1,628 research outputs found
Generalized Calogero-Moser systems from rational Cherednik algebras
We consider ideals of polynomials vanishing on the W-orbits of the
intersections of mirrors of a finite reflection group W. We determine all such
ideals which are invariant under the action of the corresponding rational
Cherednik algebra hence form submodules in the polynomial module. We show that
a quantum integrable system can be defined for every such ideal for a real
reflection group W. This leads to known and new integrable systems of
Calogero-Moser type which we explicitly specify. In the case of classical
Coxeter groups we also obtain generalized Calogero-Moser systems with added
quadratic potential.Comment: 36 pages; the main change is an improvement of section 7 so that it
now deals with an arbitrary complex reflection group; Selecta Math, 201
Spherical geometry and integrable systems
We prove that the cosine law for spherical triangles and spherical tetrahedra
defines integrable systems, both in the sense of multidimensional consistency
and in the sense of dynamical systems.Comment: 15 pages, 5 figure
Effects of Electron-Electron and Electron-Phonon Interactions in Weakly Disordered Conductors and Heterostuctures
We investigate quantum corrections to the conductivity due to the
interference of electron-electron (electron-phonon) scattering and elastic
electron scattering in weakly disordered conductors. The electron-electron
interaction results in a negative -correction in a 3D conductor. In
a quasi-two-dimensional conductor, ( is the thickness, is
the Fermi velocity), with 3D electron spectrum this correction is linear in
temperature and differs from that for 2D electrons (G. Zala et. al., Phys.
Rev.B {\bf 64}, 214204 (2001)) by a numerical factor. In a
quasi-one-dimensional conductor, temperature-dependent correction is
proportional to . The electron interaction via exchange of virtual phonons
also gives -correction. The contribution of thermal phonons interacting
with electrons via the screened deformation potential results in -term and
via unscreened deformation potential results in -term. The interference
contributions dominate over pure electron-phonon scattering in a wide
temperature range, which extends with increasing disorder.Comment: 6 pages, 2figure
Ballistic propagation of thermal excitations near a vortex in superfluid He3-B
Andreev scattering of thermal excitations is a powerful tool for studying
quantized vortices and turbulence in superfluid He3-B at very low temperatures.
We write Hamilton's equations for a quasiparticle in the presence of a vortex
line, determine its trajectory, and find under wich conditions it is Andreev
reflected. To make contact with experiments, we generalize our results to the
Onsager vortex gas, and find values of the intervortex spacing in agreement
with less rigorous estimates
Collective and fractal properties of pion jets in the four-velocity space at intermediate energies
Experimental results are presented for study of collective and fractal
properties of soft pion jets in the space of relative four-dimensional
velocities. Significant decreasing is obtained for mean square of second
particle distances from jet axis for pion-proton interactions at initial
energies GeV in comparison with hadron-nuclear collisions at close
energies. The decreasing results in power dependence of distance variable on
collision energy for range GeV. The observation allows us to
estimate the low boundary of manifestation of color degree of freedom in pion
jet production. Cluster dimension values were deduced for pion jets in various
reactions. Fractional values of this dimension indicate on the manifestation of
fractal-like properties by pion jets. Changing of mean kinetic energy of jet
particles and fractal dimension with initial energy increasing is consistent
with suggestion for presence of color degrees of freedom in pion jet production
at intermediate energies.Comment: The conference "Physics of fundamental interactions". ITEP, Moscow,
Russia. November 23 - 27, 200
On generalisations of Calogero-Moser-Sutherland quantum problem and WDVV equations
It is proved that if the Schr\"odinger equation of
Calogero-Moser-Sutherland type with
has a solution of the product form then the function satisfies the
generalised WDVV equations.Comment: 10 page
Orthogonal polynomials of discrete variable and Lie algebras of complex size matrices
We give a uniform interpretation of the classical continuous Chebyshev's and
Hahn's orthogonal polynomials of discrete variable in terms of Feigin's Lie
algebra gl(N), where N is any complex number. One can similarly interpret
Chebyshev's and Hahn's q-polynomials and introduce orthogonal polynomials
corresponding to Lie superlagebras.
We also describe the real forms of gl(N), quasi-finite modules over gl(N),
and conditions for unitarity of the quasi-finite modules. Analogs of tensors
over gl(N) are also introduced.Comment: 25 pages, LaTe
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