2,394 research outputs found
New and Old Results in Resultant Theory
Resultants are getting increasingly important in modern theoretical physics:
they appear whenever one deals with non-linear (polynomial) equations, with
non-quadratic forms or with non-Gaussian integrals. Being a subject of more
than three-hundred-year research, resultants are of course rather well studied:
a lot of explicit formulas, beautiful properties and intriguing relationships
are known in this field. We present a brief overview of these results,
including both recent and already classical. Emphasis is made on explicit
formulas for resultants, which could be practically useful in a future physics
research.Comment: 50 pages, 15 figure
Realistic interatomic potential for MD simulations
The coefficients of interatomic potential of simple form Exp-6 for neon are
obtained. Repulsive part is calculated ab-initio in the Hartree-Fock
approximation using the basis of atomic orbitals orthogonalized exactly on
different lattice sites. Attractive part is determined empirically using single
fitting parameter. The potential obtained describes well the equation of state
and elastic moduli of neon crystal in wide range of interatomic distances and
it is appropriate for molecular dynamic simulations of high temperature
properties and phenomena in crystals and liquids.Comment: MikTex v.2.1 (AMS-TEX),11 pages, 3 EPS figure
Dynamical lattice instability versus spin liquid state in a frustrated spin chain system
The low-dimensional s=1/2 compound (NO)[Cu(NO3)3] has recently been suggested
to follow the Nersesyan-Tsvelik model of coupled spin chains. Such a system
shows unbound spinon excitations and a resonating valence bond ground state due
spin frustration. Our Raman scattering study demonstrates phonon anomalies as
well as the suppression of a broad magnetic scattering continuum for
temperatures below a characteristic temperature, T<T*=100K. We interpret these
effects as evidence for a dynamical interplay of spin and lattice degrees of
freedom that might lead to a further transition into a dimerized or
structurally distorted phase at lower temperatures.Comment: 5 pages, 6 figure
M-Theory of Matrix Models
Small M-theories unify various models of a given family in the same way as
the M-theory unifies a variety of superstring models. We consider this idea in
application to the family of eigenvalue matrix models: their M-theory unifies
various branches of Hermitean matrix model (including Dijkgraaf-Vafa partition
functions) with Kontsevich tau-function. Moreover, the corresponding duality
relations look like direct analogues of instanton and meron decompositions,
familiar from Yang-Mills theory.Comment: 12 pages, contribution to the Proceedings of the Workshop "Classical
and Quantum Integrable Systems", Protvino, Russia, January, 200
Application of Johnson disribution to the problemof aerospace images classification
Solving the problem of aerospace images classification it was suggested to approximate distribution density of image characteristics by Johnson distribution. The possibilities of such approach were investigated and its availability was show
Partition Functions of Matrix Models as the First Special Functions of String Theory I. Finite Size Hermitean 1-Matrix Model
Even though matrix model partition functions do not exhaust the entire set of
tau-functions relevant for string theory, they seem to be elementary building
blocks for many others and they seem to properly capture the fundamental
symplicial nature of quantum gravity and string theory. We propose to consider
matrix model partition functions as new special functions. This means they
should be investigated and put into some standard form, with no reference to
particular applications. At the same time, the tables and lists of properties
should be full enough to avoid discoveries of unexpected peculiarities in new
applications. This is a big job, and the present paper is just a step in this
direction. Here we restrict our consideration to the finite-size Hermitean
1-matrix model and concentrate mostly on its phase/branch structure arising
when the partition function is considered as a D-module. We discuss the role of
the CIV-DV prepotential (as generating a possible basis in the linear space of
solutions to the Virasoro constraints, but with a lack of understanding of why
and how this basis is distinguished) and evaluate first few multiloop
correlators, which generalize semicircular distribution to the case of
multitrace and non-planar correlators.Comment: 64 pages, LaTe
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