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1995-12-28
|
MSSM radiative contributions to the WW$γ$ and WWZ form factors
|
We evaluate one-loop contributions to the C and P conserving $WW\gamma, WWZ$
form factors in the Minimal Supersymmetric Standard Model (MSSM), and in a more
constrained Supergravity Grand Unified Theory (SUGRA-GUT). A systematic search
of maximal effects in the available parameter space, shows that at LEP2 energy
MSSM contributions can hardly reach the border of the most optimistic accuracy
expected on those couplings, even for particles close to their production
thresholds. At NLC energies, the effects are more comfortably of the order of
the expected sensitivity, and may therefore provide useful information on MSSM
parameter values which will not be available from direct particle production.
We also discuss briefly some variance with other studies.
|
9512437v2
|
1998-07-10
|
Inverting the Supersymmetric Standard Model Spectrum: from Physical to Lagrangian Ino Parameters
|
We examine the possibility of recovering the supersymmetric (and soft
supersymmetry breaking) Lagrangian parameters as direct {\em analytical}
expressions of appropriate physical masses, for the unconstrained (but CP and
R-parity conserving) minimal supersymmetric standard model. We concentrate
mainly on the algebraically non-trivial "inversion" for the ino parameters, and
obtain, for given values of $\tan\beta$, simple analytical expressions for the
$\mu$, $M_1$ and $M_2$ parameters in terms of three arbitrary input physical
masses, namely either two chargino and one neutralino masses, or alternatively
one chargino and two neutralino masses. We illustrate and discuss in detail the
possible occurrence of ambiguities in this reconstruction. The dependence of
the resulting ino Lagrangian parameters upon physical masses is illustrated,
and some simple generic behaviour uncovered in this way. We finally briefly
sketch generalizing such an inversion to the full set of MSSM Lagrangian
parameters.
|
9807336v2
|
1999-07-01
|
A convergent scheme for one-loop evolutions of the Yukawa couplings in the MSSM
|
Integrated forms of the one-loop evolution equations are given for the Yukawa
couplings in the MSSM, valid for any value of $\tan \beta$, generalizable to
virtually any number of Yukawa fermions, and including all gauge couplings.
These forms turn out to have nice mathematical convergence properties which we
prove, and we determine the ensuing convergence criteria. Furthermore, they
allow to write down general sufficient and necessary conditions to avoid
singularities in the evolution of the Yukawa couplings over physically relevant
energy ranges. We also comment briefly on the possible use of these features
for physics issues and give a short numerical illustration.
|
9907204v1
|
1999-07-14
|
Phases in the gaugino sector: direct reconstruction of the basic parameters and impact on the neutralino pair production
|
We consider recovering analytically the (generally complex) parameters $\mu$,
$M_1$ and $M_2$ of the gaugino and Higgsino Lagrangian, from appropriate
physical input in the chargino and neutralino sectors. For given $\tan\beta$,
we obtain very simple analytic solutions for $M_2$, $| \mu|$, $Arg[\mu]$ in the
chargino sector and a twofold $| M_1 |$, $Arg[M_1]$ analytic solution in the
neutralino sector, assuming two chargino, two neutralino masses, and one of the
chargino mixing angles as physical input. The twofold ambiguity in the
neutralino parameters reconstruction may be essentially resolved by measuring
the $e^+e^- \to \chi^0_1 \chi^0_2$ production cross-section at future linear
collider energies, which we study explicitly with the phase dependences. Some
salient features and specific properties of this complex case gaugino "spectrum
inversion" are illustrated and compared with the similar inversion in the real
case. In particular, our algorithms exhibit in a direct and transparent way the
non-trivial theoretical correlation among the chargino and neutralino
parameters, and the resulting allowed domains when only a subset of the
required physical input masses and production cross-sections is known.
|
9907360v1
|
1999-12-08
|
Analytical Study of Non-Universality of the Soft Terms in the MSSM
|
We obtain general analytical forms for the solutions of the one-loop
renormalization group equations in the top/bottom/$\tau$ sector of the MSSM.
These solutions are valid for any value of $\tan \beta$ as well as any
non-universal initial conditions for the soft SUSY breaking parameters and
non-unification of the Yukawa couplings. We establish analytically a generic
screening effect of non-universality, in the vicinity of the infrared quasi
fixed point, which allows to determine sector-wise a hierarchy of sensitivity
to initial conditions. We give also various numerical illustrations of this
effect away from the quasi fixed point and assess the sensitivity of the Higgs
and sfermion spectra to the non-universality of the various soft breaking
sectors. As a by-product, a typical anomaly-mediated non-universality of the
gaugino sector would have marginal influence on the scalar spectrum.
|
9912271v1
|
2001-01-22
|
General one-loop renormalization group evolutions and electroweak symmetry breaking in the (M+1)SSM
|
We study analytically the general features of electroweak symmetry breaking
in the context of the Minimal Supersymmetric Standard Model extended by one
Higgs singlet. The exact analytical forms of the renormalization group
evolutions of the Yukawa couplings and of the soft supersymmetry breaking
parameters are derived to one-loop order. They allow on one hand controllable
approximations in closed analytical form, and on the other a precise study of
the behaviour of infrared quasi fixed point regimes which we carry out. Some of
these regimes are shown to be phenomenologically inconsistent, leading to too
small an effective $\mu$-parameter. The remaining ones serve as a suitable
benchmark to understand analytically some salient aspects, often noticed
numerically in the literature, in relation to the electroweak symmetry breaking
in this model. The study does not need any specific assumption on $\tan \beta$
or on boundary conditions for the soft supersymmetry breaking parameters, thus
allowing a general insight into the sensitivity of the low energy physics to
high energy assumptions.
|
0101237v1
|
2001-12-28
|
Infrared Quasi Fixed Point Structure in Extended Yukawa Sectors and Application to R-parity Violation
|
We investigate one-loop renormalization group evolutions of extended sectors
of Yukawa type couplings. It is shown that Landau Poles which usually provide
necessary low energy upper bounds that saturate quickly with increasing initial
value conditions, lead in some cases to the opposite behaviour: some of the low
energy couplings decrease and become vanishingly small for increasingly large
initial conditions. We write down the general criteria for this to happen in
typical situations, highlighting a concept of {\sl repulsive} quasi-fixed
points, and illustrate the case both within a two-Yukawa toy model as well as
in the minimal supersymmetric standard model with R-parity violation. In the
latter case we consider the theoretical upper bounds on the various couplings,
identifying regimes where $\lambda_{kl3}, \lambda'_{kkk}, \lambda''_{3kl}$ are
dynamically suppressed due to the Landau Pole. We stress the importance of
considering a large number of couplings simultaneously. This leads altogether
to a phenomenologically interesting seesaw effect in the magnitudes of the
various R-parity violating couplings, complementing and in some cases improving
the existing limits.
|
0112353v1
|
2005-04-04
|
Natural gravitino dark matter in SO(10) gauge mediated supersymmetry breaking
|
It is shown that gravitinos with mass m_{3/2} ~ 0.1-1 MeV may provide
suitable cold dark matter candidates in scenarios of gauge mediated
supersymmetry breaking (GMSB) under SO(10) grand unification coupled to
supergravity, which accommodate a messenger sector of mass scale M_X ~ 10^6
GeV. This is due to the combined effects of renormalizable loop-suppressed
operators and generic non-renormalizable ones governing the dilution of a
pre-existing equilibrium gravitino abundance via messenger decay. The above
range of gravitino and messenger masses can be accommodated in indirect GMSB
scenarios. The gravitino abundance does not depend on the post-inflationary
reheat temperature and it is shown that leptogenesis can generate successfully
the baryon asymmetry.
|
0504021v2
|
2005-06-14
|
Gravitino dark matter in gauge mediated supersymmetry breaking
|
This paper investigates the parameter space of theories with gauge mediated
supersymmetry breaking leading to gravitino (cold) dark matter with mass
m_{3/2}= 1keV - 10MeV. We pay particular attention to the cosmological role of
messenger fields. Cosmology requires that these messengers decay to the visible
sector if the lightest messenger mass M_X > 30TeV. We then examine the various
possible messenger number violating interactions allowed by the symmetries of
the theory and by phenomenology. Late messenger decay generally results in
entropy production hence in the dilution of pre-existing gravitinos. We find
that in SU(5) grand unification only specific messenger-matter couplings allow
to produce the required amount of gravitino dark matter particles. Gravitino
dark matter with the correct abundance is however expected in larger gauge
groups such as SO(10) for generic non-renormalizable messenger-matter
interactions and for arbritrarily high post-inflationary reheating
temperatures.
|
0506129v2
|
1991-08-22
|
On the Perturbations of String-Theoretic Black Holes
|
The perturbations of string-theoretic black holes are analyzed by
generalizing the method of Chandrasekhar. Attention is focussed on the case of
the recently considered charged string-theoretic black hole solutions as a
representative example. It is shown that string-intrinsic effects greatly alter
the perturbed motions of the string-theoretic black holes as compared to the
perturbed motions of black hole solutions of the field equations of general
relativity, the consequences of which bear on the questions of the scattering
behavior and the stability of string-theoretic black holes. The explicit forms
of the axial potential barriers surrounding the string-theoretic black hole are
derived. It is demonstrated that one of these, for sufficiently negative values
of the asymptotic value of the dilaton field, will inevitably become negative
in turn, in marked contrast to the potentials surrounding the static black
holes of general relativity. Such potentials may in principle be used in some
cases to obtain approximate constraints on the value of the string coupling
constant. The application of the perturbation analysis to the case of
two-dimensional string-theoretic black holes is discussed.
|
9108012v1
|
1992-10-31
|
All Or Nothing: On the Small Fluctuations of Two-Dimensional String-Theoretic Black Holes
|
A comprehensive analysis of small fluctuations about two-dimensional
string-theoretic and string-inspired black holes is presented. It is shown with
specific examples that two-dimensional black holes behave in a radically
different way from all known black holes in four dimensions. For both the
$SL(2,R)/U(1)$ black hole and the two-dimensional black hole coupled to a
massive dilaton with constant field strength, it is shown that there are a {\it
continuous infinity} of solutions to the linearized equations of motion, which
are such that it is impossible to ascertain the classical linear response. It
is further shown that the two-dimensional black hole coupled to a massive,
linear dilaton admits {\it no small fluctuations at all}. We discuss possible
implications of our results for the Callan-Giddings-Harvey-Strominger black
hole.
|
9210165v3
|
1993-04-01
|
Wavelet transforms versus Fourier transforms
|
This note is a very basic introduction to wavelets. It starts with an
orthogonal basis of piecewise constant functions, constructed by dilation and
translation. The ``wavelet transform'' maps each $f(x)$ to its coefficients
with respect to this basis. The mathematics is simple and the transform is fast
(faster than the Fast Fourier Transform, which we briefly explain), but
approximation by piecewise constants is poor. To improve this first wavelet, we
are led to dilation equations and their unusual solutions. Higher-order
wavelets are constructed, and it is surprisingly quick to compute with them ---
always indirectly and recursively. We comment informally on the contest between
these transforms in signal processing, especially for video and image
compression (including high-definition television). So far the Fourier
Transform --- or its 8 by 8 windowed version, the Discrete Cosine Transform ---
is often chosen. But wavelets are already competitive, and they are ahead for
fingerprints. We present a sample of this developing theory.
|
9304214v1
|
1998-04-24
|
Enumeration of m-ary cacti
|
The purpose of this paper is to enumerate various classes of cyclically
colored m-gonal plane cacti, called m-ary cacti. This combinatorial problem is
motivated by the topological classification of complex polynomials having at
most m critical values, studied by Zvonkin and others. We obtain explicit
formulae for both labelled and unlabelled m-ary cacti, according to i) the
number of polygons, ii) the vertex-color distribution, iii) the vertex-degree
distribution of each color. We also enumerate m-ary cacti according to the
order of their automorphism group. Using a generalization of Otter's formula,
we express the species of m-ary cacti in terms of rooted and of pointed cacti.
