometry. For N=2 unbroken supersymmetry in three dimensions we recover previously known results, and we find a new condition for breaking supersymmetry from N=2 to N=1, i.e. from four to two supercharges. An example of a Calabi-Yau hypersurface in a toric variety that satisfies this condition is provided.Comment: 26 page

Force-velocity relation and density profiles for biased diffusion in an adsorbed monolayer

In this paper, which completes our earlier short publication [Phys. Rev. Lett. 84, 511 (2000)], we study dynamics of a hard-core tracer particle (TP) performing a biased random walk in an adsorbed monolayer, composed of mobile hard-core particles undergoing continuous exchanges with a vapor phase. In terms of an approximate approach, based on the decoupling of the third-order correlation functions, we obtain the density profiles of the monolayer particles around the TP and derive the force-velocity relation, determining the TP terminal velocity, V_{tr}, as the function of the magnitude of external bias and other system's parameters. Asymptotic forms of the monolayer particles density profiles at large separations from the TP, and behavior of V_{tr} in the limit of small external bias are found explicitly.Comment: Latex, 31 pages, 3 figure