Fixed points in a Hopfield model with random asymmetric interactions

We calculate analytically the average number of fixed points in the Hopfield model of associative memory when a random antisymmetric part is added to the otherwise symmetric synaptic matrix. Addition of the antisymmetric part causes an exponential decrease in the total number of fixed points. If the relative strength of the antisymmetric component is small, then its presence does not cause any substantial degradation of the quality of retrieval when the memory loading level is low. We also present results of numerical simulations which provide qualitative (as well as quantitative for some aspects) confirmation of the predictions of the analytic study. Our numerical results suggest that the analytic calculation of the average number of fixed points yields the correct value for the typical number of fixed points.

New Massive Gravity and AdS(4) Counterterms

We show that the recently proposed Dirac-Born-Infeld extension of new massive gravity emerges naturally as a counterterm in four-dimensional anti-de Sitter space (AdS(4)). The resulting on-shell Euclidean action is independent of the cutoff at zero temperature. We also find that the same choice of counterterm gives the usual area law for the AdS(4) Schwarzschild black hole entropy in a cutoff-independent manner. The parameter values of the resulting counterterm action correspond to a c = 0 theory in the context of the duality between AdS(3) gravity and two-dimensional conformal field theory. We rewrite this theory in terms of the gauge field that is used to recast 3D gravity as a Chern-Simons theory.

Tunable Brownian vortex at the interface

A general kind of Brownian vortices is demonstrated by applying an external nonconservative force field to a colloidal particle bound by a conservative optical trapping force at a liquid-air interface. As the liquid medium is translated at a constant velocity with the bead trapped at the interface, the drag force near the surface provides enough rotational component to bias the particle's thermal fluctuations in a circulatory motion. The interplay between the thermal fluctuations and the advection of the bead in constituting the vortex motions is studied, and we infer that the angular velocity of the circulatory motion offers a comparative measure of the interface fluctuations.

Fluctuation-dissipation relation for nonlinear Langevin equations

It is shown that the fluctuation-dissipation theorem is satisfied by the solutions of a general set of nonlinear Langevin equations with a quadratic free-energy functional (constant susceptibility) and field-dependent kinetic coefficients, provided the kinetic coefficients satisfy the Onsager reciprocal relations for the irreversible terms and the antisymmetry relations for the reversible terms. The analysis employs a perturbation expansion of the nonlinear terms, and a functional integral calculation of the correlation and response functions, and it is shown that the fluctuation-dissipation relation is satisfied at each order in the expansion.

Work fluctuations in an elastic dumbbell model of polymers in planar elongational flow

We use a path-integral approach to calculate the distribution P(w, t) of the fluctuations in the work W at time t of a polymer molecule (modeled as an elastic dumbbell in a viscous solvent) that is acted on by an elongational flow field having a flow rate (gamma) over dot. We find that P(w, t) is non-Gaussian and that, at long times, the ratio P(w, t)/ P (-w, t) is equal to expw/(k(B)T)], independent of (gamma) over dot. On the basis of this finding, we suggest that polymers in elongational flows satisfy a fluctuation theorem.

Transport coefficients for the shear dynamo problem at small Reynolds numbers

We build on the formulation developed in S. Sridhar and N. K. Singh J. Fluid Mech. 664, 265 (2010)] and present a theory of the shear dynamo problem for small magnetic and fluid Reynolds numbers, but for arbitrary values of the shear parameter. Specializing to the case of a mean magnetic field that is slowly varying in time, explicit expressions for the transport coefficients alpha(il) and eta(iml) are derived. We prove that when the velocity field is nonhelical, the transport coefficient alpha(il) vanishes. We then consider forced, stochastic dynamics for the incompressible velocity field at low Reynolds number. An exact, explicit solution for the velocity field is derived, and the velocity spectrum tensor is calculated in terms of the Galilean-invariant forcing statistics. We consider forcing statistics that are nonhelical, isotropic, and delta correlated in time, and specialize to the case when the mean field is a function only of the spatial coordinate X-3 and time tau; this reduction is necessary for comparison with the numerical experiments of A. Brandenburg, K. H. Radler, M. Rheinhardt, and P. J. Kapyla Astrophys. J. 676, 740 (2008)]. Explicit expressions are derived for all four components of the magnetic diffusivity tensor eta(ij) (tau). These are used to prove that the shear-current effect cannot be responsible for dynamo action at small Re and Rm, but for all values of the shear parameter.

Implications of the recent high statistics determination of the pion electromagnetic form factor in the timelike region

The recently evaluated two-pion contribution to the muon g - 2 and the phase of the pion electromagnetic form factor in the elastic region, known from pi pi scattering by Fermi-Watson theorem, are exploited by analytic techniques for finding correlations between the coefficients of the Taylor expansion at t = 0 and the values of the form factor at several points in the spacelike region. We do not use specific parametrizations, and the results are fully independent of the unknown phase in the inelastic region. Using for instance, from recent determinations, < r(pi)(2)> = (0.435 +/- 0.005) fm(2) and F(-1.6 GeV2) = 0.243(-0.014)(+0.022), we obtain the allowed ranges 3.75 GeV-4 less than or similar to c less than or similar to 3.98 GeV-4 and 9.91 GeV-6 less than or similar to d less than or similar to 10.46 GeV-6 for the curvature and the next Taylor coefficient, with a strong correlation between them. We also predict a large region in the complex plane where the form factor cannot have zeros.

