45 research outputs found
Spin effects in Kapitza-Dirac scattering at light with elliptical polarization
The Kapitza-Dirac effect, which refers to electron scattering at standing
light waves, is studied in the Bragg regime with counterpropagating
elliptically polarized electromagnetic waves with the same intensity,
wavelength, and degree of polarization for two different setups. In the first
setup, where the electric-field components of the counterpropagating waves have
the same sense of rotation, we find distinct spin effects. The spins of the
scattered electrons and of the nonscattered electrons, respectively, precess
with a frequency that is of the order of the Bragg-reflection Rabi frequency.
When the electric-field components of the counterpropagating waves have an
opposite sense of rotation, which is the second considered setup, the standing
wave has linear polarization, and no spin effects can be observed. Our results
are based on numerical solutions of the time-dependent Dirac equation and the
analytical solution of a relativistic Pauli equation, which accounts for the
leading relativistic effects
Pseudo Random Coins Show More Heads Than Tails
Tossing a coin is the most elementary Monte Carlo experiment. In a computer
the coin is replaced by a pseudo random number generator. It can be shown
analytically and by exact enumerations that popular random number generators
are not capable of imitating a fair coin: pseudo random coins show more heads
than tails. This bias explains the empirically observed failure of some random
number generators in random walk experiments. It can be traced down to the
special role of the value zero in the algebra of finite fields.Comment: 10 pages, 12 figure
Accelerating the Fourier split operator method via graphics processing units
Current generations of graphics processing units have turned into highly
parallel devices with general computing capabilities. Thus, graphics processing
units may be utilized, for example, to solve time dependent partial
differential equations by the Fourier split operator method. In this
contribution, we demonstrate that graphics processing units are capable to
calculate fast Fourier transforms much more efficiently than traditional
central processing units. Thus, graphics processing units render efficient
implementations of the Fourier split operator method possible. Performance
gains of more than an order of magnitude as compared to implementations for
traditional central processing units are reached in the solution of the time
dependent Schr\"odinger equation and the time dependent Dirac equation
Electron-spin dynamics in elliptically polarized light waves
We investigate the coupling of the spin angular momentum of light beams with
elliptical polarization to the spin degree of freedom of free electrons. It is
shown that this coupling, which is of similar origin as the well-known
spin-orbit coupling, can lead to spin precession. The spin-precession frequency
is proportional to the product of the laser-field's intensity and its spin
density. The electron-spin dynamics is analyzed by employing exact numerical
methods as well as time-dependent perturbation theory based on the fully
relativistic Dirac equation and on the nonrelativistic Pauli equation that is
amended by a relativistic correction that accounts for the light's spin
density