Related papers: Square-roots and Lax-pairs for supersymmetrizable …
We study the factorization of the PT symmetric Hamiltonian. The general expression for the superpotential corresponding to the PT symmetric potential is obtained and explicit examples are presented.
In the context of the interacting boson model with $s$, $d$ and $g$ bosons, the conditions for obtaining an intrinsic shape with octahedral symmetry are derived for a general Hamiltonian with up to two-body interactions.
Orthosymplectic Lie superalgebras are fundamental symmetries in modern physics, such as massive supergravity. However, their representations are far from being thoroughly understood. In the present paper, we completely determine the…
We show that for a class of dynamical systems, Hamiltonian with respect to three distinct Poisson brackets (P_0, P_1, P_2), separation coordinates are provided by the common roots of a set of bivariate polynomials. These polynomials, which…
In the literature, the existence of Darboux polynomials and additional polynomial first integrals has been considered in the case of Hamiltonian systems. In this article such problem is formulated in the more general framework of Poisson…
This article establishes some elementary dualities for root systems with automorphisms. We give several applications to reductive groups over nonarchimedean local fields: (1) the proof of a conjecture of Pappas-Rapoport-Smithling…
The general solution of SUSY intertwining relations for three-dimensional Schr\"odinger operators is built using the class of second order supercharges with nondegenerate constant metric. This solution includes several models with arbitrary…
We give a new proof of a theorem of Loos stating that a Riemannian symmetric space X with rectangular unit lattice is a symmetric R-space. For this we construct explicitly an isometric extrinsically symmetric embedding of X in a Euclidean…
We construct Hamiltonians for systems of nonrelativistic particles linearly coupled to massive scalar bosons using abstract boundary conditions. The construction yields an explicit characterisation of the domain of self-adjointness in terms…
We construct the classical r-matrix structure for the Lax formulation of BC_N Ruijsenaars-Schneider systems proposed in hep-th 0006004. The r-matrix structure takes a quadratic form similar to the A_N Ruijsenaars-Schneider Poisson bracket…
We describe three different approaches to the extended (N=2) supersymmetrization of the multicomponent KP hierarchy. In the first one we utilize only superfermions while in the second only superbosons and in the third superbosons as well as…
Universal Lax pairs (the root type and the minimal type) are presented for Calogero-Moser models based on simply laced root systems, including E_8. They exist with and without spectral parameter and they work for all of the four choices of…
The subdivided double construction on 4-regular graphs was used by Poto\v{c}nik and Wilson to explore semi-symmetric (edge-transitive but not vertex-transitive) graphs, and can be used to construct every semi-symmetric 4-regular graph that…
The original Calogero and Sutherland models describe N quantum particles on the line interacting pairwise through an inverse square and an inverse sinus-square potential. They are well known to be integrable and solvable. Here we extend the…
We study a Lax pair in a $2$-parameter Lie algebra in various representations. The overlap coefficients of the eigenfunctions of $L$ and the standard basis are given in terms of orthogonal polynomials and orthogonal functions. Moreover,…
An important example of a multi-dimensional integrable system is the anti-self-dual Einstein equations. By studying the symmetries of these equations, a recursion operator is found and the associated hierarchy constructed. Owing to the…
In this work, we conduct a systematic study of Hamiltonian and quasi-Hamiltonian systems within the framework of nondecomposable generalized Poisson geometry. Our focus lies on the interplay between the algebraic structure of…
We show that supersymmetry can provide a versatile platform in synthesizing a new class of optical structures with desired properties and functionalities. By exploiting the intimate relationship between superpatners, one can systematically…
Translationally invariant symmetric polynomials as coordinates for $N$-body problems with identical particles are proposed. It is shown that in those coordinates the Calogero and Sutherland $N$-body Hamiltonians, after appropriate gauge…
Physical systems with symmetry arise abundantly in applications, and are endowed with interesting mathematical structures. The present paper focusses on linear reciprocal and input-output Hamiltonian systems. Their characterization is…