23,418 research outputs found
On the distribution of the nodal sets of random spherical harmonics
We study the length of the nodal set of eigenfunctions of the Laplacian on
the \spheredim-dimensional sphere. It is well known that the eigenspaces
corresponding to \eigval=n(n+\spheredim-1) are the spaces \eigspc of
spherical harmonics of degree , of dimension \eigspcdim. We use the
multiplicity of the eigenvalues to endow \eigspc with the Gaussian
probability measure and study the distribution of the \spheredim-dimensional
volume of the nodal sets of a randomly chosen function. The expected volume is
proportional to \sqrt{\eigval}. One of our main results is bounding the
variance of the volume to be O(\frac{\eigval}{\sqrt{\eigspcdim}}).
In addition to the volume of the nodal set, we study its Leray measure. For
every , the expected value of the Leray measure is .
We are able to determine that the asymptotic form of the variance is
\frac{const}{\eigspcdim}.Comment: 47 pages, accepted for publication in the Journal of Mathematical
Physics. Lemmas 2.5, 2.11 were proved for any dimension, some other,
suggested by the referee, modifications and corrections, were mad
Properties of Non-Abelian Fractional Quantum Hall States at Filling
We compute the physical properties of non-Abelian Fractional Quantum Hall
(FQH) states described by Jack polynomials at general filling
. For , these states are identical to the
Read-Rezayi parafermions, whereas for they represent new FQH states. The
states, multiplied by a Vandermonde determinant, are a non-Abelian
alternative construction of states at fermionic filling . We
obtain the thermal Hall coefficient, the quantum dimensions, the electron
scaling exponent, and show that the non-Abelian quasihole has a well-defined
propagator falling off with the distance. The clustering properties of the Jack
polynomials, provide a strong indication that the states with can be
obtained as correlators of fields of \emph{non-unitary} conformal field
theories, but the CFT-FQH connection fails when invoked to compute physical
properties such as thermal Hall coefficient or, more importantly, the quasihole
propagator. The quasihole wavefuntion, when written as a coherent state
representation of Jack polynomials, has an identical structure for \emph{all}
non-Abelian states at filling .Comment: 2 figure
Development of tests for measurement of primary perceptual-motor performance
Tests for measuring primary perceptual-motor performance for assessing space environment effects on human performanc
Generalized Clustering Conditions of Jack Polynomials at Negative Jack Parameter
We present several conjectures on the behavior and clustering properties of
Jack polynomials at \emph{negative} parameter , of
partitions that violate the admissibility rule of Feigin \emph{et.
al.} [\onlinecite{feigin2002}]. We find that "highest weight" Jack polynomials
of specific partitions represent the minimum degree polynomials in
variables that vanish when distinct clusters of particles are formed,
with and positive integers. Explicit counting formulas are conjectured.
The generalized clustering conditions are useful in a forthcoming description
of fractional quantum Hall quasiparticles.Comment: 12 page
A Paraconsistent Higher Order Logic
Classical logic predicts that everything (thus nothing useful at all) follows
from inconsistency. A paraconsistent logic is a logic where an inconsistency
does not lead to such an explosion, and since in practice consistency is
difficult to achieve there are many potential applications of paraconsistent
logics in knowledge-based systems, logical semantics of natural language, etc.
Higher order logics have the advantages of being expressive and with several
automated theorem provers available. Also the type system can be helpful. We
present a concise description of a paraconsistent higher order logic with
countable infinite indeterminacy, where each basic formula can get its own
indeterminate truth value (or as we prefer: truth code). The meaning of the
logical operators is new and rather different from traditional many-valued
logics as well as from logics based on bilattices. The adequacy of the logic is
examined by a case study in the domain of medicine. Thus we try to build a
bridge between the HOL and MVL communities. A sequent calculus is proposed
based on recent work by Muskens.Comment: Originally in the proceedings of PCL 2002, editors Hendrik Decker,
Joergen Villadsen, Toshiharu Waragai (http://floc02.diku.dk/PCL/). Correcte
SM(2,4k) fermionic characters and restricted jagged partitions
A derivation of the basis of states for the superconformal minimal
models is presented. It relies on a general hypothesis concerning the role of
the null field of dimension . The basis is expressed solely in terms of
modes and it takes the form of simple exclusion conditions (being thus a
quasi-particle-type basis). Its elements are in correspondence with
-restricted jagged partitions. The generating functions of the latter
provide novel fermionic forms for the characters of the irreducible
representations in both Ramond and Neveu-Schwarz sectors.Comment: 12 page
Sensitive imaging of electromagnetic fields with paramagnetic polar molecules
We propose a method for sensitive parallel detection of low-frequency
electromagnetic fields based on the fine structure interactions in paramagnetic
polar molecules. Compared to the recently implemented scheme employing
ultracold Rb atoms [B{\"o}hi \textit{et al.}, Appl. Phys. Lett.
\textbf{97}, 051101 (2010)], the technique based on molecules offers a 100-fold
higher sensitivity, the possibility to measure both the electric and magnetic
field components, and a probe of a wide range of frequencies from the dc limit
to the THz regime
Interference between independent fluctuating condensates
We consider a problem of interference between two independent condensates,
which lack true long range order. We show that their interference pattern
contains information about correlation functions within each condensate. As an
example we analyze the interference between a pair of one dimensional
interacting Bose liquids. We find universal scaling of the average fringe
contrast with system size and temperature that depends only on the Luttinger
parameter. Moreover the full distribution of the fringe contrast, which is also
equivalent to the full counting statistics of the interfering atoms, changes
with interaction strength and lends information on high order correlation
functions. We also demonstrate that the interference between two-dimensional
condensates at finite temperature can be used as a direct probe of the
Kosterlitz-Thouless transition. Finally, we discuss generalization of our
results to describe the intereference of a periodic array of independent
fluctuating condensates.Comment: 7 pages, 3 figures, published versio
Dynamics of Macroscopic Wave Packet Passing through Double Slits: Role of Gravity and Nonlinearity
Using the nonlinear Schroedinger equation (Gross-Pitaevskii equation), the
dynamics of a macroscopic wave packet for Bose-Einstein condensates falling
through double slits is analyzed. This problem is identified with a search for
the fate of a soliton showing a head-on collision with a hard-walled obstacle
of finite size. We explore the splitting of the wave packet and its
reorganization to form an interference pattern. Particular attention is paid to
the role of gravity (g) and repulsive nonlinearity (u_0) in the fringe pattern.
The peak-to-peak distance in the fringe pattern and the number of interference
peaks are found to be proportional to g^(-1/2) and u_0^(1/2)g^(1/4),
respectively. We suggest a way of designing an experiment under controlled
gravity and nonlinearity.Comment: 10 pages, 4 figures and 1 tabl
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