Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- Centre National de la Recherche ScientifiqueFR2k papers
- University of British ColumbiaCA1.9k papers
- McGill UniversityCA1.9k papers
- University of VictoriaCA1.8k papers
- University of California, Santa CruzUS1.7k papers
- Rutherford Appleton LaboratoryGB1.7k papers
- University of ManchesterGB1.7k papers
- Queen Mary University of LondonGB1.7k papers
- University of PisaIT1.6k papers
- University of EdinburghGB1.6k papers
- University of BirminghamGB1.6k papers
- Heidelberg UniversityDE1.6k papers
22 papers · 2 filters
Determinantal identity for multilevel systems and finite determinantal processes
J. Harnad, A. Yu. Orlov
We give a simple algebraic derivation of a useful determinantal identity for multilevel systems such as random matrix chains and finite determinantal point processes, with applicat…
Heisenberg Algebra, Umbral Calculus and Orthogonal Polynomials
G. Dattoli, D. Levi, P. Winternitz
Umbral calculus can be viewed as an abstract theory of the Heisenberg commutation relation . In ordinary quantum mechanics is the derivative and $\hat M…
Twisted spin Sutherland models from quantum Hamiltonian reduction
L. Feher, B. G. Pusztai
Recent general results on Hamiltonian reductions under polar group actions are applied to study some reductions of the free particle governed by the Laplace-Beltrami operator of a…
Superintegrable systems with spin in two- and three-dimensional Euclidean spaces
P. Winternitz, I. Yurdusen
The concept of superintegrability in quantum mechanics is extended to the case of a particle with spin s=1/2 interacting with one of spin s=0. Non-trivial superintegrable systems w…
Superintegrable Systems with a Third Order Integrals of Motion
Ian Marquette, Pavel Winternitz
Two-dimensional superintegrable systems with one third order and one lower order integral of motion are reviewed. The fact that Hamiltonian systems with higher order integrals of m…
First Colonization of a Spectral Outpost in Random Matrix Theory
M. Bertola, S. Y. Lee
We describe the distribution of the first finite number of eigenvalues in a newly-forming band of the spectrum of the random Hermitean matrix model. The method is rigorously based…
Symmetry preserving discretization of SL(2,R) invariant equations
A. Bourlioux, R. Rebelo, P. Winternitz
Nonlinear ODEs invariant under the group SL(2,R) are solved numerically. We show that solution methods incorporating the Lie point symmetries provide better results than standard m…
Lie symmetries of multidimensional difference equations
Decio Levi, Sébastien Tremblay, Pavel Winternitz
A method is presented for calculating the Lie point symmetries of a scalar difference equation on a two-dimensional lattice. The symmetry transformations act on the equations and o…
Invariants of the nilpotent and solvable triangular Lie algebras
Sébastien Tremblay, Pavel Winternitz
Invariants of the coadjoint representation of two classes of Lie algebras are calculated. The first class consists of the nilpotent Lie algebras , isomorphic to the algebras…
Lie point symmetries of difference equations and lattices
Decio Levi, Sébastien Tremblay, Pavel Winternitz
A method is presented for finding the Lie point symmetry transformations acting simultaneously on difference equations and lattices, while leaving the solution set of the correspon…
Integrable systems without the Painlevé property
Alfred Ramani, Basile Grammaticos, Sébastien Tremblay
We examine whether the Painlevé property is a necessary condition for the integrability of nonlinear ordinary differential equations. We show that for a large class of linearisable…
Integrable lattice equations and their growth properties
Sébastien Tremblay, Basile Grammaticos, Alfred Ramani
In this paper we investigate the integrability of two-dimensional partial difference equations using the newly developed techniques of study of the degree of the iterates. We show…
Invariants of solvable Lie algebras with triangular nilradicals and diagonal nilindependent elements
Vyacheslav Boyko, Jiri Patera, Roman O. Popovych
The invariants of solvable Lie algebras with nilradicals isomorphic to the algebra of strongly upper triangular matrices and diagonal nilindependent elements are studied exhaustive…
Invariants of triangular Lie algebras with one nilindependent diagonal element
Vyacheslav Boyko, Jiri Patera, Roman O. Popovych
The invariants of solvable triangular Lie algebras with one nilindependent diagonal element are studied exhaustively. Bases of the invariant sets of all such algebras are construct…
Hamiltonian reductions of free particles under polar actions of compact Lie groups
L. Feher, B. G. Pusztai
Classical and quantum Hamiltonian reductions of free geodesic systems of complete Riemannian manifolds are investigated. The reduced systems are described under the assumption that…
Fermionic construction of tau functions and random processes
John Harnad, Alexander Yu. Orlov
Tau functions expressed as fermionic expectation values are shown to provide a natural and straightforward description of a number of random processes and statistical models involv…
Fermionic approach to the evaluation of integrals of rational symmetric functions
John Harnad, Alexander Yu. Orlov
We use the fermionic construction of two-matrix model partition functions to evaluate integrals over rational symmetric functions. This approach is complementary to the one used in…
Fermionic construction of partition function for multi-matrix models and multi-component TL hierarchy
John Harnad, Alexander Yu. Orlov
We use -component fermions to present -fold integrals as a fermionic expectation value. This yields fermionic representation for various -matrix m…
Invariants of Triangular Lie Algebras
Vyacheslav Boyko, Jiri Patera, Roman Popovych
Triangular Lie algebras are the Lie algebras which can be faithfully represented by triangular matrices of any finite size over the real/complex number field. In the paper invarian…
On the volume of nodal sets for eigenfunctions of the Laplacian on the torus
Zeev Rudnick, Igor Wigman
We study the volume of nodal sets for eigenfunctions of the Laplacian on the standard torus in two or more dimensions. We consider a sequence of eigenvalues $4π^2\eigenvalue$ with…
Polynomial Associative Algebras for Quantum Superintegrable Systems with a Third Order Integral of Motion
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…
Conditional Symmetries and Riemann Invariants for Hyperbolic Systems of PDEs
Alfred Michel Grundland, Benoit Huard
This paper contains an analysis of rank-k solutions in terms of Riemann invariants, obtained from interrelations between two concepts, that of the symmetry reduction method and of…