Related papers: Interrelations between dualities in classical inte…
Recently, it was proposed that the chiral central charge of a gapped, two-dimensional quantum many-body system is proportional to a bulk ground state entanglement measure known as the modular commutator. While there is significant evidence…
Action-angle type variables for spin generalizations of the elliptic Ruijsenaars-Schneider system are constructed. The equations of motion of these systems are solved in terms of Riemann theta-functions. It is proved that these systems are…
We establish a Schur type duality between a coideal subalgebra of the quantum group of type A and the Hecke algebra of type B with 2 parameters. We identify the $\imath$-canonical basis on the tensor product of the natural representation…
Recently a duality between color and kinematics has been proposed, exposing a new unexpected structure in gauge theory and gravity scattering amplitudes. Here we propose that the relation goes deeper, allowing us to reorganize amplitudes…
We discuss some special classes of canonical transformations of the extended phase space, which relate integrable systems with a common Lagrangian submanifold. Various parametric forms of trajectories are associated with different integrals…
We extend duality between the quantum integrable Gaudin models with boundary and the classical Calogero-Moser systems associated with root systems of classical Lie algebras $B_N$, $C_N$, $D_N$ to the case of supersymmetric ${\rm gl}(m|n)$…
It has recently been proposed classical analogs of the purity, linear quantum entropy, and von Neumann entropy for classical integrable systems, when the corresponding quantum system is in a Gaussian state. We generalized these results by…
We show that spin generalization of elliptic Calogero-Moser system, elliptic extension of Gaudin model and their cousins can be treated as a degenerations of Hitchin systems. Applications to the constructions of integrals of motion,…
The geometry of the classical phase space C of a finite number of degrees of freedom determines the possible duality symmetries of the corresponding quantum mechanics. Under duality we understand the relativity of the notion of a quantum…
In this paper, we construct a quadratic r-matrix structure for the classical rational BC(n) Ruijsenaars-Schneider-van Diejen system with the maximal number of three independent coupling parameters. As a byproduct, we provide a Lax…
In this paper, we construct global action-angle variables for a certain two-parameter family of hyperbolic van Diejen systems. Following Ruijsenaars' ideas on the translation invariant models, the proposed action-angle variables come from a…
A special case of the geometric Langlands correspondence is given by the relationship between solutions of the Bethe ansatz equations for the Gaudin model and opers - connections on the projective line with extra structure. In this paper,…
In this paper, we investigate a family of one-dimensional multi-component quantum many-body systems. The interaction is an exchange interaction based on the familiar family of integrable systems which includes the inverse square potential.…
The correspondence principle in physics between quantum mechanics and classical mechanics suggests deep relations between spectral and geometric entities of Riemannian manifolds. We survey---in a way intended to be accessible to a wide…
The composite particle duality extends the notions of both flux attachment and statistical transmutation in spacetime dimensions beyond 2+1D. It constitutes an exact correspondence that can be understood either as a theoretical framework or…
We exploit mappings between quantum and classical systems in order to obtain a class of two-dimensional classical systems with critical properties equivalent to those of the class of one-dimensional quantum systems discussed in a companion…
We present Backlund transformations (BTs) with parameter for certain classical integrable n-body systems, namely the many-body generalised Henon-Heiles, Garnier and Neumann systems. Our construction makes use of the fact that all these…
We describe the large $N$ limit of spectral duality between rational Gaudin models introduced by Adams, Harnad and Hurtubise. The limit of the ${\rm gl}_N$ model is performed by means of a noncommutative torus algebra represented by the…
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…
We systematically derive the Lax pair formulation for both discrete and continuum integrable classical theories with consistent boundary conditions.