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The 2-dimensional charge transport with parallel (in plane) magnetic field is considered from the physical and mathematical point of view. To this end, we start with the magnetic field parallel to the plane of charge transport, in sharp…
A summary of the known results on integration theory on the space of connections modulo gauge transformations is presented and its significance to quantum theories of gauge fields and gravity is discussed. The emphasis is on the underlying…
This review discusses the physics of magnetic reconnection, a process in which the magnetic field topology changes and magnetic energy is converted to kinetic energy, in pair plasmas in the relativistic regime. We focus on recent progress…
To overcome the difficulties with the energy indefiniteness in field theories with higher derivatives, it is supposed to use the mechanical analogy, the Timoshenko theory of the transverse flexural vibrations of beams or rods well known in…
Large scale magnetic fields pervade the cosmic environment where the astrophysical black holes are often embedded and influenced by the mutual interaction. In this contribution we outline the appropriate mathematical framework to describe…
We use a variational approach to study existence and regularity of solutions for a Neumann $p$-Laplacian problem with a reaction term on metric spaces equipped with a doubling measure and supporting a Poincar\'e inequality. Trace theorems…
The relation between representations and positive definite functions is a key concept in harmonic analysis on topological groups. Recently this relation has been studied on topological groupoids. This is the first in a series of papers in…
A theory of spin-polarized transport in inhomogeneous magnetic semiconductors is developed and applied to magnetic/nonmagnetic p-n junctions. Several phenomena with possible spintronic applications are predicted, including spinvoltaic…
It is demonstrated how the right hand sides of the Lorentz Transformation equations may be written, in a Lorentz invariant manner, as 4--vector scalar products. The formalism is shown to provide a short derivation, in which the 4--vector…
The kinetic mixing of two U(1) gauge theories can result in a massless photon that has perturbative couplings to both electric and magnetic charges. This framework can be used to perturbatively calculate in a quantum field theory with both…
In this article, I propose a concept of the $p$-on which is modelled on the multi-photon absorptions in quantum optics. It provides a commutative ring structure in quantum mechanics. Using it, I will give an operator representation of the…
Sampling theory in spaces other than the space of band-limited functions has recently received considerable attention. This is in part because the band-limitedness assumption is not very realistic in many applications. In addition,…
I define a morphism on $\mathbb{C}_p$ called a lift of $p$-th power if its natural restriction to the residue field of $\mathbb{C}_p$ is a $p$-th power of some morphism. This definition generalizes from the lift of Frobenius. In this paper…
The problem of the reflectance of a photon by a metallic mirror whose position is treated quantum mechanically is considered. The interaction between the metallic surface and the light is treated classically. It is shown that the…
This licentiate thesis is concerned with an inverse boundary value problem for the magnetic Schr\"odinger equation in a half space, for compactly supported potentials $A\in W^{1,\infty}(\bar{\mathbb{R}^3_{-}},\R^3)$ and $q \in…
Eigenstates of 2D charged electron-hole complexes in magnetic fields are considered. The operator formalism that allows one to partially separate the center-of-mass motion from internal degrees of freedom is presented. The scheme using…
It is pointed out that the conventional Lie transform perturbation theory for the guiding center motion of charged particles in a magnetic field needs to be modified for ordering inconsistency. There are two reasons. First, the ordering…
It is assumed that the Lienard-Wiechert fields of an arbitrary moving charge is measured or predefined as a function of time. The position of the charge is calculated as a function of the retarded time.
A new generalized St\"ormer problem is proposed. The charged particles motion around a rotating axisymmetric magnetic planet is studied using various conditions mainly in planetary magnetospheres. It is shown that the existence of specific…
The subject of space charge in ionization detectors is reviewed, showing how the observations and the formalism used to describe the effects have evolved, starting with applications to calorimeters and reaching recent, large-size time…