A variant of the m-dimensional Lagrange inversion is then used to enumerate
these structures. The method of Liskovets for the enumeration of unrooted
planar maps can also be adapted to m-ary cacti.
|
9804119v2
|
2002-08-21
|
Toric codes over finite fields
|
In this note, a class of error-correcting codes is associated to a toric
variety associated to a fan defined over a finite field $\fff_q$, analogous to
the class of Goppa codes associated to a curve. For such a ``toric code''
satisfying certain additional conditions, we present an efficient decoding
algorithm for the dual of a Goppa code. Many examples are given. For small $q$,
many of these codes have parameters beating the Gilbert-Varshamov bound. In
fact, using toric codes, we construct a $(n,k,d)=(49,11,28)$ code over
$\fff_8$, which is better than any other known code listed in Brouwer's on-line
tables for that $n$ and $k$.
|
0208155v2
|
2002-12-05
|
Automorphisms of hyperbolic groups and graphs of groups
|
Using the canonical JSJ splitting, we describe the outer automorphism group
$\Out(G)$ of a one-ended word hyperbolic group $G$. In particular, we discuss
to what extent $\Out(G)$ is virtually a direct product of mapping class groups
and a free abelian group, and we determine for which groups $\Out(G)$ is
infinite. We also show that there are only finitely many conjugacy classes of
torsion elements in $\Out(G)$, for $G$ any torsion-free hyperbolic group.
More generally, let $\Gamma $ be a finite graph of groups decomposition of an
arbitrary group $G$ such that edge groups $G_e$ are rigid (i.e\. $\Out(G_e)$ is
finite). We describe the group of automorphisms of $G$ preserving $\Gamma $, by
comparing it to direct products of suitably defined mapping class groups of
vertex groups.
|
0212088v1
|
2004-06-08
|
The structure and labelled enumeration of K_{3,3}-subdivision-free projective-planar graphs
|
We consider the class F of 2-connected non-planar K_{3,3}-subdivision-free
graphs that are embeddable in the projective plane. We show that these graphs
admit a unique decomposition as a graph K_5 (the core) where the edges are
replaced by two-pole networks constructed from 2-connected planar graphs. A
method to enumerate these graphs in the labelled case is described. Moreover,
we enumerate the homeomorphically irreducible graphs in F and homeomorphically
irreducible 2-connected planar graphs. Particular use is made of two-pole
directed series-parallel networks. We also show that the number m of edges of
graphs in F with n vertices satisfies the bound m <=3n-6, for n >= 6.
|
0406140v5
|
2004-09-16
|
Translation equivalence in free groups
|
Motivated by the work of Leininger on hyperbolic equivalence of homotopy
classes of closed curves on surfaces, we investigate a similar phenomenon for
free groups. Namely, we study the situation when two elements $g,h$ in a free
group $F$ have the property that for every free isometric action of $F$ on an
$\mathbb{R}$-tree $X$ the translation lengths of $g$ and $h$ on $X$ are equal.
We give a combinatorial characterization of this phenomenon, called translation
equivalence, in terms of Whitehead graphs and exhibit two difference sources of
it. The first source of translation equivalence comes from representation
theory and $SL_2$ trace identities. The second source comes from geometric
properties of groups acting on real trees and a certain power redistribution
trick. We also analyze to what extent these are applicable to the tree actions
of surface groups that occur in the Thurston compactification of the
Teichmuller space.
|
0409284v2
|
2004-11-16
|
Characterization and enumeration of toroidal K_{3,3}-subdivision-free graphs
|
We describe the structure of 2-connected non-planar toroidal graphs with no
K_{3,3}-subdivisions, using an appropriate substitution of planar networks into
the edges of certain graphs called toroidal cores. The structural result is
based on a refinement of the algorithmic results for graphs containing a fixed
K_5-subdivision in [A. Gagarin and W. Kocay, "Embedding graphs containing
K_5-subdivisions'', Ars Combin. 64 (2002), 33-49]. It allows to recognize these
graphs in linear-time and makes possible to enumerate labelled 2-connected
toroidal graphs containing no K_{3,3}-subdivisions and having minimum vertex
degree two or three by using an approach similar to [A. Gagarin, G. Labelle,
and P. Leroux, "Counting labelled projective-planar graphs without a
K_{3,3}-subdivision", submitted, arXiv:math.CO/0406140, (2004)].
|
0411356v1
|
2005-01-19
|
The outer space of a free product
|
We associate a contractible ``outer space'' to any free product of groups
G=G_1*...*G_q. It equals Culler-Vogtmann space when G is free,
McCullough-Miller space when no G_i is Z. Our proof of contractibility (given
when G is not free) is based on Skora's idea of deforming morphisms between
trees.
Using the action of Out(G) on this space, we show that Out(G) has finite
virtual cohomological dimension, or is VFL (it has a finite index subgroup with
a finite classifying space), if the groups G_i and Out(G_i) have similar
properties. We deduce that Out(G) is VFL if G is a torsion-free hyperbolic
group, or a limit group (finitely generated fully residually free group).
|
0501288v3
|
2005-07-28
|
Free-group automorphisms, train tracks and the beaded decomposition
|
We study the automorphisms \phi of a finitely generated free group F.
Building on the train-track technology of Bestvina, Feighn and Handel, we
provide a topological representative f:G\to G of a power of \phi that behaves
very much like the realization on the rose of a positive automorphism. This
resemblance is encapsulated in the Beaded Decomposition Theorem which describes
the structure of paths in G obtained by repeatedly passing to f-images of an
edge and taking subpaths. This decomposition is the key to adapting our proof
of the quadratic isoperimetric inequality for $F\rtimes_\phi\mathbb Z$, with
\phi positive, to the general case. To illustrate the wider utility of our
topological normal form, we provide a short proof that for every w in F, the
function $n\mapsto |\phi^n(w)|$ grows either polynomially or exponentially.
|
0507589v2
|
2007-02-02
|
Line-of-sight percolation
|
Given $\omega\ge 1$, let $Z^2_{(\omega)}$ be the graph with vertex set $Z^2$
in which two vertices are joined if they agree in one coordinate and differ by
at most $\omega$ in the other. (Thus $Z^2_{(1)}$ is precisely $Z^2$.) Let
$p_c(\omega)$ be the critical probability for site percolation in
$Z^2_{(\omega)}$. Extending recent results of Frieze, Kleinberg, Ravi and
Debany, we show that $\lim_{\omega\to\infty} \omega\pc(\omega)=\log(3/2)$. We
also prove analogues of this result on the $n$-by-$n$ grid and in higher
dimensions, the latter involving interesting connections to Gilbert's continuum
percolation model. To prove our results, we explore the component of the origin
in a certain non-standard way, and show that this exploration is well
approximated by a certain branching random walk.
|
0702061v2
|
2000-03-06
|
Entropy Production, Fractals, and Relaxation to Equilibrium
|
The theory of entropy production in nonequilibrium, Hamiltonian systems,
previously described for steady states using partitions of phase space, is here
extended to time dependent systems relaxing to equilibrium. We illustrate the
main ideas by using a simple multibaker model, with some nonequilibrium initial
state, and we study its progress toward equilibrium. The central results are
(i) the entropy production is governed by an underlying, exponentially decaying
fractal structure in phase space, (ii) the rate of entropy production is
largely independent of the scale of resolution used in the partitions, and
(iii) the rate of entropy production is in agreement with the predictions of
nonequilibrium thermodynamics.
|
0003012v2
|
2002-03-21
|
Entropy production of diffusion in spatially periodic deterministic systems
|
This paper presents an {\it ab initio} derivation of the expression given by
irreversible thermodynamics for the rate of entropy production for different
classes of diffusive processes. The first class are Lorentz gases, where
non-interacting particles move on a spatially periodic lattice, and collide
elastically with fixed scatterers. The second class are periodic systems where
$N$ particles interact with each other, and one of them is a tracer particle
which diffuses among the cells of the lattice. We assume that, in either case,
the dynamics of the system is deterministic and hyperbolic, with positive
Lyapunov exponents. This work extends methods originally developed for a
chaotic two-dimensional model of diffusion, the multi-baker map, to higher
dimensional, continuous time dynamical systems appropriate for systems with one
or more moving particles. Here we express the rate of entropy production in
terms of hydrodynamic measures that are determined by the fractal properties of
microscopic hydrodynamic modes that describe the slowest decay of the system to
an equilibrium state.
|
0203046v1
|
2001-11-09
|
Spatial diffusion in a periodic optical lattice: revisiting the Sisyphus effect
|
We numerically study the spatial diffusion of an atomic cloud experiencing
Sisyphus cooling in a three-dimensional lin$\bot$lin optical lattice in a broad
range of lattice parameters. In particular, we investigate the dependence on
the size of the lattice sites which changes with the angle between the laser
beams. We show that the steady-state temperature is largely independent of the
lattice angle, but that the spatial diffusion changes significantly. It is
shown that the numerical results fulfil the Einstein relations of Brownian
motion in the jumping regime as well as in the oscillating regime. We finally
derive an effective Brownian motion model from first principles which gives
good agreement with the simulations.
|
0111070v2
|
2006-07-24
|
Use of specific Green's functions for solving direct problems involving a heterogeneous rigid frame porous medium slab solicited by acoustic waves
|
A domain integral method employing a specific Green's function (i.e.,
incorporating some features of the global problem of wave propagation in an
inhomogeneous medium) is developed for solving direct and inverse scattering
problems relative to slab-like macroscopically inhomogeneous porous obstacles.
