Related papers: Nonlinear Connections and Description of Photon-li…
In this paper, I introduce two new concepts (Minkowski quasi-photon and invariance of physical definitions) to elucidate the theory developed in my previous work [Can. J. Phys. 93, 1510 (2015)], and to clarify the criticisms by Partanen and…
The purpose of the present work is to show that an adequate basis for understanding the essentially nonlinear phenomena must also be essentially nonlinear however still simple enough to play the role of a basis. It is shown that such types…
The main purpose is to characterise continuous maps that are $n$-branched coverings in terms of induced maps on the rings of functions. The special properties of Frobenius $n$-homomorphisms between two function spaces that correspond to…
We explore the notion of spatial extent and structure, already alluded to in earlier literature, within the formulation of quantum mechanics on the noncommutative plane. Introducing the notion of average position and its measurement, we…
The propagation of $N$ photons in one dimensional waveguides coupled to $M$ qubits is discussed, both in the strong and ultrastrong qubit-waveguide coupling. Special emphasis is placed on the characterisation of the nonlinear response and…
We describe models of nonthermal photon emission from a homogeneous distribution of relativistic electrons and protons. Contributions from the synchrotron, inverse Compton, nonthermal bremsstrahlung and neutral-pion decay processes are…
This paper introduces a notion of integrality that is suitable for non-commutative varieties. It is compatible with the usual notion of integrality for schemes. The function field and generic point of a non-commutative integral space are…
This paper studies graded manifolds with local coordinates concentrated in non-negative degrees. We provide a canonical description of these objects in terms of classical geometric data and, building on this geometric viewpoint, we prove…
I present a simple view of nonlinear optcal phenomena as being determined mostly by the length of interaction time between photons and matter. This may explain why in the last decades the progress in developing better nonlinear materials…
We develop a non-equilibrium field-theoretical approach, based on a systematic diagrammatic expansion, for strongly interacting photons in optically dense atomic media. We consider the case where the characteristic photon-propagation range…
Nonlinear integrable equations serve as a foundation for nonlinear dynamics, and fractional equations are well known in anomalous diffusion. We connect these two fields by presenting the discovery of a new class of integrable fractional…
We study the dynamics of a particle in a space that is non-differentiable. Non-smooth geometrical objects have an inherently probabilistic nature and, consequently, introduce stochasticity in the motion of a body that lives in their realm.…
The coupled system of Boltzman equations for the interacting system of electrons, positrons and photons in high external electric, E, and arbitrary magnetic, H, fields is solved. The consideration is made under the conditions of arbitrary…
This work aims to define the concept of manifold, which has a very important place in the topology, on digital images. So, a general perspective is provided for two and three-dimensional imaging studies on digital curves and digital…
We establish a version of the complex Frobenius theorem in the context of a complex subbundle S of the complexified tangent bundle of a manifold, having minimal regularity. If the subbundle S defines the structure of a Levi-flat…
We present a theory of discontinuous motion of particles in continuous space-time. We show that the simplest nonrelativistic evolution equation of such motion is just the Schroedinger equation in quantum mechanics. This strongly implies…
The nonlinear propagation of intense incoherent photons in a photon gas is considered. The photon-photon interactions are governed by a pair of equations comprising a wave-kinetic equation for the incoherent photons in the presence of the…
The notion of a Frobenius manifold appears in relation to various topics in algebraic and analytic geometry, such and quantum cohomology, deformation of meromorphic connections, unfolding of singularities and others. In the local setting…
The subject of moving curves (and surfaces) in three dimensional space (3-D) is a fascinating topic not only because it represents typical nonlinear dynamical systems in classical mechanics, but also finds important applications in a…
An antisymmetric tensor, the photon tensor, is defined for the description of the photon as a massless relativistic particle. The photon can be visualized as an essentially two dimensional rotating object. The quantum mechanical description…