Boundary integral based polygon wall representation in the MPS method

The Boundary Integral Equation Method

An integral representation of Boundary quantum

We study boundary quantum Knizhnik-Zamolodchikov equations associated with quantum affine symmetry Uq(ŝln). We consider the case where the deformation parameter q satisfies |q| = 1, and the difference parameter λ > 0. We give an integral representation of boundary quantum Knizhnik-Zamolodchikov equations. Our approach is based on the free field realizations of the vertex operators and the bound...

Boundary temperature reconstruction in an inverse heat conduction problem using boundary integral equation method

‎In this paper‎, ‎we consider an inverse boundary value problem for two-dimensional heat equation in an annular domain‎. ‎This problem consists of determining the temperature on the interior boundary curve from the Cauchy data (boundary temperature and heat flux) on the exterior boundary curve‎. ‎To this end‎, ‎the boundary integral equation method is used‎. ‎Since the resulting system of linea...

The boundary integral method for magnetic billiards

We introduce a boundary integral method for two-dimensional quantum billiards subjected to a constant magnetic field. It allows to calculate spectra and wave functions, in particular at strong fields and semiclassical values of the magnetic length. The method is presented for interior and exterior problems with general boundary conditions. We explain why the magnetic analogues of the field-free...

Free polygon enumeration and the area of an integral polygon

We introduce the notion of free polygons as combinatorial building blocks for convex integral polygons; that is, polygons with vertices having integer coordinates. In this context, an Euler-type formula is derived for the number of integer points in the interior of an integral polygon. This leads in turn to a formula for the area of an integral polygon P via the enumeration of free integral tri...