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9 papers · 2 filters
Counting open nodal lines of random waves on planar domains
John A. Toth, Igor Wigman
We compute the asymptotic expectation of the number of {\em open} nodal lines for random waves on smooth planar domains. We find that for both the long energy window and th…
Topological expansion of the Bethe ansatz, and non-commutative algebraic geometry
Bertrand Eynard, Olivier Marchal
In this article, we define a non-commutative deformation of the "symplectic invariants" of an algebraic hyperelliptical plane curve. The necessary condition for our definition to m…
All solvable extensions of a class of nilpotent Lie algebras of dimension n and degree of nilpotency n-1
Libor Snobl, Pavel Winternitz
We construct all solvable Lie algebras with a specific n-dimensional nilradical n_(n,2) (of degree of nilpotency (n-1) and with an (n-2)-dimensional maximal Abelian ideal). We find…
Computing with almost periodic functions
R. V. Moody, M. Nesterenko, J. Patera
The paper develops a method for discrete computational Fourier analysis of functions defined on quasicrystals and other almost periodic sets. A key point is to build the analysis a…
Superintegrability with third order integrals of motion, cubic algebras and supersymmetric quantum mechanics I:Rational function potentials
Ian Marquette
We consider a superintegrable Hamiltonian system in a two-dimensional space with a scalar potential that allows one quadratic and one cubic integral of motion. We construct the mos…
Reduction of superintegrable systems: the anisotropic harmonic oscillator
Miguel A. Rodriguez, Piergiulio Tempesta, Pavel Winternitz
We introduce a new 2N--parametric family of maximally superintegrable systems in N dimensions, obtained as a reduction of an anisotropic harmonic oscillator in a 2N--dimensional co…