It is shown how to numerically solve such problems, involving both
spatially-varying density and compressibility, by means of an iterative scheme
initialized with a Born approximation. A numerical solution is obtained for a
canonical problem involving a two-layer slab.
|
0607212v1
|
2005-12-12
|
Cloning, expression and purification of the general stress protein Yhbo from Escherichia coli
|
We cloned, expressed and purified the Escherichia coli yhbO gene product,
which is homolog to the Bacillus subtilis general stress protein 18 (the yfkM
gene product), the Pyrococcus furiosus intracellular protease PfpI, and the
human Parkinson disease protein DJ-1. The gene coding for YhbO was generated by
amplifying the yhbO gene from E. coli by polymerase chain reaction. It was
inserted in the expression plasmid pET-21a, under the transcriptional control
of the bacteriophage T7 promoter and lac operator. A BL21(DE3) E. coli strain
transformed with the YhbO-expression vector pET-21a-yhbO, accumulates large
amounts of a soluble protein of 20 kDa in SDS-PAGE that matches the expected
YhbO molecular weight. YhbO was purified to homogeneity by HPLC DEAE ion
exchange chromatography and hydroxylapatite chromatography and its identity was
confirmed by N-terminal sequencing and mass spectrometry analysis. The native
protein exists in monomeric, trimeric and hexameric forms.
|
0512028v1
|
2003-01-24
|
Rayleigh Scattering and Atomic Dynamics in Dissipative Optical Lattices
|
We investigate Rayleigh scattering in dissipative optical lattices. In
particular, following recent proposals (S. Guibal {\it et al}, Phys. Rev. Lett.
{\bf 78}, 4709 (1997); C. Jurczak {\it et al}, Phys. Rev. Lett. {\bf 77}, 1727
(1996)), we study whether the Rayleigh resonance originates from the
diffraction on a density grating, and is therefore a probe of transport of
atoms in optical lattices. It turns out that this is not the case: the Rayleigh
line is instead a measure of the cooling rate, while spatial diffusion
contributes to the scattering spectrum with a much broader resonance.
|
0301139v1
|
2005-12-19
|
More on the Asymmetric Infinite Square Well: Energy Eigenstates with Zero Curvature
|
We extend the standard treatment of the asymmetric infinite square well to
include solutions that have zero curvature over part of the well. This type of
solution, both within the specific context of the asymmetric infinite square
well and within the broader context of bound states of arbitrary
piecewise-constant potential energy functions, is not often discussed as part
of quantum mechanics texts at any level. We begin by outlining the general
mathematical condition in one-dimensional time-independent quantum mechanics
for a bound-state wave function to have zero curvature over an extended region
of space and still be a valid wave function. We then briefly review the
standard asymmetric infinite square well solutions, focusing on zero-curvature
solutions as represented by energy eigenstates in position and momentum space.
|
0512156v1
|
2006-05-09
|
Communicating over adversarial quantum channels using quantum list codes
|
We study quantum communication in the presence of adversarial noise. In this
setting, communicating with perfect fidelity requires using a quantum code of
bounded minimum distance, for which the best known rates are given by the
quantum Gilbert-Varshamov (QGV) bound. By asking only for arbitrarily high
fidelity and allowing the sender and reciever to use a secret key with length
logarithmic in the number of qubits sent, we achieve a dramatic improvement
over the QGV rates. In fact, we find protocols that achieve arbitrarily high
fidelity at noise levels for which perfect fidelity is impossible. To achieve
such communication rates, we introduce fully quantum list codes, which may be
of independent interest.
|
0605086v2
|
2007-05-16
|
Quantization Bounds on Grassmann Manifolds of Arbitrary Dimensions and MIMO Communications with Feedback
|
This paper considers the quantization problem on the Grassmann manifold with
dimension n and p. The unique contribution is the derivation of a closed-form
formula for the volume of a metric ball in the Grassmann manifold when the
radius is sufficiently small. This volume formula holds for Grassmann manifolds
with arbitrary dimension n and p, while previous results are only valid for
either p=1 or a fixed p with asymptotically large n. Based on the volume
formula, the Gilbert-Varshamov and Hamming bounds for sphere packings are
obtained. Assuming a uniformly distributed source and a distortion metric based
on the squared chordal distance, tight lower and upper bounds are established
for the distortion rate tradeoff. Simulation results match the derived results.
As an application of the derived quantization bounds, the information rate of a
Multiple-Input Multiple-Output (MIMO) system with finite-rate channel-state
feedback is accurately quantified for arbitrary finite number of antennas,
while previous results are only valid for either Multiple-Input Single-Output
(MISO) systems or those with asymptotically large number of transmit antennas
but fixed number of receive antennas.
|
0705.2272v1
|
2007-05-24
|
Local spin dynamic arising from the non-perturbative SU(2) gauge field of the spin orbit effect
|
We use the non-perturbative gauge field approach to study the effects of spin
orbit coupling on the dynamic of magnetic moment. We present a general equation
of motion (EOM) which unifies i) the spin orbit coupling effect derived from
the SU(2) spin gauge field, and ii) the moment chirality effect previously
derived from the topological U(1)xU(1) rotation gauge under the adiabatic
condition. We present a modified Landau-Liftshitz-Gilbert equation and discuss
the implication of the modified EOM in various technological applications, such
as current-induced switching and trajectory of magnetic moments in spin-valve
multilayers, magnetic memory and diluted magnetic semiconductor.
|
0705.3502v1
|
2007-06-07
|
$^{77}$Se NMR measurements of the $π-d$ exchange field in the organic conductor $λ-$(BETS)$_{2}$FeCl$_{4}$
|
$^{77}$Se-NMR spectrum and frequency shift measurements in the paramagnetic
metal (PM) and antiferromagnetic insulating (AFI) phases are reported for a
small single crystal of the organic conductor $\lambda-$(BETS)$_{2}$FeCl$_{4}$
as a function of temperature ($T$) and field alignment for an applied magnetic
field $B_{0}$ = 9 T. The results show that in the low $T$ limit, where the
localized Fe$^{3+}$ spins ($S_{d}$ = 5/2) are almost fully polarized, the
conduction electrons (Se $\pi$-electrons, spin $s_{\pi}$ = 1/2) in the BETS
molecules experience an exchange field ($\bf{B}$$_{\pi d}$) from the Fe$^{3+}$
spins with a value of $-$ 32.7 $\pm$ 1.5 T at 5 K and 9 T aligned opposite to
$\bf{B}$$_{0}$. This large negative value of $\bf{B}$$_{\pi d}$ is consistent
with that predicted by the resistivity measurements and supports the
Jaccarino-Peter internal field-compensation mechanism being responsible for the
origin of field-induced superconductivity.
|
0706.0933v1
|
2007-11-05
|
Feedback Capacity of the Compound Channel
|
In this work we find the capacity of a compound finite-state channel with
time-invariant deterministic feedback. The model we consider involves the use
of fixed length block codes. Our achievability result includes a proof of the
existence of a universal decoder for the family of finite-state channels with
feedback. As a consequence of our capacity result, we show that feedback does
not increase the capacity of the compound Gilbert-Elliot channel. Additionally,
we show that for a stationary and uniformly ergodic Markovian channel, if the
compound channel capacity is zero without feedback then it is zero with
feedback. Finally, we use our result on the finite-state channel to show that
the feedback capacity of the memoryless compound channel is given by
$\inf_{\theta} \max_{Q_X} I(X;Y|\theta)$.
|
0711.0705v1
|
2007-11-12
|
Mutual phase-locking in high frequency microwave nanooscillators as function of field angle
|
We perform a qualitative analysis of phase locking in a double point-contact
spinvalve system by solving the Landau-Lifshitz-Gilbert-Slonzewski equation
using a hybrid-finite-element method. We show that the phase-locking behaviour
depends on the applied field angle. Starting from a low field angle, the
locking-current difference between the current through contact A and B
increases with increasing angle up to a maximum of 14 mA at 30 degree and it
decreases thereafter until it reaches a minimum of 1 mA at 75 degree. The
tunability of the phase-lock frequency with current decreases linearly with
increasing out of plane angle from 45 to 21 MHz/mA.
|
0711.1770v2
|
2007-11-14
|
Emergent singular solutions of non-local density-magnetization equations in one dimension
|
We investigate the emergence of singular solutions in a non-local model for a
magnetic system. We study a modified Gilbert-type equation for the
magnetization vector and find that the evolution depends strongly on the length
scales of the non-local effects. We pass to a coupled density-magnetization
model and perform a linear stability analysis, noting the effect of the length
scales of non-locality on the system's stability properties. We carry out
numerical simulations of the coupled system and find that singular solutions
emerge from smooth initial data. The singular solutions represent a collection
of interacting particles (clumpons). By restricting ourselves to the
two-clumpon case, we are reduced to a two-dimensional dynamical system that is
readily analyzed, and thus we classify the different clumpon interactions
possible.
|
0711.2177v1
|
2007-11-27
|
Nonequilibrium interacting electrons in a ferromagnet
|
Dynamics of the magnetization in ferromagnets is examined in the presence of
transport electrons allowing the latter to interact. It is found that the
existence of inhomogeneities such as domain wall (DW) structures, leads to
changes that affect the dynamical structure of the equations of motion for the
magnetization. Only in the limit of uniform magnetizations or sufficiently wide
DW's, the equations of motion maintain the form they have in the noninteracting
case. In this limit, results like the spin torques, the Gilbert parameter, and
the DW velocities become renormalized. However the length scale that defines
such a limit depends on the strength of the interaction. It is shown that if
large ferromagnetic fluctuations exist in the metallic band then the range for
which conformity with the noninteracting case holds extends to the limit of
arbitrarily narrow DW's.
|
0711.4170v2
|
2007-12-01
|
On Precision - Redundancy Relation in the Design of Source Coding Algorithms
|
We study the effects of finite-precision representation of source's
probabilities on the efficiency of classic source coding algorithms, such as
Shannon, Gilbert-Moore, or arithmetic codes. In particular, we establish the
following simple connection between the redundancy $R$ and the number of bits
$W$ necessary for representation of source's probabilities in computer's memory
($R$ is assumed to be small): \begin{equation*} W \lesssim \eta \log_2
\frac{m}{R}, \end{equation*} where $m$ is the cardinality of the source's
alphabet, and $\eta \leqslant 1$ is an implementation-specific constant. In
case of binary alphabets ($m=2$) we show that there exist codes for which $\eta
= 1/2$, and in $m$-ary case ($m > 2$) we show that there exist codes for which
$\eta = m/(m+1)$. In general case, however (which includes designs relying on
progressive updates of frequency counters), we show that $\eta = 1$. Usefulness
of these results for practical designs of source coding algorithms is also
discussed.
