Related papers: Rigorous Q Factor Formulation and Characterization…
Discrete quantum mechanics is here defined to be a quantum theory of wave functions defined on integers P_i and Q_i, while canonical quantum mechanics is assumed to be based on wave functions on the real numbers, R^n. We study reversible…
We review the electromagnetic form factor of heavy quarks with emphasis on the QCD radiative corrections at two-loop order in the perturbative expansion. We discuss important properties of the heavy-quark form factor such as its…
We construct a complete set of eigenfunctions of the q-deformed harmonic oscillator on the quantum line. In particular the eigenfunctions corresponding to the non-Fock part of the spectrum will be constructed.
The classical model of q-damped oscillator is introduced and solved in terms of Jackson q-exponential function for three different cases, under-damped, over-damped and the critical one. It is shown that in all three cases solution is…
The quantum variables that can be accessed directly by experiments are described by observables. Therefore, physical parameters can only be evaluated indirectly, via estimations based on experimental measurement results. I show that the…
We introduce a general framework of phase reduction theory for quantum nonlinear oscillators. By employing the quantum trajectory theory, we define the limit-cycle trajectory and the phase according to a stochastic Schr\"{o}dinger equation.…
Exact analytical, closed-form solutions, expressed in terms of special functions, are presented for the case of a three-dimensional nonlinear quantum oscillator with a position dependent mass. This system is the generalization of the…
The factor analysis model is a statistical model where a certain number of hidden random variables, called factors, affect linearly the behaviour of another set of observed random variables, with additional random noise. The main assumption…
Realizing the promise of quantum information processing remains a daunting task, given the omnipresence of noise and error. Adapting noise-resilient classical computing modalities to quantum mechanics may be a viable path towards near-term…
This technical report replies to the comments of [2] in detail, and corrects a possible mis-interpretation of [1] in terms of the conventional robust stability concept. After defining the robust stability and quadratic stability concepts,…
We demonstrate that non-exponential decays of unstable systems can be understood as yet another example of nonextensivity encountered in many physical systems and as such can be characterized by the nonextensivity parameter q.
Methods are described for the nonperturbative calculation of wave functions and scattering amplitudes in light-cone quantization. Form factors are computed from the boost-invariant wave functions, which appear as coefficients in a…
The author's modified Coulomb damping model has been generalized to accommodate internal friction that derives from several dissipation mechanisms acting simultaneously. Because of its fundamental nonlinear nature, internal friction damping…
A common situation in experimental physics is to have a signal which can not be separated from a non-interfering background through the use of any cut. In this paper, we describe a procedure for determining, on an event-by-event basis, a…
The nucleon axial form factor is a dominant contribution to errors in neutrino oscillation studies. Lattice QCD calculations can help control theory errors by providing first-principles information on nucleon form factors. In these…
A nonrelativistic decomposition for the quark energy by the ratio of the dispersion of quark momentum squared and the effective quark mass is investigated in the framework of the relativistic oscillator constituent quark model as bound…
We present a formal definition of superoscillating function. We discuss the limitations of previously proposed definitions and illustrate that they do not cover the full gamut of superoscillatory behaviours. We demonstrate the suitability…
A tensor ${\mathcal A}$ of order $m$ and dimension $n$ is called a ${\rm Q}$-tensor if the tensor complementarity problem has a solution for all ${\bf q} \in {\mathbb R}^{n}$. This means that for every vector ${\bf q}$, there exists a…
We compute the radiative quantum corrections to the critical exponents and amplitude ratios for O($N$) $\lambda\phi^{4}$ scalar high energy nonextensive $q$-field theories. We employ the field theoretic renormalization group approach…
The problem of calculating the period of second order nonlinear autonomous oscillators is formulated as an eigenvalue problem. We show that the period can be obtained from two integral variational principles dual to each other. Upper and…