Exact solvability of some non-Hermitian η-pseudo-Hermitian Hamiltonians is explored as a byproduct of η-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-pseudo-Hermiticity ”quasi-generator” to obtain quasiexactly solvable η-pseudo-Hermitian Hamiltonian models. PACS numbers: 03.65.Ge, 03.65.Fd,03.65.Ca

An ensemble of 2 × 2 pseudo-Hermitian random matrices is constructed that possesses real eigenvalues with level-spacing distribution exactly as for the Gaussian unitary ensemble found by Wigner. By a re-interpretation of Connes’ spectral interpretation of the zeros of Riemann zeta function, we propose to enlarge the scope of search of the Hamiltonian connected with the celebrated Riemann Hypoth...

It is often observed in practice that matrix sequences {An}n generated by discretization methods applied to linear differential equations, possess a Spectral Symbol, that is a measurable function describing the asymptotic distribution of the eigenvalues of An. Sequences composed by Hermitian matrices own real spectral symbols, that can be derived through the axioms of Generalized Locally Toepli...

Comparing the lopsided Hermitian/skew-Hermitian splitting (LHSS) method and Hermitian/skewHermitian splitting (HSS) method, a new criterion for choosing the above two methods is presented, which is better than that of Li, Huang and Liu [Modified Hermitian and skew-Hermitian splitting methods for nonHermitian positive-definite linear systems, Numer. Lin. Alg. Appl., 14 (2007): 217-235]. Key-Word...

We decompose the Hilbert space of wave functions into two subspaces, and assign to a given observable two effective representatives that act in the model space. The first serves to determine some of the eigen-values of the full observable, while the second serves to determine its matrix elements, in any basis in one of the subspaces, in terms of quantities pertaining to the model space. We also...

We investigate the classical limit of non-Hermitian quantum dynamics arising from a coherent state approximation, and show that the resulting classical phase space dynamics can be described by generalised “canonical” equations of motion, for both conservative and dissipative motion. The dynamical equations combine a symplectic flow associated with the Hermitian part of the Hamiltonian with a me...

In this paper, we propose three real representations of a generalized Segre quaternion matrix. We establish necessary and sufficient conditions for the existence ?-anti-Hermitian solution to system constrained matrix equations over algebra. also obtain expression general when it is solvable. Finally, provide numerical example verify main results paper.

One of the postulates of quantum mechanics is that the Hamiltonian is Hermitian, as this guarantees that the eigenvalues are real. Recently there has been an interest in asking if H = H is a necessary condition, and has lead to the development of PT -symmetric quantum mechanics. This note shows that any finite physically acceptable non-Hermitian Hamiltonian is equivalent to doing ordinary quant...

We describe an extension to ScaLAPACK for computing with symmetric (and hermitian) matrices stored in a packed form. This is similar to the compact storage for symmetric (and hermitian) matrices available in LAPACK [2]. This enables more efficient use of memory by storing only the lower or upper triangular part of a symmetric matrix. The capabilities include Choleksy factorization (PxSPTRF) and...