In this paper, based on the shift splitting of coefficient matrix, a generalized two-sweep (GTSS) method is introduced to solve non-Hermitian positive definite linear systems. Theoretical analysis shows that GTSS convergent unique solution systems under loose restriction iteration parameter. Numerical experiments are reported efficiency method.

We discuss non-Hermitian field theories where the spectrum of the Hamiltonian involves only real energies. We make three observations. (i) The theories obtained from supersymmetric theories by nonanticommutative deformations belong in many cases to this class. (ii) When the deformation parameter is small, the deformed theory enjoys the same supersymmetry algebra as the undeformed one. Half of t...

The long standing problem of the ordering ambiguity in the definition of the Hamilton operator for a point particle in curved space is naturally resolved by using the powerful geometric calculus based on Clifford Algebra. The momentum operator is defined to be the vector derivative (the gradient) multiplied by −i; it can be expanded in terms of basis vectors γμ as p = −iγ∂μ. The product of two ...

For a given standard Hamiltonian H = [p − A(x)]2/(2m) + V (x) with arbitrary complex scalar potential V and vector potential A, with x ∈ R, we construct an invertible antilinear operator τ such that H is τ -anti-pseudo-Hermitian, i.e., H = τHτ−1. We use this result to give the explicit form of a linear Hermitian invertible operator with respect to which any standard PT -symmetric Hamiltonian wi...

We prove that we can always construct strongly minimal linearizations of an arbitrary rational matrix from its Laurent expansion around the point at infinity, which happens to be case for polynomial matrices expressed in monomial basis. If has a particular self-conjugate structure, show how preserve it. The structures are considered Hermitian and skew-Hermitian with respect real line, para-Herm...

Let M be a mixed graph and [Formula: see text] be its Hermitian-adjacency matrix. If we add a Randić weight to every edge and arc in M, then we can get a new weighted Hermitian-adjacency matrix. What are the properties of this new matrix? Motivated by this, we define the Hermitian-Randić matrix [Formula: see text] of a mixed graph M, where [Formula: see text] ([Formula: see text]) if [Formula: ...

This article focuses on solving the generalized eigenvalue problems (GEP) arising in the source-free Maxwell equation with magnetoelectric coupling effects that models three-dimensional complex media. The goal is to compute the smallest positive eigenvalues, and the main challenge is that the coefficient matrix in the discrete Maxwell equation is indefinite and degenerate. To overcome this diff...

The spatial discretization of the single-cone Dirac Hamiltonian on surface a topological insulator or superconductor needs special "staggered" grid, to avoid appearance spurious second cone in Brillouin zone. We adapt Stacey from lattice gauge theory produce generalized eigenvalue problem, form ${\mathcal H}\psi=E {\mathcal P}\psi$, with Hermitian tight-binding operators H}$, P}$, locally conse...