46,533 research outputs found
The spectral problem and algebras associated with extended Dynkin graphs. I
There is a connection between *-representations of algebras associated with
graphs and the problem about the spectrum of a sum of Hermitian operators
(spectral problem). For algebras associated with extended Dynkin graphs we give
an explicit description of the parameters for which there are
-representations and an algorithm for constructing these representations
Cotangent cohomology of rational surface singularities
We show that the number of generators of the n-th cotangent cohomology group
(n >=2) is the same for all rational surface singularities Y. For a large class
of rational surface singularities, including quotient singularities, this
number is also the dimension. For them we obtain an explicit formula for the
corresponding Poincare series.Comment: 14 pages, LaTeX 2
Superspace Methods in String Theory, Supergravity and Gauge Theory
In these two lectures, delivered at the XXXVII Karpacz Winter School,
February 2001, I review some applications of superspace in various topics
related to string theory and M-theory. The first lecture is mainly devoted to
descriptions of brane dynamics formulated in supergravity backgrounds. The
second lecture concerns the use of superspace techniques for determining
consistent interactions in supersymmetric gauge theory and supergravity, e.g.
alpha'-corrections from string/M-theory.Comment: 15 pp., latex, aippro
Direct observation of time correlated single-electron tunneling
We report a direct detection of time correlated single-electron tunneling
oscillations in a series array of small tunnel junctions. Here the current, I,
is made up of a lattice of charge solitons moving throughout the array by time
correlated tunneling with the frequency f=I/e, where e is the electron charge.
To detect the single charges, we have integrated the array with a
radio-frequency single-electron transistor (RF-SET) and employed two different
methods to couple the array to the SET input: by direct injection through a
tunnel junction, and by capacitive coupling. In this paper we report the
results from the latter type of charge input, where we have observed the
oscillations in the frequency domain and measured currents from 50 to 250 fA by
means of electron counting.Comment: 2 pages, 1 figure; submitted to the 10th International
Superconductive Electronics Conference (ISEC'05), the Netherlands, Sept. 200
Parametric resonances in electrostatically interacting carbon nanotube arrays
We study, numerically and analytically, a model of a one-dimensional array of
carbon nanotube resonators in a two-terminal configuration. The system is
brought into resonance upon application of an AC-signal superimposed on a
DC-bias voltage. When the tubes in the array are close to each other,
electrostatic interactions between tubes become important for the array
dynamics. We show that both transverse and longitudinal parametric resonances
can be excited in addition to primary resonances. The intertube electrostatic
interactions couple modes in orthogonal directions and affect the mode
stability.Comment: 11 pages, 12 figures, RevTeX
Blocking Wythoff Nim
The 2-player impartial game of Wythoff Nim is played on two piles of tokens.
A move consists in removing any number of tokens from precisely one of the
piles or the same number of tokens from both piles. The winner is the player
who removes the last token. We study this game with a blocking maneuver, that
is, for each move, before the next player moves the previous player may declare
at most a predetermined number, , of the options as forbidden.
When the next player has moved, any blocking maneuver is forgotten and does not
have any further impact on the game. We resolve the winning strategy of this
game for and and, supported by computer simulations, state
conjectures of the asymptotic `behavior' of the -positions for the
respective games when .Comment: 14 pages, 1 Figur
Stochastic domination for the Ising and fuzzy Potts models
We discuss various aspects concerning stochastic domination for the Ising
model and the fuzzy Potts model. We begin by considering the Ising model on the
homogeneous tree of degree , \Td. For given interaction parameters ,
and external field h_1\in\RR, we compute the smallest external field
such that the plus measure with parameters and dominates
the plus measure with parameters and for all .
Moreover, we discuss continuity of with respect to the three
parameters , , and also how the plus measures are stochastically
ordered in the interaction parameter for a fixed external field. Next, we
consider the fuzzy Potts model and prove that on \Zd the fuzzy Potts measures
dominate the same set of product measures while on \Td, for certain parameter
values, the free and minus fuzzy Potts measures dominate different product
measures. For the Ising model, Liggett and Steif proved that on \Zd the plus
measures dominate the same set of product measures while on \T^2 that
statement fails completely except when there is a unique phase.Comment: 22 pages, 5 figure
The Emergence of Anticommuting Coordinates and the Dirac-Ramond-Kostant operators
The history of anticommuting coordinates is decribed.Comment: 14 pages, Contribution to the Proceedings of The Gunnar Nordstr\"om
Symposium on Theoretical Physics - The Physics of Extra Dimension
Dual Bialgebroids for Depth Two Ring Extensions
We introduce a general notion of depth two for ring homomorphism N --> M, and
derive Morita equivalence of the step one and three centralizers, R = C_M(N)
and C = End_{N-M}(M \o_N M), via dual bimodules and step two centralizers A =
End_NM_N and B = (M \o_N M)^N, in a Jones tower above N --> M. Lu's
bialgebroids End_k A' and A' \o_k {A'}^op over a k-algebra A' are generalized
to left and right bialgebroids A and B with B the R-dual bialgebroid of A. We
introduce Galois-type actions of A on M and B on End_NM when M_N is a balanced
module. In the case of Frobenius extensions M | N, we prove an endomorphism
ring theorem for depth two. Further in the case of irreducible extensions, we
extend previous results on Hopf algebra and weak Hopf algebra actions in
subfactor theory [Szymanski, Nikshych-Vainerman] and its generalizations
[Kadison-Nikshych: RA/0107064, RA/0102010] by methods other than nondegenerate
pairing. As a result, we have concrete expressions for the Hopf or weak Hopf
algebra structures on the step two centralizers. Semisimplicity of B is
equivalent to separability of the extension M | N. In the presence of depth
two, we show that biseparable extensions are QF.Comment: 2 new sections added, 37 page
Stability for random measures, point processes and discrete semigroups
Discrete stability extends the classical notion of stability to random
elements in discrete spaces by defining a scaling operation in a randomised
way: an integer is transformed into the corresponding binomial distribution.
Similarly defining the scaling operation as thinning of counting measures we
characterise the corresponding discrete stability property of point processes.
It is shown that these processes are exactly Cox (doubly stochastic Poisson)
processes with strictly stable random intensity measures. We give spectral and
LePage representations for general strictly stable random measures without
assuming their independent scattering. As a consequence, spectral
representations are obtained for the probability generating functional and void
probabilities of discrete stable processes. An alternative cluster
representation for such processes is also derived using the so-called Sibuya
point processes, which constitute a new family of purely random point
processes. The obtained results are then applied to explore stable random
elements in discrete semigroups, where the scaling is defined by means of
thinning of a point process on the basis of the semigroup. Particular examples
include discrete stable vectors that generalise discrete stable random
variables and the family of natural numbers with the multiplication operation,
where the primes form the basis.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ301 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
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