We show that some non-Hermitian Hamiltonian operators with tridiagonal matrix representation may be quasi Hermitian or similar to operators. In the class of discussed here transformation is given by a Hermitian, positive-definite, diagonal operator. there an important difference between open boundary conditions and periodic ones. illustrate theoretical results means two simple, widely used, mod...

New exact upper and lower bounds are derived on the spectrum of the square of the hermitian Wilson Dirac operator. It is hoped that the derivations and the results will be of help in the search for ways to reduce the cost of simulations using the overlap Dirac operator.

New exact upper and lower bounds are derived on the spectrum of the square of the hermitian Wilson Dirac operator. It is hoped that the derivations and the results will be of help in the search for ways to reduce the cost of simulations using the overlap Dirac operator. The bounds also apply to the Wilson Dirac operator in odd dimensions and are therefore relevant to domain wall fermions as well.

1550-7998=20 A non-Hermitian Hamiltonian has a real positive spectrum and exhibits unitary time evolution if the Hamiltonian possesses an unbroken PT (space-time reflection) symmetry. The proof of unitarity requires the construction of a linear operator called C. It is shown here that C is the complex extension of the intrinsic parity operator and that the C operator transforms under the Lorent...

The paper is devoted to an invertible linear operator whose inverse is a Hilbert Schmidt operator and imaginary Hermitian component is bounded. Numerous regular differential and integro-differential operators satisfy these conditions. A sharp norm estimate for the resolvent of the considered operator is established. It gives us estimates for the semigroup and so-called Hirsch operator functions...

We investigate a lattice version of the Yang-Lee model which is characterized by a non-Hermitian quantum spin chain Hamiltonian. We propose a new way to implement PT -symmetry on the lattice, which serves to guarantee the reality of the spectrum in certain regions of values of the coupling constants. In that region of unbroken PT -symmetry we construct a Dyson map, a metric operator and find th...

We give two characterization theorems for pseudo-Hermitian (possibly nondiagonalizable) Hamiltonians with a discrete spectrum that admit a block-diagonalization with finite-dimensional diagonal blocks. In particular, we prove that for such an operator H the following statements are equivalent. 1. H is pseudo-Hermitian; 2. The spectrum of H consists of real and/or complex-conjugate pairs of eige...

Let C , be a composition operator on L (A). Some conditions under which C, is an isometry and Hermitian are investigated in this paper. Some study of normal composition operators is also made.

The isospectrality problem is studied for the operator of the spherical hydromagnetic α−dynamo. It is shown that this operator is formally pseudo-Hermitian (J−symmetric) and lives in a Krein space. Based on the J−symmetry, an operator intertwining Ansatz with first-order differential intertwining operators is tested for its compatibility with the structure of the α−dynamo operator matrix. An in...

In arXiv:0710.5653v1 M. Znojil claims that he has found and corrected an error in my paper: [Phys. Lett. B 650, 208 (2007), arXiv:0706.1872v2] and that it is possible to escape its main conclusion, namely that the unitarity of the time-evolution and observability of the Hamiltonian imply time-independence of the metric operator. In this note I give a very short calculation showing that the anal...