6,296 research outputs found
Bounds on supremum norms for Hecke eigenfunctions of quantized cat maps
We study extreme values of desymmetrized eigenfunctions (so called Hecke
eigenfunctions) for the quantized cat map, a quantization of a hyperbolic
linear map of the torus.
In a previous paper it was shown that for prime values of the inverse Planck
constant N=1/h, such that the map is diagonalizable (but not upper triangular)
modulo N, the Hecke eigenfunctions are uniformly bounded. The purpose of this
paper is to show that the same holds for any prime N provided that the map is
not upper triangular modulo N.
We also find that the supremum norms of Hecke eigenfunctions are << N^epsilon
for all epsilon>0 in the case of N square free.Comment: 16 pages. Introduction expanded; comparison with supremum norms of
eigenfunctions of the Laplacian added. Bound for square free N adde
Superconformal symmetry in the interacting theory of (2,0) tensor multiplets and self-dual strings
We investigate the concept of superconformal symmetry in six dimensions,
applied to the interacting theory of (2,0) tensor multiplets and self-dual
strings. The action of a superconformal transformation on the superspace
coordinates is found, both from a six-dimensional perspective and by using a
superspace with eight bosonic and four fermionic dimensions. The transformation
laws for all fields in the theory are derived, as well as general expressions
for the transformation of on-shell superfields. Superconformal invariance is
shown for the interaction of a self-dual string with a background consisting of
on-shell tensor multiplet fields, and we also find an interesting relationship
between the requirements of superconformal invariance and those of a local
fermionic kappa-symmetry. Finally, we try to construct a superspace analogue of
the Poincare dual to the string world-sheet and consider its properties under
superconformal transformations.Comment: 31 pages, LaTeX. v2: clarifications and minor correction
Variation of the Nazarov-Sodin constant for random plane waves and arithmetic random waves
This is a manuscript containing the full proofs of results announced in [KW],
together with some recent updates. We prove that the Nazarov-Sodin constant,
which up to a natural scaling gives the leading order growth for the expected
number of nodal components of a random Gaussian field, genuinely depends on the
field. We then infer the same for "arithmetic random waves", i.e. random toral
Laplace eigenfunctions.Comment: 27 pages, 6 figures. To appear in Advances in Mathematic
On probability measures arising from lattice points on circles
A circle, centered at the origin and with radius chosen so that it has
non-empty intersection with the integer lattice , gives rise to
a probability measure on the unit circle in a natural way. Such measures, and
their weak limits, are said to be attainable from lattice points on circles.
We investigate the set of attainable measures and show that it contains all
extreme points, in the sense of convex geometry, of the set of all probability
measures that are invariant under some natural symmetries. Further, the set of
attainable measures is closed under convolution, yet there exist symmetric
probability measures that are not attainable. To show this, we study the
geometry of projections onto a finite number of Fourier coefficients and find
that the set of attainable measures has many singularities with a "fractal"
structure. This complicated structure in some sense arises from prime powers -
singularities do not occur for circles of radius if is square
free.Comment: 42 pages, 5 figure
Value distribution for eigenfunctions of desymmetrized quantum maps
We study the value distribution and extreme values of eigenfunctions for the
``quantized cat map''. This is the quantization of a hyperbolic linear map of
the torus. In a previous paper it was observed that there are quantum
symmetries of the quantum map - a commutative group of unitary operators which
commute with the map, which we called ``Hecke operators''. The eigenspaces of
the quantum map thus admit an orthonormal basis consisting of eigenfunctions of
all the Hecke operators, which we call ``Hecke eigenfunctions''.
In this note we investigate suprema and value distribution of the Hecke
eigenfunctions. For prime values of the inverse Planck constant N for which the
map is diagonalizable modulo N (the ``split primes'' for the map), we show that
the Hecke eigenfunctions are uniformly bounded and their absolute values
(amplitudes) are either constant or have a semi-circle value distribution as N
tends to infinity. Moreover in the latter case different eigenfunctions become
statistically independent. We obtain these results via the Riemann hypothesis
for curves over a finite field (Weil's theorem) and recent results of N. Katz
on exponential sums. For general N we obtain a nontrivial bound on the supremum
norm of these Hecke eigenfunctions
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Revolutionary insurgencies, paradigmatic cases
This essay will examine and compare the production of women's writing during and after the Nicaraguan and Cuban Revolutions, a corpus that includes novels, poetry, and testimonies, but also features considerable generic hybridity. Since both revolutions are separated by some twenty years, each must be understood in the context of the specific ideological conditions that framed women’s participation in culture and revolution, and must also be considered in light of evolving gender discourses, both national and international. As such, these texts respond to both local and transnational paradigms of feminine subjectivity, and highlight the particular problems that arise from women’s insertion into the revolution and its representation in literature. These writers also have to negotiate the evolving context of revolution itself, with its moments of euphoria and disenchantment – and it is here that the greatest contrasts can be found between the two revolutionary instances and their political features: whilst Cuba’s revolutionary process has somehow survived economic crisis and created a level of political stability and continuity (not without its own problems), the Nicaraguan case is characterised by ruptures and resentments which are clearly reflected in the work of writers before, during, and after the Sandinista revolution, and which continue to the present day. This chapter will address the work of the most prominent woman writer of the Nicaraguan revolution, Gioconda Belli, whose main work reflects her involvement in the Sandinista struggle; ex-commander Mónica Baltodano has recently compiled a four volume piece with testimonials of men and women who participated in the organization and actions led by the Frente Sandinista de Liberación Nacional, and Violeta Barrios de Chamorro, former president of Nicaragua, who has recently co-authored an autobiography. There are other women poets to consider, especially under the auspices of the Asociación de Mujeres Nicaraguenses Luisa Amanda Espinoza, such as Vidaluz Meneses, Michele Najlis and Daisy Zamora. The testimonios compiled by Margaret Randall are also important pieces to consider for both Nicaragua and Cuba. The most important voices of the Cuban revolution still resident on the island are poet Nancy Morejón and writers Mirta Yáñez and Aida Bahr, with younger writers such as Adelaida Fernández de Juan and Marilyn Bobes representing a more recent generation
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