Optical and electrical properties of hydrogen-passivated gallium antimonide

The effect of hydrogen-plasma passivation on the optical and electrical properties of gallium antimonide bulk single crystals is presented. Fundamental changes of the radiative recombination after hydrogenation in undoped, zinc-doped, tellurium-doped, and codoped (with Zn and Te) GaSb are reported. The results of optical measurements indicate that passivation of acceptors is more efficient than that of the donors and, in general, the passivation efficiency depends on the doping level. Passivation of deep nonradiative centers is reflected by the gain of photoluminescence intensity and decrease in deep-level transient spectroscopy peak height. Extended defects like grain boundaries and dislocations have also been found to be passivated. The thermal stability of the passivated deep level and extended defects is higher than that of the shallow level. The kinetics of thermally released hydrogen in the bulk has been studied by reverse-bias annealing experiments.

Persistent currents in a one-dimensional ring for a disordered Hubbard model

We consider a one-dimensional Hubbard model in the presence of disorder. We compute the charge stiffness for a mesoscopic ring as a function of the size L, which is a measure of the persistent currents. We find that for finite disorder the persistent currents of the system with repulsive interactions are larger than those of the system with attractive interactions. This counterintuitive result is due to the fact that local-density fluctuations are reduced in the presence of repulsive interactions.

Raman study of pressure-induced phase transitions in RbIO4

The pressure dependence of the Raman spectra of RbIO4 has been investigated up to 27.3 GPa at room temperature using the diamond-anvil cell. The changes in the Raman spectra show clearly two pressure-induced phase transitions at 5.3 GPa from scheelite to pseudoscheelite and at 7.2 GPa from pseudoscheelite to wolframite. There is an indication of a possible phase transition at 18.3 GPa from wolframite to a denser complex structure. These transitions follow the same sequence as in other compounds such as alkali perrehenates, which crystallize in the scheelite structure. The systematics in pressure-induced phase transitions in alkali periodates is discussed.

Reactivation kinetics of acceptors in hydrogenated InP during unbiased annealing

The reactivation kinetics of passivated Mg acceptors in hydrogenated InP during unbiased annealing of a Schottky diode is reported. The reactivation is found to slow down gradually with annealing time and this phenomenon is attributed to substantial retrapping of H at the acceptor sites. It is found from the concentration profiles and the kinetics data that the reactivation is most likely limited by H2 molecule formation processes for longer annealing times; for shorter annealing times, contributions from in-diffusion of H also become significant. The diffusion of H during the initial period follows an Arrhenius relation with an activation energy for the effective diffusion coefficient of 1.13±0.10 eV. In the H2 formation regime, the reactivation is thermally activated with an activation energy for the annealing parameter of 1.71±0.10 eV. The H2 formation-limited regime of reactivation occurs sooner as the annealing temperature is increased.

Reentrant insulator-metal transition in the half-filled Hubbard model

Using the d=infinity or local-approximation approach to the half-filled Hubbard model on a compressible lattice, we present a detailed study of the transport and structural properties near the paramagnetic metal-insulator transition. The results describe qualitatively most of the observed data in V2O3, including the metal-insulator-metal crossover [Kuwamoto et al., Phys. Rev. B 22, 2626 (1980)]. In addition, we discuss an interesting and intrinsic reentrance feature in the resistivity of the half-filled Hubbard model at high temperatures.

Shear-induced enhancement of self-diffusion in interacting colloidal suspensions

We set up the generalized Langevin equations describing coupled single-particle and collective motion in a suspension of interacting colloidal particles in a shear how and use these to show that the measured self-diffusion coefficients in these systems should be strongly dependent on shear rate epsilon. Three regimes are found: (i) an initial const+epsilon(.2), followed by (ii) a large regime of epsilon(.1/2) behavior, crossing over to an asymptotic power-law approach (iii) D-o - const x epsilon(.-1/2) to the Stokes-Einstein value D-o. The shear dependence is isotropic up to very large shear rates and increases with the interparticle interaction strength. Our results provide a straightforward explanation of recent experiments and simulations on sheared colloids.

Structural and electrical transport properties of Al-Cu-Cr quasicrystals

Transport properties of quasicrystals in rapidly solidified as well as heat-treated Al65CU20Cr15 alloys were studied over a wide temperature range as a function of structure and microstructure. The characterization was done using x-ray diffraction, transmission electron microscopy and differential scanning calorimetry. Particular attention was paid to primitive to face-centered quasicrystalline transformation which occurs on annealing and the effect of microstructures on the transport behavior. The temperature dependence of resistivity is found to depend crucially on the microstructure of the alloy. Further, ordering enhances the negative temperature coefficient of resistivity. The low-temperature (T less than or equal to 25 K) resistivity of Al65Cu20Cr15 has been compared with that of Al63.5Cu24.5Fe12 alloy. In this region p(T) can be well described by a root T contribution arising from electron-electron interaction. We discuss our results in view of current theories.

Thomas-Fermi Method For Particles Obeying Generalized Exclusion Statistics

We use the Thomas-Fermi method to examine the thermodynamics of particles obeying Haldane exclusion statistics. Specifically, we study Calogero-Sutherland particles placed in a given external potential in one dimension. For the case of a simple harmonic potential (constant density of states), we obtain the exact one-particle spatial density and a {\it closed} form for the equation of state at finite temperature, which are both new results. We then solve the problem of particles in a $x^{2/3} ~$ potential (linear density of states) and show that Bose-Einstein condensation does not occur for any statistics other than bosons.