Generation of hard twisted photons by charged particles in cholesteric liquid crystals.

We study the radiation from charged particles crossing a cholesteric plate in the shortwave approximation when the wavelength of photons is much smaller than the pitch of the cholesteric helix, whereas the escaping angle of the photon and the anisotropy of the permittivity tensor can be arbitrary. The radiation of photons is treated in the framework of quantum electrodynamics with classical currents. The radiation of the plane-wave photons and the photons with definite projection of the angular momentum (the twisted photons) produced by charged particles crossing the cholesteric plate and moving rectilinearly and uniformly is considered. The explicit expressions for the average number of radiated photons and their spectra with respect to the energy and the projection of the angular momentum are obtained in this case. It turns out that in the paraxial approximation the projection of the orbital angular momentum, l, of radiated twisted photons is related to the harmonic number n∈Z as l=2n+1, i.e., the given system is a pure source of twisted photons as expected. It is shown that in the paraxial shortwave regime the main part of radiated photons is linearly polarized with l=±1 at the harmonics n={-1,0}. The applicability conditions of the approach developed are discussed. As the examples, we consider the production of 6.3 eV twisted photons from uranium nuclei and the production of x-ray twisted photons from 120 MeV electrons.

Asymptotics of physical solutions to the Lorentz-Dirac equation for planar motion in constant electromagnetic fields.

We present a study of planar physical solutions to the Lorentz-Dirac equation in a constant electromagnetic field. In this case, we reduced the Lorentz-Dirac equation to one second-order differential equation. We obtained the asymptotics of physical solutions to this equation at large proper times. It turns out that, in a crossed constant uniform electromagnetic field with vanishing invariants, a charged particle enters a universal regime at large times. We found that the ratios of momentum components that tend to constants are determined only by the external field. This effect is essentially due to a radiation reaction. There is no such effect for the Lorentz equation in this field.

Stochastic deformation of a thermodynamic symplectic structure.

A stochastic deformation of a thermodynamic symplectic structure is studied. The stochastic deformation is analogous to the deformation of an algebra of observables such as deformation quantization, but for an imaginary deformation parameter (the Planck constant). Gauge symmetries of thermodynamics and corresponding stochastic mechanics, which describes fluctuations of a thermodynamic system, are revealed and gauge fields are introduced. A physical interpretation to the gauge transformations and gauge fields is given. An application of the formalism to a description of systems with distributed parameters in a local thermodynamic equilibrium is considered.

Fluctuations as stochastic deformation.

A notion of stochastic deformation is introduced and the corresponding algebraic deformation procedure is developed. This procedure is analogous to the deformation of an algebra of observables like deformation quantization, but for an imaginary deformation parameter (the Planck constant). This method is demonstrated on diverse relativistic and nonrelativistic models with finite and infinite degrees of freedom. It is shown that under stochastic deformation the model of a nonrelativistic particle interacting with the electromagnetic field on a curved background passes into the stochastic model described by the Fokker-Planck equation with the diffusion tensor being the inverse metric tensor. The first stochastic correction to the Newton equations for this system is found. The Klein-Kramers equation is also derived as the stochastic deformation of a certain classical model. Relativistic generalizations of the Fokker-Planck and Klein-Kramers equations are obtained by applying the procedure of stochastic deformation to appropriate relativistic classical models. The analog of the Fokker-Planck equation associated with the stochastic Lorentz-Dirac equation is derived too. The stochastic deformation of the models of a free scalar field and an electromagnetic field is investigated. It turns out that in the latter case the obtained stochastic model describes a fluctuating electromagnetic field in a transparent medium.