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We find the position-momentum decomposition of the quantum operators of the classic Meixner random variables. The position-momentum decomposition involves translation operators, which are used to give a new characterization of the Meixner…
The basic purpose of the present paper is the full solutions of the inverse problem (i.e. a finding of necessary and sufficient conditions) for the operator with complex periodic coefficients.
We scrutinize the possibility of extending the result of \cite{ccr} to the case of q-deformed oscillator for $q$ real; for this we exploit the whole range of the deformation parameter as much as possible. We split the case into two…
Jeffrey's rule of conditioning has been proposed in order to revise a probability measure by another probability function. We generalize it within the framework of the models based on belief functions. We show that several forms of…
We investigate variational methods for finding approximate solutions to the Fokker-Planck equation, especially in cases lacking detailed balance. These schemes fall into two classes: those in which a Hermitian operator is constructed from…
We analyze the situation when the Hamiltonian in field theory can be replaced by the dilatation operator.
Position uncertainty (delocalization) measures for a particle on the sphere are proposed and illustrated on several examples of states. The new measures are constructed using suitably the standard multiplication angle operator variances.…
The problem of the time is one of the open issues in the quantum gravity. This problem is particular problem in the canonical quantum gravity. Even in the loop gravity the problem of the time remain. Our work is concerning to the problem of…
We present a method for approximating the effective consequence of generic quantum gravity corrections to the Wheeler-DeWitt equation. We show that in many cases these corrections can produce departures from classical physics at large…
The block-diagonalization of the Hamiltonian is not sufficient for the transformation to the Foldy-Wouthuysen (FW) representation. The conditions enabling the transition from the Dirac representation to the FW one are formulated and proved.…
By taking the Weyl equation with external electro-magnetic potentials as the simplest representative for a system of PDOs, we give a new method of treating non-commutativity of coefficients matrices. More precisely, we construct a Fourier…
The present study focuses on a subject of significant interest in fluid dynamics: the identification of a model with decreased computational complexity from numerical code output using Koopman operator theory. A reduced-order modelling…
In quantum field theory, physicists routinely use "normal ordering" of operators, which just amounts to shuffling all creation operators to the left. Potentially confusing, then, is the occurrence in the literature of normal-ordered…
We investigate the impact of order parameter fluctuations on magnetoelectric effects in metallic systems using classical Monte Carlo simulations. We focus on a a chiral quadrupole order in a distorted kagome lattice in a model incorporating…
The dynamics of the delay logistic equation with complex parameters and arbitrary complex initial conditions is investigated. The analysis of the local stability of this difference equation has been carried out. We further exhibit several…
The dynamics at the critical-point of a general first-order quantum phase transition in a finite system is examined, from an algebraic perspective. Suitable Hamiltonians are constructed whose spectra exhibit coexistence of states…
We present a Friedmann-Robertson-Walker (FRW) quantum cosmological model within the framework of Finslerian geometry. In this work, we consider a specific fluid. We obtain the corresponding Wheeler-DeWitt equation as the usual constraint…
We present a sufficient condition for the Riemann hypothesis. This condition is the existence of a special ordering on the set of finite products of distinct odd primes.
Within the framework of self-adjoint operator of time in non-relativistic quantum mechanics the equation describing change of the state of quantum system with respect to energy is introduced. The operator of time appears to be the generator…
The uncertainty relation between angle and orbital angular momentum had not been formulated in a similar form as the uncertainty relation between position and linear momentum because the angle variable is not represented by a quantum…