Related papers: Construction of C operator for a PT symmetric mode…
Recently developed methods for PT-symmetric models are applied to quantum-mechanical matrix models. We consider in detail the case of potentials of the form $V=-(g/N^{p/2-1})Tr(iM)^{p}$ and show how the calculation of all singlet wave…
We give an explicit description of all minimal self-adjoint extensions of a densely defined, closed symmetric operator in a Hilbert space with deficiency indices $(1, 1)$.
The family of complex PT-symmetric sextic potentials is studied to show that for various cases the system is essentially quasi-solvable and possesses real, discrete energy eigenvalues. For a particular choice of parameters, we find that…
According to the necessary requirements for a chirally symmetric Dirac operator, we present a systematic construction of such operators. We formulate a criterion for the hermitian operator which enters the construction such that the doubled…
We extend some Cheney-Sharma type operators to a triangle with one curved side. We construct their product and Boolean sum, we study their interpolation properties, the orders of accuracy and we give different expressions of the…
A new construction for the form sum of positive, selfadjoint operators is given in this paper. The situation is a bit more general, because our aim is to add positive, symmetric operators. With the help of the used method, some commutation…
For every closed subset $X$ of a stratifiable [resp. metrizable] space $Y$ we construct a positive linear extension operator $T:R^{X\times X}\to R^{Y\times Y}$ preserving constant functions, bounded functions, continuous functions,…
Most recently it has been observed e.g. by Bender and Klevansky (arXiv:0905.4673 [hep-th]) that the C-operator related to a PT-symmetric non-Hermitian Hamilton operator is not unique. Moreover it has been remarked by Shi and Sun…
In this work, we show that the traditional effective field approach can be applied to the $\mathcal{PT}$-symmetric wrong sign ($-x^{4}$) quartic potential. The importance of this work lies in the possibility of its extension to the more…
We consider the one-dimensional Dirac equation for the harmonic oscillator and the associated second order separated operators giving the resonances of the problem by complex dilation. The same operators have unique extensions as closed…
All compact $AC(\sigma)$ operators have a representation analogous to that for compact normal operators. As a partial converse we obtain conditions which allow one to construct a large number of such operators. Using the results in the…
We say that an operator $T \in B(H)$ is complex symmetric if there exists a conjugate-linear, isometric involution $C:H\to H$ so that $T = CT^*C$. We prove that binormal operators, operators that are algebraic of degree two (including all…
In this article, we give conditions guaranteeing the commutativity of a bounded self-adjoint operator with an unbounded closed symmetric operator.
For a class of one-dimensional Schrodinger operators with polynomial potentials that includes Hermitian and PT-symmetric operators, we show that the zeros of scaled eigenfunctions have a limit disctibution in the complex plane as the…
It is known that the perfect absorption of two identical waves incident on a complex potential from left and right can occur at a fixed real energy and that the time-reversed setting of this system would act as a laser at threshold at the…
A real band condition is shown to exist for one dimensional periodic complex non-hermitian potentials exhibiting PT-symmetry. We use an exactly solvable ultralocal periodic potential to obtain the band structure and discuss some spectral…
We suggest a closed form expression for the path integral of quantum transition amplitudes. We introduce a quantum action with renormalized parameters. We present numerical results for the $V \sim x^{4}$ potential. The renormalized action…
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…
The aim of this paper is to develop an approach to obtain self-adjoint extensions of symmetric operators acting on anti-dual pairs. The main advantage of such a result is that it can be applied for structures not carrying a Hilbert space…
We study the Schr\"odinger operator with a potential given by the sum of the potentials for harmonic oscillator and imaginary cubic oscillator and we focus on its pseudospectral properties. A summary of known results about the operator and…