Matrix Finite-Zone Dirac-Type Equations

Boundary value problems for Dirac–type equations

We prove regularity for a class of boundary value problems for first order elliptic systems, with boundary conditions determined by spectral decompositions, under coefficient differentiability conditions weaker than previously known. We establish Fredholm properties for Dirac-type equations with these boundary conditions. Our results include sharp solvability criteria, over both compact and non...

Trace Formulas and Borg-type Theorems for Matrix-valued Jacobi and Dirac Finite Difference Operators

Borg-type uniqueness theorems for matrix-valued Jacobi operators H and supersymmetric Dirac difference operators D are proved. More precisely, assuming reflectionless matrix coefficients A,B in the self-adjoint Jacobi operator H = AS + AS + B (with S the right/left shift operators on the lattice Z) and the spectrum of H to be a compact interval [E−, E+], E− < E+, we prove that A and B are certa...

Random Matrix Models for Dirac Operators at finite Lattice Spacing

We study discretization effects of the Wilson and staggered Dirac operator with Nc > 2 using chiral random matrix theory (chRMT). We obtain analytical results for the joint probability density of Wilson-chRMT in terms of a determinantal expression over complex pairs of eigenvalues, and real eigenvalues corresponding to eigenvectors of positive or negative chirality as well as for the eigenvalue...

Non-linear Equations of Korteweg-de Vries Type, Finite-zone Linear Operators, and Abelian Varieties

Boundary value problems for Dirac–type equations, with applications

We prove regularity for a class of boundary value problems for first order elliptic systems, with boundary conditions determined by spectral decompositions, under coefficient differentiability conditions weaker than previously known. We establish Fredholm properties for Dirac-type equations with these boundary conditions. Our results include sharp solvability criteria, over both compact and non...