Abstract:
Charged particles in the geodesic trajectory of an external gravitational field do not emit electromagnetic radiation. This is expected from the application of the equivalence principle. We show here that charged particles propagating in an external gravitational field with non-zero components of the Ricci tensor can emit radiation by the \v{C}erenkov process. The external gravitational field acts like an effective refractive index for light. Since the Ricci tensor cannot be eliminated by a change of coordinates, there is no violation of the equivalence principle in this process.

Abstract:
We present a unified treatment of three cases of quasi-exactly solvable problems, namely, charged particle moving in Coulomb and magnetic fields, for both the Schr\"odinger and the Klein-Gordon case, and the relative motion of two charged particles in an external oscillator potential. We show that all these cases are reducible to the same basic equation, which is quasi-exactly solvable owing to the existence of a hidden $sl_2$ algebraic structure. A systematic and unified algebraic solution to the basic equation using the method of factorization is given. Analytic expressions of the energies and the allowed frequencies for the three cases are given in terms of the roots of one and the same set of Bethe ansatz equations.

Abstract:
Properties of the magnetic translation operators for a charged particle moving in a crystalline potential and a uniform magnetic field show that it is necessary to consider all inequivalent irreducible projective representations of the the crystal lattice translation group. These considerations lead to the concept of magnetic cells and indicate the periodicity of physical properties with respect to the charge. It is also proven that a direct product of such representations describe a system of two (many, in general) particles. Therefore, they can be applied in description of interacting electrons in a magnetic field, for example in the fractional quantum Hall effect.

Abstract:
Even a single excess electron or ion migrating on the surface of sensitive explosives can catalyze their gradual exothermic decomposition. Mechanisms underlying such a charge-induced gradual thermal decomposition of highly sensitive explosives can be different. If sensitive explosive is a polar liquid, intense charge-dipole attraction between excess surface charges and surrounding explosive molecules can result in repetitive attempts of solvation of these charges by polar explosive molecules. Every attempt of such uncompleted nonequilibrium solvation causes local exothermic decomposition of thermolabile polar molecules accompanied by further thermal jumping unsolvated excess charges to new surface sites. Thus, ionized mobile hot spots emerge on charged explosive surface. Stochastic migration of ionized hot spots on explosive surface causes gradual exothermic decomposition of the whole mass of the polar explosive. The similar gradual charge-catalyzed exothermic decomposition of both polar and nonpolar highly sensitive explosives can be also caused by intense charge-dipole attacks of surrounding water vapor molecules electrostatically attracted from ambient humid air and strongly accelerated towards charged sites on explosive surfaces. Emission of electrons, photons and heat from ionized hot spots randomly migrating on charged surface of highly sensitive explosive aerosol nanoparticles converts such particles into the form of short-circuited thermionic nanobatteries.

Abstract:
We study the screening of an external potential produced by a two-dimensional gas of charged excitons (trions). We determine the contribution to the dielectric function induced by these composite charged particles within a random phase approximation. In mixtures of free electrons and trions, the trion response is found dominant. In the long wave-length limit, trions behave as point charges with mass equal to the sum of the three particle components. For finite wave-vectors, we show how the dielectric response is sensitive to the composite nature of trions and the internal degrees of freedom. Predictions are presented for the screening of a Coulomb potential, the scattering by charged impurities and the properties of trionic plasmons.

Abstract:
Many experiments and devices in physics use static magnetic fields to guide charged particles from a source onto a detector, and we ask the innocent question: What is the distribution of particle intensity over the detector surface? One should think that the solution to this seemingly simple problem is well known. We show that, even for uniform guide fields, this is not the case and present analytical point spread functions (PSF) for magnetic transport that deviate strongly from previous results. The "magnetic" PSF shows unexpected singularities, which were recently also observed experimentally, and which make detector response very sensitive to minute changes of position, field amplitude, or particle energy. In the field of low-energy particle physics, these singularities may become a source of error in modern high precision experiments, or may be used for instrument tests, for instance in neutrino mass retardation spectrometers.

Abstract:
Thermally induced particle flow in a charged colloidal suspension is studied in a fluid-mechanical approach. The force density acting on the charged boundary layer is derived in detail. From Stokes' equation with no-slip boundary conditions at the particle surface, we obtain the particle drift velocity and the thermophoretic transport coefficients. The results are discussed in view of previous work and available experimental data.

Abstract:
We have made the first observation of a charged particle beam by means of its electro-optical effect on the polarization of laser light in a LiNbO3 crystal. The modulation of the laser light during the passage of a pulsed electron beam was observed using a fast photodiode and a digital oscilloscope. The fastest rise time measured, 120 ps, was obtained in the single shot mode and was limited by the bandwidth of the oscilloscope and the associated electronics. This technology holds promise for detectors of greatly improved spatial and temporal resolution for single relativistic charged particles as well as particle beams.

Abstract:
We derive the classical dynamics of massless charged particles in a rigorous way from first principles. Since due to ultraviolet divergences this dynamics does not follow from an action principle, we rely on a) Maxwell's equations, b) Lorentz- and reparameterization-invariance, c) local conservation of energy and momentum. Despite the presence of pronounced singularities of the electromagnetic field along Dirac-like strings, we give a constructive proof of the existence of a unique distribution-valued energy-momentum tensor. Its conservation requires the particles to obey standard Lorentz equations and they experience, hence, no radiation reaction. Correspondingly the dynamics of interacting classical massless charged particles can be consistently defined, although they do not emit bremsstrahlung end experience no self-interaction.

Abstract:
The kinetics of irreversible annihilation of charged particles performing overdamped motion induced by long-range interaction force, $F(r)\sim r^{-\lambda}$, is investigated. The system exhibits rich kinetic behaviors depending on the force exponent $\lambda$. In one dimension we find that the densities decay as $t^{-1/(2+\lambda)}$ and $t^{-1/(1+2\lambda)}$ when $\lambda>1$ and $1/2<\lambda<1$, respectively, with logarithmic correction at $\lambda=1$. For $\lambda \leq 1/2$, the asymptotic behavior is shown to be dependent on system size.