|
0712.0057v1
|
2007-12-03
|
Kinetic models of heterogeneous dissipation
|
We suggest kinetic models of dissipation for an ensemble of interacting
oriented particles, for example, moving magnetized particles. This is achieved
by introducing a double bracket dissipation in kinetic equations using an
oriented Poisson bracket, and employing the moment method to derive continuum
equations for magnetization and density evolution. We show how our continuum
equations generalize the Debye-Hueckel equations for attracting round
particles, and Landau-Lifshitz-Gilbert equations for spin waves in magnetized
media. We also show formation of singular solutions that are clumps of aligned
particles (orientons) starting from random initial conditions. Finally, we
extend our theory to the dissipative motion of self-interacting curves.
|
0712.0397v1
|
2007-12-13
|
Euler equation of the optimal trajectory for the fastest magnetization reversal of nano-magnetic structures
|
Based on the modified Landau-Lifshitz-Gilbert equation for an arbitrary
Stoner particle under an external magnetic field and a spin-polarized electric
current, differential equations for the optimal reversal trajectory, along
which the magnetization reversal is the fastest one among all possible reversal
routes, are obtained. We show that this is a Euler-Lagrange problem with
constrains. The Euler equation of the optimal trajectory is useful in designing
a magnetic field pulse and/or a polarized electric current pulse in
magnetization reversal for two reasons. 1) It is straightforward to obtain the
solution of the Euler equation, at least numerically, for a given magnetic
nano-structure characterized by its magnetic anisotropy energy. 2) After
obtaining the optimal reversal trajectory for a given magnetic nano-structure,
finding a proper field/current pulse is an algebraic problem instead of the
original nonlinear differential equation.
|
0712.2101v1
|
2007-12-18
|
Effect of Edge Roughness on Electronic Transport in Graphene Nanoribbon Channel Metal Oxide Semiconductor Field-Effect Transistors
|
Results of quantum mechanical simulations of the influence of edge disorder
on transport in graphene nanoribbon metal oxide semiconductor field-effect
transistors (MOSFETs) are reported. The addition of edge disorder significantly
reduces ON-state currents and increases OFF-state currents, and introduces wide
variability across devices. These effects decrease as ribbon widths increase
and as edges become smoother. However the bandgap decreases with increasing
width, thereby increasing the band-to-band tunneling mediated subthreshold
leakage current even with perfect nanoribbons. These results suggest that
without atomically precise edge control during fabrication, MOSFET performance
gains through use of graphene will be difficult to achieve.
|
0712.3068v1
|
2007-12-22
|
Explicit Non-Adaptive Combinatorial Group Testing Schemes
|
Group testing is a long studied problem in combinatorics: A small set of $r$
ill people should be identified out of the whole ($n$ people) by using only
queries (tests) of the form "Does set X contain an ill human?". In this paper
we provide an explicit construction of a testing scheme which is better
(smaller) than any known explicit construction. This scheme has $\bigT{\min[r^2
\ln n,n]}$ tests which is as many as the best non-explicit schemes have. In our
construction we use a fact that may have a value by its own right: Linear
error-correction codes with parameters $[m,k,\delta m]_q$ meeting the
Gilbert-Varshamov bound may be constructed quite efficiently, in $\bigT{q^km}$
time.
|
0712.3876v5
|
2007-12-31
|
Risk management for analytical methods: conciliating objectives of methods, validation phase and routine decision rules
|
In the industries that involved either chemistry or biology, such as
pharmaceutical industries, chemical industries or food industry, the analytical
methods are the necessary eyes and hear of all the material produced or used.
If the quality of an analytical method is doubtful, then the whole set of
decision that will be based on those measures is questionable. For those
reasons, being able to assess the quality of an analytical method is far more
than a statistical challenge; it's a matter of ethic and good business
practices. Many regulatory documents have been releases, primarily ICH and FDA
documents in the pharmaceutical industry (FDA, 1995, 1997, 2001) to address
that issue.
|
0801.0207v1
|
2008-01-06
|
An Efficient Method for Quantum Transport Calculations in Nanostructures using Full Band Structure
|
Scaling of semiconductor devices has reached a stage where it has become
absolutely imperative to consider the quantum mechanical aspects of transport
in these ultra small devices. In these simulations, often one excludes a
rigorous band structure treatment, since it poses a huge computational
challenge. We have proposed here an efficient method for calculating full
three-dimensionally coupled quantum transport in nanowire transistors including
full band structure. We have shown the power of the method by simulating hole
transport in p-type Ge nanowire transistors. The hole band structure obtained
from our nearest neighbor sp3s* tight binding Hamiltonian agrees well
qualitatively with more complex and accurate calculations that take third
nearest neighbors into account. The calculated I-V results show how shifting of
the energy bands due to confinement can be accurately captured only in a full
band full quantum simulation.
|
0801.0880v1
|
2008-01-07
|
Magnetization reversal driven by spin-injection : a mesoscopic spin-transfer effect
|
A mesoscopic description of spin-transfer effect is proposed, based on the
spin-injection mechanism occurring at the junction with a ferromagnet. The
effect of spin-injection is to modify locally, in the ferromagnetic
configuration space, the density of magnetic moments. The corresponding
gradient leads to a current-dependent diffusion process of the magnetization.
In order to describe this effect, the dynamics of the magnetization of a
ferromagnetic single domain is reconsidered in the framework of the
thermokinetic theory of mesoscopic systems. Assuming an Onsager
cross-coefficient that couples the currents, it is shown that spin-dependent
electric transport leads to a correction of the Landau-Lifshitz-Gilbert
equation of the ferromagnetic order parameter with supplementary diffusion
terms. The consequence of spin-injection in terms of activation process of the
ferromagnet is deduced, and the expressions of the effective energy barrier and
of the critical current are derived. Magnetic fluctuations are calculated: the
correction to the fluctuations is similar to that predicted for the activation.
These predictions are consistent with the measurements of spin-transfer
obtained in the activation regime and for ferromagnetic resonance under
spin-injection.
|
0801.1019v1
|
2008-01-25
|
New Lower Bounds on Sizes of Permutation Arrays
|
A permutation array(or code) of length $n$ and distance $d$, denoted by
$(n,d)$ PA, is a set of permutations $C$ from some fixed set of $n$ elements
such that the Hamming distance between distinct members
$\mathbf{x},\mathbf{y}\in C$ is at least $d$. Let $P(n,d)$ denote the maximum
size of an $(n,d)$ PA. This correspondence focuses on the lower bound on
$P(n,d)$. First we give three improvements over the Gilbert-Varshamov lower
bounds on $P(n,d)$ by applying the graph theorem framework presented by Jiang
and Vardy. Next we show another two new improved bounds by considering the
covered balls intersections. Finally some new lower bounds for certain values
of $n$ and $d$ are given.
|
0801.3986v1
|
2008-01-30
|
Femtosecond Control of the Magnetization in Ferromagnetic Semiconductors
|
We develop a theory of collective spin dynamics triggered by ultrafast
optical excitation of ferromagnetic semiconductors. Using the density matrix
equations of motion in the mean field approximation and including magnetic
anisotropy and hole spin dephasing effects, we predict the development of a
light--induced magnetization tilt during ultra--short time intervals comparable
to the pulse duration. This femtosecond dynamics in the coherent temporal
regime is governed by the interband nonlinear optical polarizations and is
followed by a second temporal regime governed by the magnetic anisotropy of the
Fermi sea. We interpret our numerical results by deriving a
Landau--Gilbert--like equation for the collective spin, which demonstrates an
ultrafast correction to the magnetic anisotropy effective field due to second
order coherent nonlinear optical processes. Using the Lindblad semigroup
method, we also derive a contribution to the interband polarization dephasing
determined by the Mn spin and the hole spin dephasing. Our predicted
magnetization tilt and subsequent nonlinear dynamics due to the magnetic
anisotropy can be controlled by varying the optical pulse intensity, duration,
and helicity and can be observed with pump--probe magneto--optical
spectroscopy.
|
0801.4641v1
|
2008-02-01
|
Vortex Ferroelectric Domains
|
We show experimental switching data on microscale capacitors of
lead-zirconate-titanate (PZT), which reveal time-resolved domain behavior
during switching on a 100-ns scale. For small circular capacitors, an
unswitched domain remains in the center while complete switching is observed in
square capacitors. The observed effect is attributed to the formation of vortex
domain during polarization switching in circular capacitors. This dynamical
behavior is modeled using the Landau-Liftshitz-Gilbert equations and found to
be in detailed agreement with experiment. This simulation implies rotational
motion of polarization in the xy-plane, a Heisenberg-like result supported by
the recent model of Naumov and Fu [Phys. Rev. Lett. 98, 077603 (2007)],
although not directly measurable by the present quasi-static measurements.
|
0802.0186v1
|
2008-02-11
|
Structure and Optimality of Myopic Policy in Opportunistic Access with Noisy Observations
|
A restless multi-armed bandit problem that arises in multichannel
opportunistic communications is considered, where channels are modeled as
independent and identical Gilbert-Elliot channels and channel state
observations are subject to errors. A simple structure of the myopic policy is
established under a certain condition on the false alarm probability of the
channel state detector. It is shown that the myopic policy has a semi-universal
structure that reduces channel selection to a simple round-robin procedure and
obviates the need to know the underlying Markov transition probabilities. The
optimality of the myopic policy is proved for the case of two channels and
conjectured for the general case based on numerical examples.
|
0802.1379v2
|
2008-02-12
|
Domain walls in (Ga,Mn)As diluted magnetic semiconductor
|
We report experimental and theoretical studies of magnetic domain walls in an
in-plane magnetized (Ga,Mn)As dilute moment ferromagnetic semiconductor. Our
high-resolution electron holography technique provides direct images of domain
wall magnetization profiles. The experiments are interpreted based on
microscopic calculations of the micromagnetic parameters and
Landau-Lifshitz-Gilbert simulations. We find that the competition of uniaxial
and biaxial magnetocrystalline anisotropies in the film is directly reflected
in orientation dependent wall widths, ranging from approximately 40 nm to 120
nm. The domain walls are of the N\'eel type and evolve from near-$90^{\circ}$
walls at low-temperatures to large angle [1$\bar{1}$0]-oriented walls and small
angle [110]-oriented walls at higher temperatures.
|
0802.1574v1
|
2008-02-21
|
Solving functional reliability issue for an optical electrostatic switch
|
In this paper, we report the advantage of using AC actuating signal for
driving MEMS actuators instead of DC voltages. The study is based upon micro
mirror devices used in digital mode for optical switching operation. When the
pull-in effect is used, charge injection occurs when the micro mirror is
maintained in the deflected position. To avoid this effect, a geometrical
solution is to realize grounded landing electrodes which are electro-statically
separated from the control electrodes. Another solution is the use of AC signal
which eliminates charge injection particularly if a bipolar signal is used.
