1,705 research outputs found
Explicit Free Parameterization of the Modified Tetrahedron Equation
The Modified Tetrahedron Equation (MTE) with affine Weyl quantum variables at
N-th root of unity is solved by a rational mapping operator which is obtained
from the solution of a linear problem. We show that the solutions can be
parameterized in terms of eight free parameters and sixteen discrete phase
choices, thus providing a broad starting point for the construction of
3-dimensional integrable lattice models. The Fermat curve points parameterizing
the representation of the mapping operator in terms of cyclic functions are
expressed in terms of the independent parameters. An explicit formula for the
density factor of the MTE is derived. For the example N=2 we write the MTE in
full detail. We also discuss a solution of the MTE in terms of bosonic
continuum functions.Comment: 28 pages, 3 figure
Quantum 2+1 evolution model
A quantum evolution model in 2+1 discrete space - time, connected with 3D
fundamental map R, is investigated. Map R is derived as a map providing a zero
curvature of a two dimensional lattice system called "the current system". In a
special case of the local Weyl algebra for dynamical variables the map appears
to be canonical one and it corresponds to known operator-valued R-matrix. The
current system is a kind of the linear problem for 2+1 evolution model. A
generating function for the integrals of motion for the evolution is derived
with a help of the current system. The subject of the paper is rather new, and
so the perspectives of further investigations are widely discussed.Comment: LaTeX, 37page
Quantum geometry of 3-dimensional lattices
We study geometric consistency relations between angles on 3-dimensional (3D)
circular quadrilateral lattices -- lattices whose faces are planar
quadrilaterals inscribable into a circle. We show that these relations generate
canonical transformations of a remarkable ``ultra-local'' Poisson bracket
algebra defined on discrete 2D surfaces consisting of circular quadrilaterals.
Quantization of this structure leads to new solutions of the tetrahedron
equation (the 3D analog of the Yang-Baxter equation). These solutions generate
an infinite number of non-trivial solutions of the Yang-Baxter equation and
also define integrable 3D models of statistical mechanics and quantum field
theory. The latter can be thought of as describing quantum fluctuations of
lattice geometry. The classical geometry of the 3D circular lattices arises as
a stationary configuration giving the leading contribution to the partition
function in the quasi-classical limit.Comment: 27 pages, 10 figures. Minor corrections, references adde
Reverberation Mapping Results from MDM Observatory
We present results from a multi-month reverberation mapping campaign
undertaken primarily at MDM Observatory with supporting observations from
around the world. We measure broad line region (BLR) radii and black hole
masses for six objects. A velocity-resolved analysis of the H_beta response
shows the presence of diverse kinematic signatures in the BLR.Comment: To appear in the Proceedings of the IAU Symposium No. 267:
Co-Evolution of Central Black Holes and Galaxies, Rio de Janeiro, 200
The level set method for the two-sided eigenproblem
We consider the max-plus analogue of the eigenproblem for matrix pencils
Ax=lambda Bx. We show that the spectrum of (A,B) (i.e., the set of possible
values of lambda), which is a finite union of intervals, can be computed in
pseudo-polynomial number of operations, by a (pseudo-polynomial) number of
calls to an oracle that computes the value of a mean payoff game. The proof
relies on the introduction of a spectral function, which we interpret in terms
of the least Chebyshev distance between Ax and lambda Bx. The spectrum is
obtained as the zero level set of this function.Comment: 34 pages, 4 figures. Changes with respect to the previous version: we
explain relation to mean-payoff games and discrete event systems, and show
that the reconstruction of spectrum is pseudopolynomia
Interaction of ballistic quasiparticles and vortex configurations in superfluid He3-B
The vortex line density of turbulent superfluid He3-B at very low temperature
is deduced by detecting the shadow of ballistic quasiparticles which are
Andreev reflected by quantized vortices. Until now the measured total shadow
has been interpreted as the sum of shadows arising from interactions of a
single quasiparticle with a single vortex. By integrating numerically the
quasi-classical Hamiltonian equations of motion of ballistic quasiparticles in
the presence of nontrivial but relatively simple vortex systems (such as
vortex-vortex and vortex-antivortex pairs and small clusters of vortices) we
show that partial screening can take place, and the total shadow is not
necessarily the sum of the shadows. We have also found that it is possible
that, upon impinging on complex vortex configurations, quasiparticles
experience multiple reflections, which can be classical, Andreev, or both.Comment: To appear in Phys Rev
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
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