Related papers: A short note on the eigenvalues of regular Hall-pl…
This article is a contribution to the classification of quadratically integrable systems with vector potentials whose integrals are of the nonstandard, nonseparable type. We focus on generalized parabolic cylindrical case, related to…
A Toeplitz matrix is one in which the matrix elements are constant along diagonals. The Fisher-Hartwig matrices are much-studied singular matrices in the Toeplitz family. The matrices are defined for all orders, $N$. They are parametrized…
The behaviour of the critical point between quantum Hall plateaux, as the Zeeman energy is varied, is analysed using modular symmetry of the Hall conductivities following from the law of corresponding states. Flow diagrams for the…
Properties of the magnetic translation operators for a charged particle moving in a crystalline potential and a uniform magnetic field show that it is necessary to consider all inequivalent irreducible projective representations of the the…
The thermodynamic potential of an ideal nonrelativistic gas of two-dimensional electrons in crossed uniform magnetic and electric fields is constructed. For low temperatures and very weak electric fields, it is shown that the Hall…
We consider here square tilings of the plane. By extending the formalism introduced in [3] we build a correspondence between plane maps endowed with an harmonic vector and square tilings satisfying a condition of regularity. In the case of…
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…
Using the Jordan-Schwinger form of the quantum angular momentum eigenstates, it is straight-forward to define rotational correlation tables such that the columns are Molien sequences for finite rotational subgroup $G$. This realization…
To any quiver with relations we associate a consistent scattering diagram taking values in the motivic Hall algebra of its category of representations. We show that the chamber structure of this scattering diagram coincides with the natural…
In this paper we express the eigenvalues of a sort of real heptadiagonal symmetric matrices as the zeros of explicit rational functions establishing upper and lower bounds for each of them. From these prescribed eigenvalues we compute also…
A concept of generalized regular polytope is introduced in this work. The number of its (1...n-1)-dimensional elements is not necessarily integer, though all the combinatorial and metric properties meet those of regular polytopes in a…
We consider harmonic maps on simply connected Riemann surfaces into the group $\mathrm{U}(n)$ of unitary matrices of order $n$. It is known that a harmonic map with an associated algebraic extended solution can be deformed into a new…
We introduce the notion of fully simple maps, which are maps with non self-intersecting disjoint boundaries. In contrast, maps where such a restriction is not imposed are called ordinary. We study in detail the combinatorics of fully simple…
In this document we study the uniform local path connectivity of sets of $m$-tuples of pairwise commuting normal matrices with some additional constraints. More specifically, given given $\varepsilon>0$, a fixed metric $\eth$ in…
In this paper we define generalised spheres in buildings using the simplicial structure and Weyl distance in the building, and we derive an explicit formula for the cardinality of these spheres. We prove a generalised notion of distance…
The theory of waves and instabilities in a differentially rotating disc containing a poloidal magnetic field is developed within the framework of ideal magnetohydrodynamics. A continuous spectrum, for which the eigenfunctions are localized…
We investigate some geometric properties of the real algebraic variety $\Delta$ of symmetric matrices with repeated eigenvalues. We explicitly compute the volume of its intersection with the sphere and prove a Eckart-Young-Mirsky-type…
Two dimensional inversion symmetry ($180^{\circ}$ rotations in the ``Hall plane'' that hosts the incompressible electron fluid that exhibits the quantized Hall effect) is identified as its fundamental unbroken symmetry. A consequence is…
Low-energy transport measurements in Quantum Hall systems have been argued to be governed by emergent modular symmetries whose predictions are robust against many of the detailed microscopic dynamics. We propose the recently-observed…
We introduce a general first-principles methodology for computing electronic structure in a finite uniform magnetic field which allows for an arbitrary rational magnetic flux and nonlocal pseudopotentials, at a comparable time complexity of…