Long term experiments have demonstrated the reliability of such a signal
command to avoid injection of electric charges.
|
0802.3075v1
|
2008-02-21
|
First principles calculation of spin-interactions and magnetic ground states of Cr trimers on Au(111)
|
We present calculations of the magnetic ground states of Cr trimers in
different geometries on top of a Au(111) surface. By using a least square fit
method based on a fully relativistic embedded-cluster Green's function method
first we determined the parameters of a classical vector-spin model consisting
of second and fourth order interactions. The newly developed method requires no
symmetry constraints, therefore, it is throughout applicable for small
nanoparticles of arbitrary geometry. The magnetic ground states were then found
by solving the Landau-Lifshitz-Gilbert equations. In all considered cases the
configurational energy of the Cr trimers is dominated by large
antiferromagnetic nearest neighbor interactions, whilst biquadratic
spin-interactions have the second largest contributions to the energy. We find
that an equilateral Cr trimer exhibits a frustrated 120$^\circ$ N\'eel type of
ground state with a small out-of-plane component of the magnetization and we
show that the Dzyaloshinsky-Moriya interactions determine the chirality of the
magnetic ground state. In cases of a linear chain and an isosceles trimer
collinear antiferromagnetic ground states are obtained with a magnetization
lying parallel to the surface.
|
0802.3113v1
|
2008-04-07
|
Energy equilibriation processes of electrons, magnons and phonons on the femtosecond timescale
|
By means of time-resolved Kerr spectroscopy experiments we relate the energy
dissipation processes on the femtosecond (electron-spin relaxation time
$\tau_{el-sp}$) and nanosecond timescale (Gilbert relaxation $\tau_{\alpha}$)
and compare the results to the first microscopic model, which was proposed by
Koopmans. For both energy dissipation processes, Elliot-Yafet scattering is
proposed as the dominant contributor. We controllably manipulate the energy
dissipation processes by transition metal doping (Pd) and rare earth doping
(Dy) of a Permalloy film and find that while a change of $\tau_{\alpha}$ of
more than a factor two is observed, \tau_{el-sp}$ remains constant, contrary to
the predictions of the model. We explain the discrepancies by relaxation
channels not considered in the original microscopic model and identify thereby
the applicability of the model and possible necessary extensions to the model.
|
0804.0985v1
|
2008-04-07
|
Woven Graph Codes: Asymptotic Performances and Examples
|
Constructions of woven graph codes based on constituent block and
convolutional codes are studied. It is shown that within the random ensemble of
such codes based on $s$-partite, $s$-uniform hypergraphs, where $s$ depends
only on the code rate, there exist codes satisfying the Varshamov-Gilbert (VG)
and the Costello lower bound on the minimum distance and the free distance,
respectively. A connection between regular bipartite graphs and tailbiting
codes is shown. Some examples of woven graph codes are presented. Among them an
example of a rate $R_{\rm wg}=1/3$ woven graph code with $d_{\rm free}=32$
based on Heawood's bipartite graph and containing $n=7$ constituent rate
$R^{c}=2/3$ convolutional codes with overall constraint lengths $\nu^{c}=5$ is
given. An encoding procedure for woven graph codes with complexity proportional
to the number of constituent codes and their overall constraint length
$\nu^{c}$ is presented.
|
0804.0996v2
|
2008-05-26
|
Photometric Follow-up Observations of the Transiting Neptune-Mass Planet GJ 436b
|
This paper presents multi-band photometric follow-up observations of the
Neptune-mass transiting planet GJ 436b, consisting of 5 new ground-based
transit light curves obtained in May 2007. Together with one already published
light curve we have at hand a total of 6 light curves, spanning 29 days. The
analysis of the data yields an orbital period P = 2.64386+-0.00003 days,
mid-transit time T_c [HJD] =2454235.8355+-0.0001, planet mass M_p = 23.1+-0.9
M_{\earth} = 0.073+-0.003 M_{Jup}, planet radius R_p = 4.2+-0.2 R_{\earth} =
0.37+-0.01 R_{Jup} and stellar radius R_s = 0.45+-0.02 R_{\sun}. Our typical
precision for the mid transit timing for each transit is about 30 seconds. We
searched the data for a possible signature of a second planet in the system
through transit timing variations (TTV) and variation of the impact parameter.
The analysis could not rule out a small, of the order of a minute, TTV and a
long-term modulation of the impact parameter, of the order of +0.2 year^{-1}.
|
0805.3915v2
|
2008-06-04
|
Broadband electrical detection of spin excitations in (Ga,Mn)As using a photovoltage technique
|
We report on microwave photovoltage and simultaneous magnetotransport
measurements in a (Ga,Mn)As film oriented normal to the magnetic field. We
detect the ferromagnetic resonance over a broad frequency range of 2 GHz to
18.5 GHz and determine the spectroscopic g-factor and separate the Gilbert from
the inhomogeneous contribution to magnetization relaxation. Temperature
dependent measurements below the saturation magnetization indicate that the
photovoltage signal can serve as a sensitive tool to study the crystal
anisotropy. We demonstrate that the combination of spin dynamics with charge
transport is a promising tool to study microstructured ferromagnetic
semiconductor samples.
|
0806.0785v1
|
2008-07-10
|
Mechanical and Electronic Properties of Ferromagnetic GaMnAs Using Ultrafast Coherent Acoustic Phonons
|
Ultrafast two-color pump-probe measurements, involving coherent acoustic
phonon (CAP) waves, have provided information simultaneously on the mechanical
properties and on the electronic structure of ferromagnetic GaMnAs. The elastic
constant C11 of Ga1-xMnxAs (0.03<x<0.07) are observed to be systematically
smaller than those of GaAs. Both C11 and Vs of GaMnAs are found to increase
with temperature (78 K<T<295 K), again in contrast to the opposite behavior in
GaAs. In addition, the fundamental bandgap (at E0 critical point) of Ga1-xMnxAs
is found to shift slightly to higher energies with Mn concentration.
|
0807.1740v2
|
2008-08-05
|
A Proof of George Andrews' and Dave Robbins' q-TSPP Conjecture (modulo a finite amount of routine calculations)
|
In the historic conference Combinatoire Enumerative[LL] wonderfully organized
by Gilbert Labelle and Pierre Leroux there were many stimulating lectures,
including a very interesting one by Pierre Leroux himself, who talked about his
joint work with Xavier Viennot[LV], on solving differential equations
combinatorially! During the problem session of that very same colloque, chaired
by Pierre Leroux, Richard Stanley raised some intriguing problems about the
enumeration of plane partitions, that he later expanded into a fascinating
article[Sta1]. Most of these problems concerned the enumeration of symmetry
classes of plane partitions, that were discussed in more detail in another
article of Stanley[Sta2]. All of the conjectures in the latter article have
since been proved (see Dave Bressoud's modern classic[B]), except one, that, so
far, resisted the efforts of the greatest minds in enumerative combinatorics.
It concerns the proof of an explicit formula for the q-enumeration of totally
symmetric plane partitions, conjectured independently by George Andrews and
Dave Robbins([Sta2],[Sta1](conj. 7), [B](conj. 13)). In this tribute to Pierre
Leroux, we describe how to prove that last stronghold.
|
0808.0571v2
|
2008-08-09
|
On some deterministic dictionaries supporting sparsity
|
We describe a new construction of an incoherent dictionary, referred to as
the oscillator dictionary, which is based on considerations in the
representation theory of finite groups. The oscillator dictionary consists of
order of p^5 unit vectors in a Hilbert space of dimension p, where p is an odd
prime, whose pairwise inner products have magnitude of at most 4/sqrt(p). An
explicit algorithm to construct a large portion of the oscillator dictionary is
presented.
|
0808.1368v2
|
2008-08-13
|
Spin Filter, Spin Amplifier and Other Spintronic Applications in Graphene Nanodisks
|
Graphene nanodisk is a graphene derivative with a closed edge. The trigonal
zigzag nanodisk with size $N$ has $N$-fold degenerated zero-energy states. A
nanodisk can be interpletted as a quantum dot with an internal degree of
freedom. The grand state of nanodisk has been argued to be a quasi-ferromagnet,
which is a ferromagnetic-like states with a finite but very long life time. We
investigate the spin-filter effects in the system made of nanodisks and leads
based on the master equation. The finite-size effect on spin filter is
intriguing due to a reaction from the polarization of incoming current to a
quasi-ferromagnet. Analyzing the relaxation process with the use of the
Landau-Lifshitz-Gilbert equation, we explore the response to four types of
incoming currents, namely, unpolarized current, perfectly polarized current,
partially polarized current and pulse polarized current. We propose some
applications for spintronics, such as spin memory, spin amplifier, spin valve,
spin-field-effect transistor and spin diode.
|
0808.1779v1
|
2008-08-26
|
Codes on hypergraphs
|
Codes on hypergraphs are an extension of the well-studied family of codes on
bipartite graphs. Bilu and Hoory (2004) constructed an explicit family of codes
on regular t-partite hypergraphs whose minimum distance improves earlier
estimates of the distance of bipartite-graph codes. They also suggested a
decoding algorithm for such codes and estimated its error-correcting
capability.
In this paper we study two aspects of hypergraph codes. First, we compute the
weight enumerators of several ensembles of such codes, establishing conditions
under which they attain the Gilbert-Varshamov bound and deriving estimates of
their distance. In particular, we show that this bound is attained by codes
constructed on a fixed bipartite graph with a large spectral gap.
We also suggest a new decoding algorithm of hypergraph codes that corrects a
constant fraction of errors, improving upon the algorithm of Bilu and Hoory.
|
0808.3453v2
|
2008-09-26
|
Ultra-fast spin dynamics: the effect of colored noise
|
Recent experimental results have pushed the limits of magnetization dynamics
to pico- and femtosecond timescales. This ultra-fast spin dynamics occurs in
extreme conditions of strong and rapidly varying fields and high temperatures.
