12,037 research outputs found
SU(3) Spin-Orbit Coupling in Systems of Ultracold Atoms
Motivated by the recent experimental success in realizing synthetic
spin-orbit coupling in ultracold atomic systems, we consider N-component atoms
coupled to a non-Abelian SU(N) gauge field. More specifically, we focus on the
case, referred to here as "SU(3) spin-orbit-coupling," where the internal
states of three-component atoms are coupled to their momenta via a matrix
structure that involves the Gell-Mann matrices (in contrast to the Pauli
matrices in conventional SU(2) spin-orbit-coupled systems). It is shown that
the SU(3) spin-orbit-coupling gives rise to qualitatively different phenomena
and in particular we find that even a homogeneous SU(3) field on a simple
square lattice enables a topologically non-trivial state to exist, while such
SU(2) systems always have trivial topology. In deriving this result, we first
establish an exact equivalence between the Hofstadter model with a 1/N Abelian
flux per plaquette and a homogeneous SU(N) non-Abelian model. The former is
known to have a topological spectrum for N>2, which is thus inherited by the
latter. It is explicitly verified by an exact calculation for N=3, where we
develop and use a new algebraic method to calculate topological indices in the
SU(3) case. Finally, we consider a strip geometry and establish the existence
of three gapless edge states -- the hallmark feature of such an SU(3)
topological insulator.Comment: 4.2 pages, 1 figur
Analog-digital simulation of transient-induced logic errors and upset susceptibility of an advanced control system
A simulation study is described which predicts the susceptibility of an advanced control system to electrical transients resulting in logic errors, latched errors, error propagation, and digital upset. The system is based on a custom-designed microprocessor and it incorporates fault-tolerant techniques. The system under test and the method to perform the transient injection experiment are described. Results for 2100 transient injections are analyzed and classified according to charge level, type of error, and location of injection
Theory of the high-frequency chiral optical response in a p_x+ip_y superconductor
The optical Hall conductivity and the polar Kerr angle are calculated as
functions of temperature for a two-dimensional chiral p_x+ip_y superconductor,
where the time-reversal symmetry is spontaneously broken. The theoretical
estimate for the polar Kerr angle agrees by the order of magnitude with the
recent experimental measurement in Sr2RuO4 by Xia et al. cond-mat/0607539. The
theory predicts that the Kerr angle is proportional to the square of the
superconducting energy gap and is inversely proportional to the cube of
frequency, which can be verified experimentally.Comment: 4 pages, no figures, RevTeX. V.2: one reference and discussion of
horizontal lines of nodes added. V.3: a typo corrected, and one reference
added. V.4: two references added and minor stylistic changes made, as in the
published versio
Mean- Field Approximation and Extended Self-Similarity in Turbulence
Recent experimental discovery of extended self-similarity (ESS) was one of
the most interesting developments, enabling precise determination of the
scaling exponents of fully developed turbulence. Here we show that the ESS is
consistent with the Navier-Stokes equations, provided the pressure -gradient
contributions are expressed in terms of velocity differences in the mean field
approximation (Yakhot, Phys.Rev. E{\bf 63}, 026307, (2001)). A sufficient
condition for extended self-similarity in a general dynamical systemComment: 8 pages, no figure
Three-Omega Thermal-Conductivity Measurements with Curved Heater Geometries
The three-omega method, a powerful technique to measure the thermal
conductivity of nanometer-thick films and the interfaces between them, has
historically employed straight conductive wires to act as both heaters and
thermometers. When investigating stochastically prepared samples such as
two-dimensional materials and nanomembranes, residue and excess material can
make it difficult to fit the required millimeter-long straight wire on the
sample surface. There are currently no available criteria for how diverting
three-omega heater wires around obstacles affects the validity of the thermal
measurement. In this Letter, we quantify the effect of wire curvature by
performing three-omega experiments with a wide range of frequencies using both
curved and straight heater geometries on SiO/Si samples. When the heating
wire is curved, we find that the measured Si substrate thermal conductivity
changes by only 0.2%. Similarly, we find that wire curvature has no significant
effect on the determination of the thermal resistance of a 65 nm SiO
layer, even for the sharpest corners considered here, for which the largest
measured ratio of the thermal penetration depth of the applied thermal wave to
radius of curvature of the heating wire is 4.3. This result provides useful
design criteria for three-omega experiments by setting a lower bound for the
maximum ratio of thermal penetration depth to wire radius of curvature.Comment: 4 pages, 3 figure
Thermodynamic Properties of Generalized Exclusion Statistics
We analytically calculate some thermodynamic quantities of an ideal -on
gas obeying generalized exclusion statistics. We show that the specific heat of
a -on gas () vanishes linearly in any dimension as when
the particle number is conserved and exhibits an interesting dual symmetry that
relates the particle-statistics at to the hole-statistics at at low
temperatures. We derive the complete solution for the cluster coefficients
as a function of Haldane's statistical interaction in
dimensions. We also find that the cluster coefficients and the virial
coefficients are exactly mirror symmetric (=odd) or antisymmetric
(=even) about . In two dimensions, we completely determine the closed
forms about the cluster and the virial coefficients of the generalized
exclusion statistics, which exactly agree with the virial coefficients of an
anyon gas of linear energies. We show that the -on gas with zero chemical
potential shows thermodynamic properties similar to the photon statistics. We
discuss some physical implications of our results.Comment: 24 pages, Revtex, Corrected typo
Silicon nanoparticles and interstellar extinction
To examine a recently proposed hypothesis that silicon nanoparticles are the
source of extended red emission (ERE) in the interstellar medium, we performed
a detailed modeling of the mean Galactic extinction in the presence of silicon
nanoparticles. For this goal we used the appropriate optical constants of
nanosized Si, essentially different from those of bulk Si due to quantum
confinement. It was found that a dust mixture of silicon nanoparticles, bare
graphite grains, silicate core-organic refractory mantle grains and three-layer
silicate-water ice-organic refractory grains works well in explaining the
extinction and, in addition, results in the acceptable fractions of UV/visible
photons absorbed by silicon nanoparticles: 0.071-0.081. Since these fractions
barely agree with the fraction of UV/visible photons needed to excite the
observed ERE, we conclude that the intrinsic photon conversion efficiency of
the photoluminescence by silicon nanoparticles must be near 100%, if they are
the source of the ERE.Comment: Latex2e, uses emulateapj.sty (included), multicol.sty, epsf.sty, 6
pages, 3 figures (8 Postscript files), accepted for publication in ApJ
Letters, complete Postscript file is also available at
http://physics.technion.ac.il/~zubko/eb.html#SNP
Deformations of Fuchsian Systems of Linear Differential Equations and the Schlesinger System
We consider holomorphic deformations of Fuchsian systems parameterized by the
pole loci. It is well known that, in the case when the residue matrices are
non-resonant, such a deformation is isomonodromic if and only if the residue
matrices satisfy the Schlesinger system with respect to the parameter. Without
the non-resonance condition this result fails: there exist non-Schlesinger
isomonodromic deformations. In the present article we introduce the class of
the so-called isoprincipal deformations of Fuchsian systems. Every isoprincipal
deformation is also an isomonodromic one. In general, the class of the
isomonodromic deformations is much richer than the class of the isoprincipal
deformations, but in the non-resonant case these classes coincide. We prove
that a deformation is isoprincipal if and only if the residue matrices satisfy
the Schlesinger system. This theorem holds in the general case, without any
assumptions on the spectra of the residue matrices of the deformation. An
explicit example illustrating isomonodromic deformations, which are neither
isoprincipal nor meromorphic with respect to the parameter, is also given
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