As will be shown in this paper, there always exists an R such that (1.1) holds. We present a stable O(n3) algorithm that computes an R that has the form of a permuted triangular matrix. Our motivation comes from eigenvalue problems with Hamiltonian structure. A matrix H ∈ R is said to be Hamiltonian if (JH) = JH and skew-Hamiltonian if (JH) = −JH . EXAMPLE 1. The study of corner singularities i...

The fermion doubling theorem plays a pivotal role in Hermitian topological materials. It states, for example, that Weyl points must come pairs three-dimensional semimetals. Here, we present an extension of the to non-Hermitian lattice Hamiltonians. We focus on two-dimensional systems without any symmetry constraints, which can host two different types point nodes, namely, (i) Fermi and (ii) exc...

We propose a quantum walk defined by digraphs (mixed graphs). This is like Grover that perturbed certain complex-valued function digraphs. The discriminant of this matrix normalization generalized Hermitian adjacency matrices. Furthermore, we give definitions the positive and negative supports transfer matrix, clarify explicit formulas their square. In addition, tables computer on identificatio...

Effective interaction operators usually act on a restricted model space and give the same energies (for Hamiltonian) and matrix elements (for transition operators, etc.) as those of the original operators between the corresponding true eigenstates. Various types of effective operators are possible. Those well defined effective operators have been shown to be related to each other by similarity ...

The generalized Higham matrix is a complex symmetric matrix A = B + iC, where both B ∈ Cn×n and C ∈ Cn×n are Hermitian positive definite, and i = √−1 is the imaginary unit. The growth factor in Gaussian elimination is less than 3 √ 2 for this kind of matrices. In this paper, we give a new brief proof on this result by different techniques, which can be understood very easily, and obtain some ne...

in this paper we define a new type of rings ”almost powerhermitian rings” (a generalization of almost hermitian rings) and establish several sufficient conditions over a ring r such that, every regular matrix admits a diagonal power-reduction.

In the study of bi-Hamiltonian systems (both classical and quantum) one starts with a given dynamics and looks for all alternative Hamiltonian descriptions it admits. In this paper we start with two compatible Hermitian structures (the quantum analog of two compatible classical Poisson brackets) and look for all the dynamical systems which turn out to be bi-Hamiltonian with respect to them.

In this paper energy bands and Berry curvature of graphene was studied. Desired Hamiltonian regarding the next-nearest neighbors obtained by tight binding model. By using the second quantization approach, the transformation matrix is calculated and the Hamiltonian of system is diagonalized. With this Hamiltonian, the band structure and wave function can be calculated. By using calculated wave f...

Exact solvability of some non-Hermitian η-weak-pseudo-Hermitian Hamiltonians is explored as a byproduct of η-weak-pseudo-Hermiticity generators. A class of Veff (x) = V (x) + iW (x) potentials is considered, where the imaginary part W (x) is used as an η-weak-pseudo-Hermiticity generator to obtain exactly solvable η-weak-pseudo-Hermitian Hamiltonian models. PACS numbers: 03.65.Ge, 03.65.Fd,03.6...

A class η-weak-pseudo-Hermiticity generators for spherically symmetric non-Hermitian Hamiltonians are presented. An operators-based procedure is introduced so that the results for the 1D Schrödinger Hamiltonian may very well be reproduced. A generalization beyond the nodeless states is proposed. Our illustrative examples include η-weak-pseudo-Hermiticity generators for the non-Hermitian weakly ...