This situation requires new description of magnetization dynamics, even on a
phenomenological level of the atomistic Landau-Lifshitz-Gilbert equation,
taking into account that the correlation time for electron system could be of
the order of the inverse characteristic spin frequency. For this case we
introduce the thermodynamically correct phenomenological approach for spin
dynamics based on the Landau-Lifshitz-Miyasaki-Seki equation. The influence of
the noise correlation time on longitudinal and transverse magnetization
relaxation is investigated. We also demonstrate the effect of the noise
correlation time on demagnetisation rate of different materials during
laser-induced dynamics.
|
0809.4595v1
|
2008-10-08
|
Magnetic particle hyperthermia: Neel relaxation in magnetic nanoparticles under circularly polarized field
|
The mechanism of magnetization reversal in single-domain ferromagnetic
particles is of interest in many applications, in most of which losses must be
minimized. In cancer therapy by hyperthermia the opposite requirement prevails:
the specific loss power should be maximized. Of the mechanisms of dissipation,
here we study the effect of Neel relaxation on magnetic nanoparticles unable to
move or rotate and compare the losses in linearly and circularly polarized
field. We present exact analytical solutions of the Landau-Lifshitz equation as
derived from the Gilbert equation and use the calculated time-dependent
magnetizations to find the energy loss per cycle. In frequencies lower than the
Larmor frequency linear polarization is found to be the better source of heat
power, at high frequencies (beyond the Larmor frequency) circular polarization
is preferable.
|
0810.1455v2
|
2008-10-10
|
SOSEMANUK: a fast software-oriented stream cipher
|
Sosemanuk is a new synchronous software-oriented stream cipher, corresponding
to Profile 1 of the ECRYPT call for stream cipher primitives. Its key length is
variable between 128 and 256 bits. It ac- commodates a 128-bit initial value.
Any key length is claimed to achieve 128-bit security. The Sosemanuk cipher
uses both some basic design principles from the stream cipher SNOW 2.0 and some
transformations derived from the block cipher SERPENT. Sosemanuk aims at
improv- ing SNOW 2.0 both from the security and from the efficiency points of
view. Most notably, it uses a faster IV-setup procedure. It also requires a
reduced amount of static data, yielding better performance on several
architectures.
|
0810.1858v1
|
2008-11-14
|
Trees of cylinders and canonical splittings
|
Let T be a tree with an action of a finitely generated group G. Given a
suitable equivalence relation on the set of edge stabilizers of T (such as
commensurability, co-elementarity in a relatively hyperbolic group, or
commutation in a commutative transitive group), we define a tree of cylinders
T_c. This tree only depends on the deformation space of T; in particular, it is
invariant under automorphisms of G if T is a JSJ splitting. We thus obtain
Out(G)-invariant cyclic or abelian JSJ splittings. Furthermore, T_c has very
strong compatibility properties (two trees are compatible if they have a common
refinement).
|
0811.2383v2
|
2008-11-21
|
Numerical Study of Current-Induced Domain-Wall Dynamics: Crossover from Spin Transfer to Momentum Transfer
|
We study current-induced dynamics of a magnetic domain wall by solving a
time-dependent Schr\"{o}dinger equation combined with Landau-Lifshitz-Gilbert
equation in a one-dimensional electron system coupled to localized spins. Two
types of domain-wall motions are observed depending on the hard-axis
anisotropy, $K_{\perp}$, of the localized spin system. For small values of
$K_{\perp}$, the magnetic domain wall shows a streaming motion driven by spin
transfer. In contrast, for large values of $K_{\perp}$, a stick-slip motion
driven by momentum transfer is obtained. We clarify the origin of these
characters of domain-wall motions in terms of the dynamics of one-particle
energy levels and distribution functions.
|
0811.3545v2
|
2008-12-02
|
Application of Conformal Mapping to the determination of Magnetic Moment Distributions in typical Antidot Film Nanostructures
|
There has been an increasing technological interest on magnetic thin films
containing antidot arrays of hexagonal or square symmetry. Part of this
interest is related to the possibility of domain formation and pinning at the
antidots boundaries. In this paper, we develop a method for the calculation of
the magnetic moment distribution for such arrays which concentrates on the
immediate vicinity of each antidot. For each antidot distribution (square or
hexagonal) a suitable system of coordinates is defined to exploit the shape of
the unit-cells of the overall nanostructure. The Landau-Lifshitz-Gilbert-Brown
equations that govern the distribution of moments are rewritten in terms of
these coordinates. The equilibrium moments orientation is calculated for each
position in a Cartesian grid defined for these new coordinate systems, and then
a conformal transformation is applied to insert the moment vectors into the
actual unit-cell. The resulting vector maps display quite clearly regions of
different moment orientation around the antidots, which can be associated with
nanoscale domains. These results are similar to the ones obtained by other
authors[1-4] using the NIST oommf method.
|
0812.0566v1
|
2009-01-09
|
A Better Way to Deal the Cards
|
This paper considers the effect of riffle shuffling on decks of cards,
allowing for some cards to be indistinguishable from other cards. The dual
problem of dealing a game with hands, such as bridge or poker, is also
considered. The Gilbert-Shannon-Reeds model of card shuffling is used, along
with variation distance for measuring how close to uniform a deck has become.
The surprising results are that for a deck with only two types of cards (such
as red and black), the shuffler can greatly improve the randomness of the deck
by insuring that the top and bottom cards are the same before shuffling. And in
the case of dealing cards for a game with "hands", such as bridge or poker, the
normal method of dealing cyclically around the table is very far from optimal.
In the case of a well-shuffled bridge deck, changing to another dealing method
is as good as doing 3.7 extra shuffles. How the deck is cut in poker affects
its randomness as well.
|
0901.1324v4
|
2009-03-12
|
Accuracy thresholds of topological color codes on the hexagonal and square-octagonal lattices
|
Accuracy thresholds of quantum error correcting codes, which exploit
topological properties of systems, defined on two different arrangements of
qubits are predicted. We study the topological color codes on the hexagonal
lattice and on the square-octagonal lattice by the use of mapping into the spin
glass systems. The analysis for the corresponding spin glass systems consists
of the duality, and the gauge symmetry, which has succeeded in deriving
locations of special points, which are deeply related with the accuracy
thresholds of topological error correcting codes. We predict that the accuracy
thresholds for the topological color codes would be $1-p_c = 0.1096-8 $ for the
hexagonal lattice and $1-p_c = 0.1092-3$ for the square-octagonal lattice,
where $1-p$ denotes the error probability on each qubit. Hence both of them are
expected to be slightly lower than the probability $1-p_c = 0.110028$ for the
quantum Gilbert-Varshamov bound with a zero encoding rate.
|
0903.2102v5
|
2009-03-12
|
Designing Optimal Flow Networks
|
We investigate the problem of designing a minimum cost flow network
interconnecting n sources and a single sink, each with known locations and
flows. The network may contain other unprescribed nodes, known as Steiner
points. For concave increasing cost functions, a minimum cost network of this
sort has a tree topology, and hence can be called a Minimum Gilbert
Arborescence (MGA). We characterise the local topological structure of Steiner
points in MGAs for linear cost functions. This problem has applications to the
design of drains, gas pipelines and underground mine access.
|
0903.2124v1
|
2009-04-13
|
Refined Coding Bounds and Code Constructions for Coherent Network Error Correction
|
Coherent network error correction is the error-control problem in network
coding with the knowledge of the network codes at the source and sink nodes.
With respect to a given set of local encoding kernels defining a linear network
code, we obtain refined versions of the Hamming bound, the Singleton bound and
the Gilbert-Varshamov bound for coherent network error correction. Similar to
its classical counterpart, this refined Singleton bound is tight for linear
network codes. The tightness of this refined bound is shown by two construction
algorithms of linear network codes achieving this bound. These two algorithms
illustrate different design methods: one makes use of existing network coding
algorithms for error-free transmission and the other makes use of classical
error-correcting codes. The implication of the tightness of the refined
Singleton bound is that the sink nodes with higher maximum flow values can have
higher error correction capabilities.
|
0904.1897v2
|
2009-04-27
|
Effect of resistance feedback on spin torque-induced switching of nanomagnets
|
In large magnetoresistance devices spin torque-induced changes in resistance
can produce GHz current and voltage oscillations which can affect magnetization
reversal. In addition, capacitive shunting in large resistance devices can
further reduce the current, adversely affecting spin torque switching. Here, we
simultaneously solve the Landau-Lifshitz-Gilbert equation with spin torque and
the transmission line telegrapher's equations to study the effects of
resistance feedback and capacitance on magnetization reversal of both spin
valves and magnetic tunnel junctions. While for spin valves parallel (P) to
anti-parallel (AP) switching is adversely affected by the resistance feedback
due to saturation of the spin torque, in low resistance magnetic tunnel
junctions P-AP switching is enhanced. We study the effect of resistance
feedback on the switching time of MTJ's, and show that magnetization switching
is only affected by capacitive shunting in the pF range.
|
0904.4159v2
|
2009-04-30
|
A microscopic model for current-induced switching of magnetization for half-metallic leads
|
We study the behaviour of the magnetization in a half-metallic
ferromagnet/nonmagnetic insulator/ferromagnetic metal/paramagnetic metal
(FM1/NI/FM2/PM) tunnel junction. It is calculated self-consistently within the
nonequilibrium Keldysh formalism. The magnetic regions are treated as band
ferromagnets and are described by the single-band Hubbard model. We developed a
nonequilibrium spectral density approach to solve the Hubbard model
approximately in the switching magnet. By applying a voltage to the junction it
is possible to switch between antiparallel (AP) and parallel (P) alignment of
the magnetizations of the two ferromagnets. The transition from AP to P occurs
for positive voltages while the inverse transition from P to AP can be induced
by negative voltages only. This behaviour is in agreement with the Slonczewski
model of current-induced switching and appears self-consistently within the
model, i.e. without using half-classical methods like the
Landau-Lifshitz-Gilbert equation.
|
0904.4821v1
|
2009-05-26
|
Scattering Theory of Charge-Current Induced Magnetization Dynamics
|
In ferromagnets, charge currents can excite magnons via the spin-orbit
coupling. We develop a novel and general scattering theory of charge current
induced macrospin magnetization torques in normal metal$|$ferromagnet$|$normal
metal layers. We apply the formalism to a dirty GaAs$|$(Ga,Mn)As$|$GaAs system.
By computing the charge current induced magnetization torques and solving the
Landau-Lifshitz-Gilbert equation, we find magnetization switching for current
densities as low as $ 5\times 10^{6}$~A/cm$^2$. Our results are in agreement
with a recent experimental observation of charge-current induced magnetization
switching in (Ga,Mn)As.
|
0905.4170v2
|
2009-05-28
|
Riffle shuffles of a deck with repeated cards
|
We study the Gilbert-Shannon-Reeds model for riffle shuffles and ask
'How many times must a deck of cards be shuffled for the deck to be in close
to random order?'. In 1992, Bayer and Diaconis gave a solution which gives
exact and asymptotic results for all decks of practical interest, e.g. a deck
of 52 cards. But what if one only cares about the colors of the cards or
disregards the suits focusing solely on the ranks? More generally, how does the
rate of convergence of a Markov chain change if we are interested in only
certain features? Our exploration of this problem takes us through random walks
on groups and their cosets, discovering along the way exact formulas leading to
interesting combinatorics, an 'amazing matrix', and new analytic methods which
produce a completely general asymptotic solution that is remarkable accurate.
|
0905.4698v1
|
2009-07-20
|
Correcting Limited-Magnitude Errors in the Rank-Modulation Scheme
|
We study error-correcting codes for permutations under the infinity norm,
motivated by a novel storage scheme for flash memories call rank modulation. In
this scheme, a set of $n$ flash cells are combined to create a single virtual
multi-level cell. Information is stored in the permutation induced by the cell
charge levels. Spike errors, which are characterized by a limited-magnitude
change in cell charge levels, correspond to a low-distance change under the
infinity norm.
