Related papers: A conjecture for the superintegrable chiral Potts …

The geometric Langlands program can be described in a natural way by compactifying on a Riemann surface C a twisted version of N=4 super Yang-Mills theory in four dimensions. The key ingredients are electric-magnetic duality of gauge…

We study a class of determinantal ideals arising from conditional independence (CI) statements with hidden variables. Such CI statements translate into determinantal conditions on a matrix whose entries represent the probabilities of events…

Consider a semiclassical Hamiltonian $H := h^{2} \Delta + V - E$ where $\Delta$ is the positive Laplacian on $\mathbb{R}^{d}$, $V \in C^{\infty}_{0}(\mathbb{R}^{d})$ and $E > 0$ is an energy level. We prove that under an appropriate…

We consider symmetry operators a from the group ring C[S_N] which act on the Hilbert space H of the 1D spin-1/2 Heisenberg magnetic ring with N sites. We investigate such symmetry operators a which are self-adjoint (in a sence defined in…

The response of pseudoscalar and vector mesons to strong magnetic fields is studied within a simple constituent quark model using analogy with bound states of Positronium. Magnetic moments of charged vector mesons K*, D*, B* are predicted…

In the framework of standard electrodynamics with linear local response, we construct a model that provides spontaneously broken transparency. The functional dependence of the medium parameter turns out to be of the Higgs type.

Effects of spontaneous toroidal ordering on magnetic excitation are theoretically investigated for a localized spin model that includes a staggered Dzyaloshinsky-Moriya interaction and anisotropic exchange interactions, which arise from the…

A smooth projective toric variety $X=X_\Sigma$ has a geometric quotient description $V /\!/ T$. Using $2|1$-pointed quasimap invariants, one can define a quantum $H^*(T)$-module $QM(X)$, which deforms a natural module structure given by the…

We relate Nekrasov partition functions, with arbitrary values of $\epsilon_1,\epsilon_2$ parameters, to matrix models for $\beta$-ensembles. We find matrix models encoding the instanton part of Nekrasov partition functions, whose measure,…

We show that quadratic Hamiltonians in involution coming from a St\"ackel system are quantizable, in the sense that one can construct commutative self-adjoint operators whose symbols are the quadratic Hamiltonians. Moreover, they allow…

We study H^*(P), the mod p cohomology of a finite p--group P, viewed as an Out(P)--module. In particular, we study the conjecture, first considered by Martino and Priddy, that, if e_S in Z/p[Out(P)] is a primitive idempotent associated to…

Using classical Monte Carlo simulations, we study a simple statistical mechanical model of relevance to the emergence of polarisation from local displacements on the square and cubic lattices. Our model contains two key ingredients: a…

Spin polarization in chiral molecules is a magnetic molecular response associated with electron transport and enantioselective bond polarization that occurs even in the absence of an external magnetic field. An unexpected finding by Santos…

Employing a relativistic version of a hypervirial result, recurrence relations for arbitrary non-diagonal radial hydrogenic matrix elements have recently been obtained in Dirac relativistic quantum mechanics. In this contribution honoring…

While dealing in [1] with the supersymmetry of a tridiagonal Hamiltonian H, we have proved that its partner Hamiltonian H(+) also have a tridiagonal matrix representation in the same basis and that the polynomials associated with the…

We develop, from first principles, a general and compact formalism for predicting the electromagnetic response of a metamaterial with non-magnetic inclusions in the long wavelength limit, including spatial dispersion up to the second order.…

Let M be a matroid on E, representable over a field of characteristic zero. We show that h-vectors of the following simplicial complexes are log-concave: 1. The matroid complex of independent subsets of E. 2. The broken circuit complex of…

We analyze statistical properties of complex eigenvalues of random matrices $\hat{A}$ close to unitary. Such matrices appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with…

We show that the matrix elements of integrable models computed by the Algebraic Bethe Ansatz can be put in direct correspondence with the Form Factors of integrable relativistic field theories. This happens when the S-matrix of a Bethe…

We show that the one dimensional unitary matrix model with potential of the form $a U + b U^2 + h.c.$ is integrable. By reduction to the dynamics of the eigenvalues, we establish the integrability of a system of particles in one space…