A non-Hermitian PφTφ-symmetrized spherically-separable Dirac Hamiltonian is considered. It is observed that the descendant Hamiltonians Hr, Hθ, and Hφ play essential roles and offer some ”user-feriendly” options as to which one (or ones) of them is (or are) non-Hermitian. Considering a PφTφ-symmetrized Hφ, we have shown that the conventional relativistic energy eigenvalues are recoverable. We h...

Recently Scholtz and Geyer proposed a very efficient method to compute metric operators for non-Hermitian Hamiltonians from Moyal products. We develop these ideas further and suggest to use a more symmetrical definition for the Moyal products, because they lead to simpler differential equations. In addition, we demonstrate how to use this approach to determine the Hermitian counterpart for a Ps...

We present multi-point algebraic geometric codes overstepping the Gilbert-Varshamov bound. The construction is based on the generalized Hermitian curve introduced by A. Bassa, P. Beelen, A. Garcia, and H. Stichtenoth. These codes are described in detail by constrcting a generator matrix. It turns out that these codes have nice properties similar to those of Hermitian codes. It is shown that the...

Let ‖| · ‖| be any give unitarily invariant norm. We obtain some exponential relations in the context of semisimple Lie group. On one hand they extend the inequalities (1) ‖|e‖| ≤ ‖|eReA‖| for all A ∈ Cn×n, where ReA denotes the Hermitian part of A, and (2) ‖|e‖| ≤ ‖|ee‖|, where A and B are n×n Hermitian matrices. On the other hand, the inequalities of Weyl, Ky Fan, Golden-Thompson, Lenard-Thom...

This paper classifies the even unimodular lattices that have a structure as a Hermitian OK-lattice of rank r ≤ 12 for rings of integers in imaginary quadratic number fields K of class number 1. The Hermitian theta series of such a lattice is a Hermitian modular form of weight r for the full modular group, therefore we call them theta lattices. For arbitrary imaginary quadratic fields we derive ...

Quantum canonical transformations of the second kind and the non-Hermitian realizations of the basic canonical commutation relations are investigated with a special interest in the generalization of the conventional ladder operators. The opeator ordering problem is shown to be resolved when the non-Hermitian realizations for the canonical variables which can not be measured simultaneously with ...

This paper is concerned with the solution of systems of linear equations ANx = b, where fANg N2N denotes a sequence of positive deenite Hermitian ill{conditioned Toeplitz matrices arising from a (real{valued) nonnegative generating function f 2 C2 with zeros. We construct positive deenite Hermitian preconditioners MN such that the eigenvalues of M ?1 N AN are clustered at 1 and the correspondin...

Using the techniques of quasi-Hermitian quantum mechanics and quantum field theory we use a similarity transformation to construct an equivalent Hermitian Hamiltonian for the Lee model. In the field theory confined to the V/Nθ sector it effectively decouples V , replacing the three-point interaction of the original Lee model by an additional mass term for the V particle and a four-point interac...

Coherent states (CS) for non-Hermitian systems are introduced as eigenstates of pseudo-Hermitian boson annihilation operators. The set of these CS includes two subsets which form bi-normalized and bi-overcomplete system of states. The subsets consist of eigenstates of two complementary lowering pseudo-Hermitian boson operators. Explicit constructions are provided on the example of one-parameter...

Computing the exponential of large-scale skew-Hermitian matrices or parts thereof is frequently required in applications. In this work, we consider the task of extracting finite diagonal blocks from a doubly-infinite skew-Hermitian matrix. These matrices usually have unbounded entries which impede the application of many classical techniques from approximation theory. We analyze the decay prope...