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The use of operator methods of algebraic nature is shown to be a very powerful tool to deal with different forms of relativistic wave equations. The methods provide either exact or approximate solutions for various forms of differential…
With the advent of quantum technologies, control issues are becoming increasingly important. In this article, we address the control in phase space under a global constraint provided by a minimal energy-like cost function and a local (in…
A set of exactly computable orthonormal basis functions that are useful in computations involving constituent quarks is presented. These basis functions are distinguished by the property that they fall off algebraically in momentum space…
The paper solves the problem of tracking control of a quadrotor with unmeasurable pitch and roll angles based on the geometric approach with the use of the enhanced extended observer and the internal model. The proposed approach makes it…
In this paper, we show how to use the analysis of the Lie algebra associated with a quantum mechanical system to study its dynamics and facilitate the design of controls. We give algorithms to decompose the dynamics and describe their…
Friction incorporates the close connection between classical mechanics in irreversible thermodynamics. The translation to a quantum mechanical foundation is not trivial and requires a generalization of the Lagrange function. A change to…
Some new physics models of quantum gravity or dark matter predict drifts or oscillations of the fundamental constants. A relatively simple model relates molecular vibrations to the proton-to-electron mass ratio $\mu$. Many vibrational…
We analytically tackle opto-vibronic interactions in molecular systems driven by either classical or quantum light fields. In particular, we examine a simple model of molecules with two relevant electronic levels, characterized by potential…
{\bf Purpose}: Manipulation of the radio-sensitivity of the nucleotide-base driven by the spin blockade mechanism of diffusive free radicals against ionizing radiation. {\bf Materials and methods}: We theoretically propose a mechanism which…
By considering mirror oscillation in a "tripod-scheme" laser-atom system, we advocate explorative studies of driven Dirac-like equations. Both analytical and numerical studies show that mirror oscillation can be used to drive an effective…
The vibration of various structures such as blades of turbines, helicopters, and all kinds of rotating robot arms can damage the structures and disrupt their performance and balance. Thus, investigation of the reduction and control of…
We describe a multi-scale resolution approach to analyzing problems in Quantum Mechanics using Daubechies wavelet basis. The expansion of the wavefunction of the quantum system in this basis allows a natural interpretation of each basis…
A survey of algebraic approaches to various problems in nuclear physics is given. Examples are chosen from pairing of many-nucleon systems, nuclear structure, fusion reactions below the Coulomb barrier, and supernova neutrino physics to…
Following de Broglie and Vigier, a fully relativistic causal interpretation of quantum mechanics is given within the context of a geometric theory of gravitation and electromagnetism. While the geometric model shares the essential…
We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also…
The Boltzmann-Langevin dynamics of harmonic modes in nuclear matter is analyzed within linear-response theory, both with an elementary treatment and by using the frequency-dependent response function. It is shown how the source terms…
A generalization of the Gram-Schmidt procedure is achieved by providing equations for updating and downdating oblique projectors. The work is motivated by the problem of adaptive signal representation outside the orthogonal basis setting.…
The mechanics of an oriented point (point with "spin") based on 3D and 4D Frenet equations is considered. In such mechanics there is an opportunity to describe formally any physical trajectory of a particle with own rotation. We use…
Inspiralling and coalescing binary black holes are promising sources of gravitational radiation. The orbital motion and gravitational-wave emission of such system can be modelled using a variety of approximation schemes and numerical…
Two-dimensional systems with time-dependent controls admit a quadratic Hamiltonian modelling near potential minima. Independent, dynamical normal modes facilitate inverse Hamiltonian engineering to control the system dynamics, but some…