Related papers: Quantum-classical duality for Gaudin magnets with …
Hilbert bimodules are morphisms between C*-algebraic models of quantum systems, while symplectic dual pairs are morphisms between Poisson geometric models of classical systems. Both of these morphisms preserve representation-theoretic…
The standard quantum mechanical harmonic oscillator has an exact, dual relationship with a completely classical system: a classical particle running along a circle. Duality here means that there is a one-to-one relation between all…
The imprints left by quantum mechanics in classical (Hamiltonian) mechanics are much more numerous than is usually believed. We show Using no physical hypotheses) that the Schroedinger equation for a nonrelativistic system of spinless…
We examine classical and quantum aspects of the planar non-compact spin system coupled with Chern-Simons gauge field in the presence of background charge. We first define our classical spin system as non- relativistic non-linear sigma model…
It is well known that classical and quantum theories carry distinct types of representations, each type of representation corresponding to possible values of generalized charges in the classical or quantum context. This paper demonstrates a…
We study quantum intergrable systems of interacting particles from the point of view, proposed in our previous paper. We obtain Calogero-Moser and Sutherland systems as well their Ruijsenaars relativistic generalization by a Hamiltonian…
We introduce spin Calogero-Moser systems associated with root systems of simple Lie algebras and give the associated Lax representations (with spectral parameter) and fundamental Poisson bracket relations. The associated integrable models…
We show that Hecke algebra of type B and a coideal subalgebra of the type A quantum group satisfy a double centralizer property, generalizing the Schur-Jimbo duality in type A. The quantum group of type A and its coideal subalgebra form a…
A quantum integrable model is considered which describes a quantization of affine hyper-elliptic Jacobian. This model is shown to possess the property of duality: a dual model with inverse Planck constant exists such that the…
One classical theory, as determined by an equation of motion or set of classical trajectories, can correspond to many unitarily {\em in}equivalent quantum theories upon canonical quantization. This arises from a remarkable ambiguity, not…
This thesis presents our results on Liouville integrable systems of Calogero-Ruijsenaars type: 1. We prove an explicit formula providing canonical spectral coordinates for the rational Calogero-Moser system. 2. We explore action-angle…
${\rm SU}(2|1)$ supersymmetric multi-particle quantum mechanics with additional semi-dynamical spin degrees of freedom is considered. In particular, we provide an $\mathcal{N}{=}\,4$ supersymmetrization of the quantum ${\rm U}(2)$ spin…
We consider classical and quantum mechanics for an extended Heisenberg algebra with additional canonical commutation relations for position and momentum coordinates. In our approach this additional noncommutativity is removed from the…
We study a model of massive photons with a parity invariant and non-local mass term. We identify a discrete symmetry of the classical equations of motion and show that this symmetry can be thought of as an electric-magnetic duality valid…
We reconcile the Hamiltonian formalism and the zero curvature representation in the approach to integrable boundary conditions for a classical integrable system in 1+1 space-time dimensions. We start from an ultralocal Poisson algebra…
A general procedure to get the explicit solution of the equations of motion for N-body classical Hamiltonian systems equipped with coalgebra symmetry is introduced by defining a set of appropriate collective variables which are based on the…
The aim of this paper is two-fold. First, we prove the existence of Lieb-Robinson bounds for classical particle systems describing harmonic oscillators interacting with arbitrarily many neighbors, both on lattices and on more general…
We construct a two parameter family of 2-particle Hamiltonians closed under the duality operation of interchanging the (relative) momentum and coordinate. Both coordinate and momentum dependence are elliptic, and the modulus of the momentum…
We describe relationships between integrable systems with N degrees of freedom arising from the AGT conjecture. Namely, we prove the equivalence (spectral duality) between the N-cite Heisenberg spin chain and a reduced gl(N) Gaudin model…
We construct cubic Hamiltonians for quantum Gaudin models of affine types $\hat{\mathfrak{sl}}_M$. They are given by hypergeometric integrals of a form we recently conjectured in arXiv:1804.01480. We prove that they commute amongst…