18,170 research outputs found
Hidden Translation and Translating Coset in Quantum Computing
We give efficient quantum algorithms for the problems of Hidden Translation
and Hidden Subgroup in a large class of non-abelian solvable groups including
solvable groups of constant exponent and of constant length derived series. Our
algorithms are recursive. For the base case, we solve efficiently Hidden
Translation in , whenever is a fixed prime. For the induction
step, we introduce the problem Translating Coset generalizing both Hidden
Translation and Hidden Subgroup, and prove a powerful self-reducibility result:
Translating Coset in a finite solvable group is reducible to instances of
Translating Coset in and , for appropriate normal subgroups of
. Our self-reducibility framework combined with Kuperberg's subexponential
quantum algorithm for solving Hidden Translation in any abelian group, leads to
subexponential quantum algorithms for Hidden Translation and Hidden Subgroup in
any solvable group.Comment: Journal version: change of title and several minor update
Scattering of solitary waves in granular media
A detailed numerical study of the scattering of solitary waves by a barrier,
in a granular media with Hertzian contact, shows the existence of secondary
multipulse structures generated at the interface of two "sonic vacua", which
have a similar structure as the one previously found by Nesterenko and
coworkers.Comment: 4 pages, 9 figures (fig 5, replaced). Submitted to PR
CHL Dyons and Statistical Entropy Function from D1-D5 System
We give a proof of the recently proposed formula for the dyon spectrum in CHL
string theories by mapping it to a configuration of D1 and D5-branes and
Kaluza-Klein monopole. We also give a prescription for computing the degeneracy
as a systematic expansion in inverse powers of charges. The computation can be
formulated as a problem of extremizing a duality invariant statistical entropy
function whose value at the extremum gives the logarithm of the degeneracy.
During this analysis we also determine the locations of the zeroes and poles of
the Siegel modular forms whose inverse give the dyon partition function in the
CHL models.Comment: LaTeX file, 48 pages; v2: typos correcte
Two Centered Black Holes and N=4 Dyon Spectrum
The exact spectrum of dyons in a class of N=4 supersymmetric string theories
is known to change discontinuously across walls of marginal stability. We show
that the change in the degeneracy across the walls of marginal stability can be
accounted for precisely by the entropy of two centered small black holes which
disappear as we cross the walls of marginal stability.Comment: LaTeX file, 12 pages; v3: added footnote 2 regarding overall sign of
the index, expanded footnote 3, added reference
From Fundamental Strings to Small Black Holes
We give evidence in favour of a string/black hole transition in the case of
BPS fundamental string states of the Heterotic string. Our analysis goes beyond
the counting of degrees of freedom and considers the evolution of dynamical
quantities in the process. As the coupling increases, the string states
decrease their size up to the string scale when a small black hole is formed.
We compute the absorption cross section for several fields in both the black
hole and the perturbative string phases. At zero frequency, these cross
sections can be seen as order parameters for the transition. In particular, for
the scalars fixed at the horizon the cross section evolves to zero when the
black hole is formed.Comment: 36 pages, 4 figures, argument about minimally coupled scalar
absorption cross section clarifie
Dyon Spectrum in CHL Models
We propose a formula for the degeneracy of quarter BPS dyons in a class of
CHL models. The formula uses a modular form of a subgroup of the genus two
modular group Sp(2,Z). Our proposal is S-duality invariant and reproduces
correctly the entropy of a dyonic black hole to first non-leading order for
large values of the charges.Comment: LaTeX file, 38 pages, minor changes in section 3.3(v2), minor changes
in introduction, appendix A and C(v3
Rare Decay Modes of Quarter BPS Dyons
The degeneracy of quarter BPS dyons in N=4 supersymmetric string theories is
known to jump across walls of marginal stability on which a quarter BPS dyon
can decay into a pair of half BPS dyons. We show that as long as the electric
and magnetic charges of the original dyon are primitive elements of the charge
lattice, the subspaces of the moduli space on which a quarter BPS dyon becomes
marginally unstable against decay into a pair of quarter BPS dyons or a half
BPS dyon and a quarter BPS dyon are of codimension two or more. As a result any
pair of generic points in the moduli space can be connected by a path avoiding
these subspaces and there is no jump in the spectrum associated with these
subspaces.Comment: LaTeX file, 9 pages; v2: a minor logical error corrected with no
change in the result
Experimental study of nonlinear dust acoustic solitary waves in a dusty plasma
The excitation and propagation of finite amplitude low frequency solitary
waves are investigated in an Argon plasma impregnated with kaolin dust
particles. A nonlinear longitudinal dust acoustic solitary wave is excited by
pulse modulating the discharge voltage with a negative potential. It is found
that the velocity of the solitary wave increases and the width decreases with
the increase of the modulating voltage, but the product of the solitary wave
amplitude and the square of the width remains nearly constant. The experimental
findings are compared with analytic soliton solutions of a model Kortweg-de
Vries equation.Comment: The manuscripts includes six figure
Inhomogeneous Fragmentation of the Rolling Tachyon
Dirac-Born-Infeld type effective actions reproduce many aspects of string
theory classical tachyon dynamics of unstable Dp-branes. The inhomogeneous
tachyon field rolling from the top of its potential forms topological defects
of lower codimensions. In between them, as we show, the tachyon energy density
fragments into a p-dimensional web-like high density network evolving with
time. We present an analytic asymptotic series solution of the non-linear
equations for the inhomogeneous tachyon and its stress energy. The generic
solution for a tachyon field with a runaway potential in arbitrary dimensions
is described by the free streaming of noninteracting massive particles whose
initial velocities are defined by the gradients of the initial tachyon profile.
Thus, relativistic particle mechanics is a dual picture of the tachyon field
effective action. Implications of this picture for inflationary models with a
decaying tachyon field are discussed.Comment: 10 pages, 1 figur
How Hertzian solitary waves interact with boundaries in a 1-D granular medium
We perform measurements, numerical simulations, and quantitative comparisons
with available theory on solitary wave propagation in a linear chain of beads
without static preconstrain. By designing a nonintrusive force sensor to
measure the impulse as it propagates along the chain, we study the solitary
wave reflection at a wall. We show that the main features of solitary wave
reflection depend on wall mechanical properties. Since previous studies on
solitary waves have been performed at walls without these considerations, our
experiment provides a more reliable tool to characterize solitary wave
propagation. We find, for the first time, precise quantitative agreements.Comment: Proof corrections, ReVTeX, 11 pages, 3 eps (Focus and related papers
on http://www.supmeca.fr/perso/jobs/
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