4 research outputs found
Photon plasma--wave interaction via Compton scattering
The Kompaneets theory of photon kinetic evolution due to the Compton effect
in the absence of absorption and emission is extended to the case of the Vlasov
plasma wave oscillations. Under the assumption that the electron distribution
function at equilibrium is perturbed by a solution of the linearised Vlasov
equation in the long-wavelength limit, a solution of the Kompaneets kinetic
equation for the photon distribution function is found and discussed
Time fractional Schrodinger equation
The Schrodinger equation is considered with the first order time derivative
changed to a Caputo fractional derivative, the time fractional Schrodinger
equation. The resulting Hamiltonian is found to be non-Hermitian and non-local
in time. The resulting wave functions are thus not invariant under time
reversal. The time fractional Schrodinger equation is solved for a free
particle and for a potential well. Probability and the resulting energy levels
are found to increase over time to a limiting value depending on the order of
the time derivative. New identities for the Mittag-Leffler function are also
found and presented in an appendix.Comment: 23 page