We review the Krein-Gel'fand-Lidskii theory of strong stability of Hamiltonian and symplectic matrices in order to nd a quantitative measure of the strong stability. As a result, formulas for the 2-norm distance from a strongly stable Hamiltonian or symplectic matrix to the set of unstable matrices are derived. 1 Deenition and simple properties of symplectic and Hamiltonian matrices Throughout ...

for solving large sparse non-hermitian positive definite linear equations, bai et al. proposed the hermitian and skew-hermitian splitting methods (hss). they recently generalized this technique to the normal and skew-hermitian splitting methods (nss). in this paper, we present an accelerated normal and skew-hermitian splitting methods (anss) which involve two parameters for the nss iteration. w...

Conventional convergence acceleration techniques for the SCF procedure like the direct inversion in the iterative subspace and the level-shifting can not be applied in the general case of non-Hermitian Fock operators. The commutator of the Fock matrix and the density matrix do not vanish upon convergence of nonHermitian SCF equations and hence the usual error vector choice is not applicable. In...

We address the problem of coupling non-Hermitian systems, treated as fundamental rather than effective theories, to the electromagnetic field. In such theories the observables are not the x and p appearing in the Hamiltonian, but quantities X and P constructed by means of the metric operator. Following the analogous procedure of gauging a global symmetry in Hermitian quantum mechanics we find t...

The observation that the existence of the amazing reality and discreteness of the spectrum need not necessarily be attributed to the Hermiticity of the Hamiltonian is reemphasized in the context of the non-Hermitian Dirac and Klein-Gordon Hamiltonians. Complex Coulombic potentials are considered. In one of the first explicit studies of the non-Hermitian Schrödinger Hamiltonians, Caliceti et al ...

The observation that the existence of the amazing reality and discreteness of the spectrum need not necessarily be attributed to the Hermiticity of the Hamiltonian is reemphasized in the context of the non-Hermitian Dirac and Klein-Gordon Hamiltonians. Complex Coulombic potentials are considered. In one of the first explicit studies of the non-Hermitian Schrödinger Hamiltonians, Caliceti et al ...

For a T -periodic non-Hermitian Hamiltonian H(t), we construct a class of adiabatic cyclic states of period T which are not eigenstates of the initial Hamiltonian H(0). We show that the corresponding adiabatic geometric phase angles are real and discuss their relationship with the conventional complex adiabatic geometric phase angles. We present a detailed calculation of the new adiabatic cycli...

Currently, it has been claimed that certain Hermitian Hamiltonians have parity (P) and they are PT-invariant. We propose generalized definitions of time-reversal operator (T) and orthonormality such that all Hermitian Hamil-tonians are P, T, PT, and CPT invariant. The PT-norm and CPT-norm are indefinite and definite respectively. The energy-eigenstates are either E-type (e.g., even) or O-type (...

Currently, it has been claimed that certain Hermitian Hamiltonians have parity (P) and they are PT-invariant. We propose generalized definitions of time-reversal operator (T) and orthonormality such that all Hermitian Hamil-tonians are P,T,PT,CPT invariant. The PT-norm and CPT-norm are indefinite and definite respectively. The energy-eigenstates are either E-type (e.g., even) or O-type (e.g., o...