Pseudo-Hermitian position and momentum operators, Hermitian Hamiltonian, and deformed oscillators

The recently introduced by us, two- and three-parameter (p, q)- and (p, q, [Formula: see text])-deformed extensions of the Heisenberg algebra were explored under the condition of their direct link with the respective (nonstandard) deformed quantum oscillator algebras. In this paper, we explore certain Hermitian Hamiltonians build in terms of non-Hermitian position and momentum operators obeying definite [Formula: see text](N)-pseudo-hermiticity properties. A generalized nonlinear (with the coefficients depending on the particle number operator N) one-mode Bogoliubov transformation is developed as main tool for the corresponding study. Its application enables to obtain the spectrum of “almost free” (but essentially nonlinear) Hamiltonian.

New version of pseudo-hermiticity in the two-sided deformation of Heisenberg algebra

The recently introduced two- and three-parameter [Formula: see text]- and [Formula: see text]-deformed extensions of the Heisenberg algebra (HA) were explored under the condition of their connectedness with the respective nonstandard (other than known ones) deformed quantum oscillator algebras. In this paper, we show that such connection dictates certain new [Formula: see text]-pseudo-Hermitian conjugation rule between the creation and annihilation operators with [Formula: see text] depending on the particle number operator [Formula: see text]. In turn, that leads to the related [Formula: see text]-pseudo-hermiticity of the position–momentum operators, though the involved Hamiltonian is Hermitian. Different possible cases are studied, and some interesting features implied by the use of such [Formula: see text]-based conjugation rule are emphasized.

On an Unusual Quantization Procedure of Heat Conduction

We have shown in our previous works how to introduce the quantization procedure into the theory of heat conduction. In the present paper we point out where and why we need to complete the previous results to obtain the Hamiltonian by which we can bring “zero point” energy into the theory of thermal field. We calculate the energy and the quasi-particle number operator for heat conduction.