We define codes protecting against spike errors, called limited-magnitude
rank-modulation codes (LMRM codes), and present several constructions for these
codes, some resulting in optimal codes. These codes admit simple recursive, and
sometimes direct, encoding and decoding procedures.
We also provide lower and upper bounds on the maximal size of LMRM codes both
in the general case, and in the case where the codes form a subgroup of the
symmetric group. In the asymptotic analysis, the codes we construct out-perform
the Gilbert-Varshamov-like bound estimate.
|
0907.3387v2
|
2009-07-22
|
Searching for variable stars in Galactic Open Clusters
|
A long-term project, aiming at systematic search for variable stars in
Galactic Open Clusters, was started at the Geneva Observatory in 2002. We have
been observing regularly a sample of twenty-seven Galactic Open Clusters in the
U, B, V Geneva filters. The goal is to identify and to study their variable
stars, as well as the connection between the variable stars in a cluster and
the cluster properties. We present the status of this work in progress, and
show preliminary results for one of these clusters, IC 4651.
|
0907.3834v1
|
2009-07-23
|
Variability morphologies in the color-magnitude diagram. Searching for secular variability
|
This work is part of an effort to detect secular variable objects in large
scale surveys by analysing their path in color-magnitude diagrams. To this aim,
we first present the variability morphologies in the V/V-I diagram of several
types of variable stars. They comprise both periodic and non periodic variable
stars from the Large Magellanic Cloud, such as classical Cepheids, long period
variables or Be and R Coronae Borealis stars, as well as two of the detected
secular variable stars in the Galaxy, FG Sge and V4334 Sgr. The study of the
different variability morphologies allows the identification of regions in the
color-magnitude diagram where those secular variable stars could be detected.
We also estimate the number of such secular variable stars expected in the
Large Magellanic Cloud.
|
0907.4090v1
|
2009-08-03
|
Regret Bounds for Opportunistic Channel Access
|
We consider the task of opportunistic channel access in a primary system
composed of independent Gilbert-Elliot channels where the secondary (or
opportunistic) user does not dispose of a priori information regarding the
statistical characteristics of the system. It is shown that this problem may be
cast into the framework of model-based learning in a specific class of
Partially Observed Markov Decision Processes (POMDPs) for which we introduce an
algorithm aimed at striking an optimal tradeoff between the exploration (or
estimation) and exploitation requirements. We provide finite horizon regret
bounds for this algorithm as well as a numerical evaluation of its performance
in the single channel model as well as in the case of stochastically identical
channels.
|
0908.0319v1
|
2009-08-14
|
Non-Gaussian Scatter in Cluster Scaling Relations
|
We investigate the impact of non-Gaussian scatter in the cluster
mass-observable scaling relation on the mass and redshift distribution of
clusters detected by wide area surveys. We parameterize non-Gaussian scatter by
incorporating the third and forth moments (skewness and kurtosis) into the
distribution P(Mobs|M). We demonstrate that for low scatter mass proxies the
higher order moments do not significantly affect the observed cluster mass and
redshift distributions. However, for high scatter mass indicators it is
necessary for the survey limiting mass threshold to be less than 10^14 h^-1
Msol to prevent the skewness from having a significant impact on the observed
number counts, particularly at high redshift. We also show that an unknown
level of non-Gaussianity in the scatter is equivalent to an additional
uncertainty on the variance in P(Mobs|M) and thus may limit the constraints
that can be placed on the dark energy equation of state parameter w.
Furthermore, positive skewness flattens the mass function at the high mass end,
and so one must also account for skewness in P(Mobs|M) when using the shape of
the mass function to constrain cluster scaling-relations.
|
0908.1978v1
|
2009-08-17
|
A local moment approach to the degenerate Anderson impurity model
|
The local moment approach is extended to the orbitally-degenerate [SU(2N)]
Anderson impurity model (AIM). Single-particle dynamics are obtained over the
full range of energy scales, focussing here on particle-hole symmetry in the
strongly correlated regime where the onsite Coulomb interaction leads to
many-body Kondo physics with entangled spin and orbital degrees of freedom. The
approach captures many-body broadening of the Hubbard satellites, recovers the
correct exponential vanishing of the Kondo scale for all N, and its universal
scaling spectra are found to be in very good agreement with numerical
renormalization group (NRG) results. In particular the high-frequency
logarithmic decays of the scaling spectra, obtained here in closed form for
arbitrary N, coincide essentially perfectly with available numerics from the
NRG. A particular case of an anisotropic Coulomb interaction, in which the
model represents a system of N `capacitively-coupled' SU(2) AIMs, is also
discussed. Here the model is generally characterised by two low-energy scales,
the crossover between which is seen directly in its dynamics.
|
0908.2245v1
|
2009-10-20
|
Bifurcation and chaos in spin-valve pillars in a periodic applied magnetic field
|
We study the bifurcation and chaos scenario of the macro-magnetization vector
in a homogeneous nanoscale-ferromagnetic thin film of the type used in
spin-valve pillars. The underlying dynamics is described by a generalized
Landau-Lifshitz-Gilbert (LLG) equation. The LLG equation has an especially
appealing form under a complex stereographic projection, wherein the
qualitative equivalence of an applied field and a spin-current induced torque
is transparent. Recently chaotic behavior of such a spin vector has been
identified by Zhang and Li using a spin polarized current passing through the
pillar of constant polarization direction and periodically varying magnitude,
owing to the spin-transfer torque effect. In this paper we show that the same
dynamical behavior can be achieved using a periodically varying applied
magnetic field, in the presence of a constant DC magnetic field and constant
spin current, which is technically much more feasible, and demonstrate
numerically the chaotic dynamics in the system for an infinitely thin film.
Further, it is noted that in the presence of a nonzero crystal anisotropy field
chaotic dynamics occurs at much lower magnitudes of the spin-current and DC
applied field.
|
0910.3776v1
|
2009-12-08
|
Evidence of superconductivity on the border of quasi-2D ferromagnetism in Ca2RuO4 at high pressure
|
The layered perovskite Ca2RuO4 is a spin-one Mott insulator at ambient
pressure and exhibits metallic ferromagnetism at least up to ~ 80 kbar with a
maximum Curie temperature of 28 K. Above ~ 90 kbar and up to 140 kbar, the
highest pressure reached, the resistivity and ac susceptibility show pronounced
downturns below ~ 0.4 K in applied magnetic fields of up to ~10 mT. This
indicates that our specimens of Ca2RuO4 are weakly superconducting on the
border of a quasi-2D ferromagnetic state.
|
0912.1513v1
|
2010-02-24
|
JSJ decompositions: definitions, existence, uniqueness. II. Compatibility and acylindricity
|
This paper and its companion arXiv:0911.3173 have been replaced by
arXiv:1602.05139.
We define the compatibility JSJ tree of a group G over a class of subgroups.
It exists whenever G is finitely presented and leads to a canonical tree (not a
deformation space) which is invariant under automorphisms. Under acylindricity
hypotheses, we prove that the (usual) JSJ deformation space and the
compatibility JSJ tree exist, and we describe their flexible subgroups. We
apply these results to finitely generated CSA groups, \Gamma-limit groups
(allowing torsion), and relatively hyperbolic groups.
|
1002.4564v3
|
2010-03-05
|
Magnetoresistance in nanostructures: the role of nonuniform current
|
We developed a method to calculate the magnetoresistance of magnetic
nanostructures. We discretize a magnetic disk in small cells and numerically
solve the Landau-Lifshitz-Gilbert (LLG) equation in order to obtain its
magnetization profile. We consider a anisotropic magnetoresistance (AMR) that
depends on the local magnetization as the main source of the magnetoresistance.
We then use it as an input to calculate the resistance and current distribution
numerically, using a relaxation method. We show how magnetoresistance
measurements can be useful to obtain information on the magnetic structure.
Additionally, we obtain non-homogeneous current distributions for different
magnetic configurations in static and dynamical regimes.
|
1003.1323v2
|
2010-03-21
|
Current-induced domain wall motion with adiabatic spin torque only in cylindrical nanowires
|
We investigate current-driven domain wall (DW) propagation in magnetic
nanowires in the framework of the modified Landau-Lifshitz-Gilbert equation
with both adiabatic and nonadiabatic spin torque (NAST) terms. Contrary to the
common opinion that NAST is indispensable for DW motion[1,2], we point out that
adiabatic spin torque (AST) only is enough for current-driven DW motion in a
cylindrical (uniaxial) nanowire. Apart from a discussion of the rigid DW motion
from the energy and angular momentum viewpoint, we also propose an experimental
scheme to measure the spin current polarization by combining both field and
current driven DW motion in a flat (biaxial) wire.
|
1003.3976v1
|
2010-04-01
|
Multipliers of locally compact quantum groups via Hilbert C$^*$-modules
|
A result of Gilbert shows that every completely bounded multiplier $f$ of the
Fourier algebra $A(G)$ arises from a pair of bounded continuous maps
$\alpha,\beta:G \rightarrow K$, where $K$ is a Hilbert space, and $f(s^{-1}t) =
(\beta(t)|\alpha(s))$ for all $s,t\in G$. We recast this in terms of
adjointable operators acting between certain Hilbert C$^*$-modules, and show
that an analogous construction works for completely bounded left multipliers of
a locally compact quantum group. We find various ways to deal with right
multipliers: one of these involves looking at the opposite quantum group, and
this leads to a proof that the (unbounded) antipode acts on the space of
completely bounded multipliers, in a way which interacts naturally with our
representation result. The dual of the universal quantum group (in the sense of
Kustermans) can be identified with a subalgebra of the completely bounded
multipliers, and we show how this fits into our framework. Finally, this
motivates a certain way to deal with two-sided multipliers.
|
1004.0215v3
|
2010-04-22
|
Optimal time-dependent polarized current pattern for fast domain wall propagation in nanowires: Exact solutions for biaxial and uniaxial anisotropies
|
One of the important issues in nanomagnetism is to lower the current needed
for a technologically useful domain wall (DW) propagation speed. Based on the
modified Landau-Lifshitz-Gilbert (LLG) equation with both Slonczewski
spin-transfer torque and the field-like torque, we derive the optimal spin
current pattern for fast DW propagation along nanowires. Under such conditions,
the DW velocity in biaxial wires can be enhanced as much as ten times compared
to the velocities achieved in experiments so far. Moreover, the fast variation
of spin polarization can help DW depinning. Possible experimental realizations
are discussed.
