191 research outputs found
Multidimensional Toda Lattices: Continuous and Discrete Time
In this paper we present multidimensional analogues of both the continuous-
and discrete-time Toda lattices. The integrable systems that we consider here
have two or more space coordinates. To construct the systems, we generalize the
orthogonal polynomial approach for the continuous and discrete Toda lattices to
the case of multiple orthogonal polynomials
A classification of generalized quantum statistics associated with classical Lie algebras
Generalized quantum statistics such as para-Fermi statistics is characterized
by certain triple relations which, in the case of para-Fermi statistics, are
related to the orthogonal Lie algebra B_n=so(2n+1). In this paper, we give a
quite general definition of ``a generalized quantum statistics associated to a
classical Lie algebra G''. This definition is closely related to a certain
Z-grading of G. The generalized quantum statistics is then determined by a set
of root vectors (the creation and annihilation operators of the statistics) and
the set of algebraic relations for these operators. Then we give a complete
classification of all generalized quantum statistics associated to the
classical Lie algebras A_n, B_n, C_n and D_n. In the classification, several
new classes of generalized quantum statistics are described
Chirplet approximation of band-limited, real signals made easy
In this paper we present algorithms for approximating real band-limited
signals by multiple Gaussian Chirps. These algorithms do not rely on matching
pursuit ideas. They are hierarchial and, at each stage, the number of terms in
a given approximation depends only on the number of positive-valued maxima and
negative-valued minima of a signed amplitude function characterizing part of
the signal. Like the algorithms used in \cite{gre2} and unlike previous
methods, our chirplet approximations require neither a complete dictionary of
chirps nor complicated multi-dimensional searches to obtain suitable choices of
chirp parameters
Computing recurrence coefficients of multiple orthogonal polynomials
Multiple orthogonal polynomials satisfy a number of recurrence relations, in
particular there is a -term recurrence relation connecting the type II
multiple orthogonal polynomials near the diagonal (the so-called step-line
recurrence relation) and there is a system of recurrence relations
connecting the nearest neighbors (the so-called nearest neighbor recurrence
relations). In this paper we deal with two problems. First we show how one can
obtain the nearest neighbor recurrence coefficients (and in particular the
recurrence coefficients of the orthogonal polynomials for each of the defining
measures) from the step-line recurrence coefficients. Secondly we show how one
can compute the step-line recurrence coefficients from the recurrence
coefficients of the orthogonal polynomials of each of the measures defining the
multiple orthogonality.Comment: 22 pages, 2 figures in Numerical Algorithms (2015
Holographic Meson Melting
The plasma phase at high temperatures of a strongly coupled gauge theory can
be holographically modelled by an AdS black hole. Matter in the fundamental
representation and in the quenched approximation is introduced through
embedding D7-branes in the AdS-Schwarzschild background. Low spin mesons
correspond to the fluctuations of the D7-brane world volume. As is well known
by now, there are two different kinds of embeddings, either reaching down to
the black hole horizon or staying outside of it. In the latter case the
fluctuations of the D7-brane world volume represent stable low spin mesons. In
the plasma phase we do not expect mesons to be stable but to melt at
sufficiently high temperature. We model the late stages of this meson melting
by the quasinormal modes of D7-brane fluctuations for the embeddings that do
reach down to the horizon. The inverse of the imaginary part of the quasinormal
frequency gives the typical relaxation time back to equilibrium of the meson
perturbation in the hot plasma. We briefly comment on the possible application
of our model to quarkonium suppression.Comment: 25+1 pages, 6 figures; v4: references adde
- …