Related papers: Duality in Integrable Systems and Generating Funct…
We introduce a family of $n$-dimensional Hamiltonian systems which, contain, as special reductions, several superintegrable systems as the Tremblay-Turbiner-Winternitz system, a generalized Kepler potential and the anisotropic harmonic…
The current applications of non-Hermitian but ${\cal PT}-$symmetric Hamiltonians $H$ cover several, mutually not too closely connected subdomains of quantum physics. Mathematically, the split between the open and closed systems can be…
By the theory of Eisenstein series, generating functions of various divisor functions arise as modular forms. It is natural to ask whether further divisor functions arise systematically in the theory of mock modular forms. We establish,…
In this paper, we present a general scheme to construct integrable systems based on realization in the coboundary dynamical Poisson groupoids of Etingof and Varchenko. We also present a factorization method for solving the Hamiltonian…
We introduce two-types of topologically twisted Chern-Simons-matter theories on the direct product of circle and genus-h Riemann surface (S^1 \times \Sigma_h). The partition functions of first model agrees with the partition functions of a…
We are able to perform the duality transformation of the spin system which was found before as a lattice realization of the string with linear action. In four and higher dimensions this spin system can be described in terms of a…
The possible functional forms of the effective conductivity sigma_{eff} of the randomly inhomogeneous two-phase system at arbitrary values of concentrations are discussed. A new functional equation, generalizing the duality relation, is…
We study issues of duality in 3D field theory models over a canonical noncommutative spacetime and obtain the noncommutative extension of the Self-Dual model induced by the Seiberg-Witten map. We apply the dual projection technique to…
In this paper, we formulate and present ample evidence towards the conjecture that the partition function (i.e. the exponential of the generating series of intersection numbers with monomials in psi classes) of the Pixton class on the…
We construct a Hamiltonian whose dynamics simulate the dynamics of every other Hamiltonian up to exponentially long times in the system size. The Hamiltonian is time-independent, local, one-dimensional, and translation invariant. As a…
We define two types of Witten's zeta functions according to Cartan's classification of compact symmetric spaces. The type II is the original Witten zeta function constructed by means of irreducible representations of the simple compact Lie…
We define quantum bi-Hamiltonian systems, by analogy with the classical case, as derivations in operator algebras which are inner derivations with respect to two compatible associative structures. We find such structures by means of the…
Searching for the integrable structures of supersymmetric gauge theories and topological strings, we study melting crystal, which is known as random plane partition, from the viewpoint of integrable systems. We show that a series of…
A duality invariant first order action is constructed on the loop group of a Drinfeld double. It gives at the same time the description of both of the pair of $\sigma$-models related by Poisson-Lie T-duality. Remarkably, the action contains…
The semiclassical limit of full non-commutative gauge theory is known as Poisson gauge theory. In this work we revise the construction of Poisson gauge theory paying attention to the geometric meaning of the structures involved and advance…
In this paper, we construct the Sato theory including the Hirota bilinear equations and tau function of a new $q$-deformed Toda hierarchy(QTH). Meanwhile the Block type additional symmetry and bi-Hamiltonian structure of this hierarchy are…
We consider the pairing Hamiltonian and systematically construct its density functional in the strong-coupling limit and in the limit of large particle number. In the former limit, the functional is an expansion into central moments of…
A new class of bivariate poly-analytic Hermite polynomials is considered. We show that they are realizable as the Fourier-Wigner transform of the univariate complex Hermite functions and form a nontrivial orthogonal basis of the classical…
We discuss a spectrum generating algebra in the supersymmetric quantum mechanical system which is defined as a series of solutions to a specific differential equation. All Hamiltonians have equally spaced eigenvalues, and we realize both…
We construct super Hamiltonian integrable systems within the theory of Supersymmetric Poisson vertex algebras (SUSY PVAs). We provide a powerful tool for the understanding of SUSY PVAs called the super master formula. We attach some Lie…