|
1004.3840v1
|
2010-05-03
|
Criticality of an isotropic-to-smectic transition induced by anisotropic quenched disorder
|
We report combined optical birefringence and neutron scattering measurements
on the liquid crystal 12CB nanoconfined in mesoporous silicon layers. This
liquid crystal exhibits strong nematic-smectic coupling responsible for a
discontinuous isotropic-to-smectic phase transition in the bulk state. Confined
in porous silicon, 12CB is subjected to strong anisotropic quenched disorder: a
short-ranged smectic state evolves out of a paranematic phase. This
transformation appears continuous, losing its bulk first order character. This
contrasts with previously reported observations on liquid crystals under
isotropic quenched disorder. In the low temperature phase, both orientational
and translational order parameters obey the same power-law.
|
1005.0240v1
|
2010-05-21
|
A Study on Potential of Integrating Multimodal Interaction into Musical Conducting Education
|
With the rapid development of computer technology, computer music has begun
to appear in the laboratory. Many potential utility of computer music is
gradually increasing. The purpose of this paper is attempted to analyze the
possibility of integrating multimodal interaction such as vision-based hand
gesture and speech interaction into musical conducting education. To achieve
this purpose, this paper is focus on discuss some related research and the
traditional musical conducting education. To do so, six musical conductors had
been interviewed to share their musical conducting learning/ teaching
experience. These interviews had been analyzed in this paper to show the
syllabus and the focus of musical conducting education for beginners.
|
1005.4014v1
|
2010-05-28
|
Dissipative structures in a nonlinear dynamo
|
This paper considers magnetic field generation by a fluid flow in a system
referred to as the Archontis dynamo: a steady nonlinear magnetohydrodynamic
(MHD) state is driven by a prescribed body force. The field and flow become
almost equal and dissipation is concentrated in cigar-like structures centred
on straight-line separatrices. Numerical scaling laws for energy and
dissipation are given that extend previous calculations to smaller
diffusivities. The symmetries of the dynamo are set out, together with their
implications for the structure of field and flow along the separatrices. The
scaling of the cigar-like dissipative regions, as the square root of the
diffusivities, is explained by approximations near the separatrices. Rigorous
results on the existence and smoothness of solutions to the steady, forced MHD
equations are given.
|
1005.5259v2
|
2010-06-11
|
Spherical single-roll dynamos at large magnetic Reynolds numbers
|
This paper concerns kinematic helical dynamos in a spherical fluid body
surrounded by an insulator. In particular, we examine their behaviour in the
regime of large magnetic Reynolds number $\Rm$, for which dynamo action is
usually concentrated upon a simple resonant stream-surface. The dynamo
eigensolutions are computed numerically for two representative single-roll
flows using a compact spherical harmonic decomposition and fourth-order
finite-differences in radius. These solutions are then compared with the growth
rates and eigenfunctions of the Gilbert and Ponty (2000) large $\Rm$ asymptotic
theory. We find good agreement between the growth rates when $\Rm>10^4$, and
between the eigenfunctions when $\Rm>10^5$.
|
1006.2308v2
|
2010-06-11
|
On the Queueing Behavior of Random Codes over a Gilbert-Elliot Erasure Channel
|
This paper considers the queueing performance of a system that transmits
coded data over a time-varying erasure channel. In our model, the queue length
and channel state together form a Markov chain that depends on the system
parameters. This gives a framework that allows a rigorous analysis of the queue
as a function of the code rate. Most prior work in this area either ignores
block-length (e.g., fluid models) or assumes error-free communication using
finite codes. This work enables one to determine when such assumptions provide
good, or bad, approximations of true behavior. Moreover, it offers a new
approach to optimize parameters and evaluate performance. This can be valuable
for delay-sensitive systems that employ short block lengths.
|
1006.2403v1
|
2010-06-16
|
Storing Small Photonic Cluster States in a Dephasing Environment
|
We consider the effects of decoherence on the entanglement of photonic
cluster states. Large photonic cluster states can be built by fusing together
smaller photonic cluster states via probabilistic fusion operations. For this
construction process it is necessary to store these smaller cluster states in
some way so as to have them available for attempted fusion operations. While in
storage the photonic cluster states may undergo dephasing. The effects of
dephasing on small, primitive cluster states is explored here with the aim of
determining how to locally rotate the qubits of the cluster state so as to lose
the least amount of entanglement due to the dephasing process.
|
1006.3192v1
|
2010-08-05
|
Subsystem codes with spatially local generators
|
We study subsystem codes whose gauge group has local generators in the 2D
geometry. It is shown that there exists a family of such codes defined on
lattices of size LxL with the number of logical qubits k and the minimum
distance d both proportional to L. The gauge group of these codes involves only
two-qubit generators of type XX and ZZ coupling nearest neighbor qubits (and
some auxiliary one-qubit generators). Our proof is not constructive as it
relies on a certain version of the Gilbert-Varshamov bound for classical codes.
Along the way we introduce and study properties of generalized Bacon-Shor codes
which might be of independent interest. Secondly, we prove that any 2D
subsystem [n,k,d] code with spatially local generators obeys upper bounds
kd=O(n) and d^2=O(n). The analogous upper bound proved recently for 2D
stabilizer codes is kd^2=O(n). Our results thus demonstrate that subsystem
codes can be more powerful than stabilizer codes under the spatial locality
constraint.
|
1008.1029v1
|
2010-08-14
|
Escape of resources in distributed clustering processes
|
In a distributed clustering algorithm introduced by Coffman, Courtois,
Gilbert and Piret \cite{coffman91}, each vertex of $\mathbb{Z}^d$ receives an
initial amount of a resource, and, at each iteration, transfers all of its
resource to the neighboring vertex which currently holds the maximum amount of
resource. In \cite{hlrnss} it was shown that, if the distribution of the
initial quantities of resource is invariant under lattice translations, then
the flow of resource at each vertex eventually stops almost surely, thus
solving a problem posed in \cite{berg91}. In this article we prove the
existence of translation-invariant initial distributions for which resources
nevertheless escape to infinity, in the sense that the the final amount of
resource at a given vertex is strictly smaller in expectation than the initial
amount. This answers a question posed in \cite{hlrnss}.
|
1008.2426v1
|
2010-08-25
|
The self-avoiding walk in a strip
|
We review the existence of the infinite length self-avoiding walk in the half
plane and its relationship to bridges. We prove that this probability measure
is also given by the limit as $\beta \rightarrow \beta_c-$ of the probability
measure on all finite length walks $\omega$ with the probability of $\omega$
proportional to $\beta_c^{|\omega|}$ where $|\omega|$ is the number of steps in
$\omega$. The self-avoiding walk in a strip $\{z : 0<\Im(z)<y\}$ is defined by
considering all self-avoiding walks $\omega$ in the strip which start at the
origin and end somewhere on the top boundary with probability proportional to
$\beta_c^{|\omega|}$ We prove that this probability measure may be obtained by
conditioning the SAW in the half plane to have a bridge at height $y$. This
observation is the basis for simulations to test conjectures on the
distribution of the endpoint of the SAW in a strip and the relationship between
the distribution of this strip SAW and SLE$_{8/3}$.
|
1008.4321v2
|
2010-08-29
|
Chirality control via double vortices in asymmetric Co dots
|
Reproducible control of the magnetic vortex state in nanomagnets is of
critical importance. We report on chirality control by manipulating the size
and/or thickness of asymmetric Co dots. Below a critical diameter and/or
thickness, chirality control is achieved by the nucleation of single vortex.
Interestingly, above these critical dimensions chirality control is realized by
the nucleation and subsequent coalescence of two vortices, resulting in a
single vortex with the opposite chirality as found in smaller dots.
Micromagnetic simulations and magnetic force microscopy highlight the role of
edge-bound halfvortices in facilitating the coalescence process.
|
1008.4963v2
|
2010-09-18
|
Composite excitation of Josephson phase and spin waves in Josephson junctions with ferromagnetic insulator
|
Coupling of Josephson-phase and spin-waves is theoretically studied in a
superconductor/ferromagnetic insulator/superconductor (S/FI/S) junction.
Electromagnetic (EM) field inside the junction and the Josephson current
coupled with spin-waves in FI are calculated by combining Maxwell and
Landau-Lifshitz-Gilbert equations. In the S/FI/S junction, it is found that the
current-voltage (I-V) characteristic shows two resonant peaks. Voltages at the
resonant peaks are obtained as a function of the normal modes of EM field,
which indicates a composite excitation of the EM field and spin-waves in the
S/FI/S junction. We also examine another type of junction, in which a
nonmagnetic insulator (I) is located at one of interfaces between S and FI. In
such a S/I/FI/S junction, three resonant peaks appear in the I-V curve, since
the Josephson-phase couples to the EM field in the I layer.
|
1009.3551v3
|
2010-09-21
|
On the Flow-Level Delay of a Spatial Multiplexing MIMO Wireless Channel
|
The MIMO wireless channel offers a rich ground for quality of service
analysis. In this work, we present a stochastic network calculus analysis of a
MIMO system, operating in spatial multiplexing mode, using moment generating
functions (MGF). We quantify the spatial multiplexing gain, achieved through
multiple antennas, for flow level quality of service (QoS) performance.
Specifically we use Gilbert-Elliot model to describe individual spatial paths
between the antenna pairs and model the whole channel by an N-State Markov
Chain, where N depends upon the degrees of freedom available in the MIMO
system. We derive probabilistic delay bounds for the system and show the impact
of increasing the number of antennas on the delay bounds under various
conditions, such as channel burstiness, signal strength and fading speed.
Further we present results for multi-hop scenarios under statistical
independence.
|
1009.4091v1
|
2010-09-22
|
Optimal control of magnetization dynamics in ferromagnetic heterostructures by spin--polarized currents
|
We study the switching-process of the magnetization in a
ferromagnetic-normal-metal multilayer system by a spin polarized electrical
current via the spin transfer torque. We use a spin drift-diffusion equation
(SDDE) and the Landau-Lifshitz-Gilbert equation (LLGE) to capture the coupled
dynamics of the spin density and the magnetization dynamic of the
heterostructure. Deriving a fully analytic solution of the stationary SDDE we
obtain an accurate, robust, and fast self-consistent model for the
spin-distribution and spin transfer torque inside general ferromagnetic/normal
metal heterostructures. Using optimal control theory we explore the switching
and back-switching process of the analyzer magnetization in a seven-layer
system. Starting from a Gaussian, we identify a unified current pulse profile
which accomplishes both processes within a specified switching time.
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1009.4296v2
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