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Singlet-triplet avoided crossings and effective factor versus spatial orientation of spin-orbit-coupled quantum dots
We study avoided crossings opened by spin-orbit interaction in the energy
spectra of one- and two-electron anisotropic quantum dots in perpendicular
magnetic field. We find that for simultaneously present Rashba and Dresselhaus
interactions the width of avoided crossings and the effective factor depend
on the dot orientation within (001) crystal plane. The extreme values of these
quantities are obtained for [110] and [10] orientations of the dot.
The width of singlet-triplet avoided crossing changes between these two
orientations by as much as two orders of magnitude. The discussed modulation
results from orientation-dependent strength of the Zeeman interaction which
tends to polarize the spins in the direction of the external magnetic field and
thus remove the spin-orbit coupling effects
Time dependent configuration interaction simulations of spin swap in spin orbit coupled double quantum dots
We perform time-dependent simulations of spin exchange for an electron pair
in laterally coupled quantum dots. The calculation is based on configuration
interaction scheme accounting for spin-orbit (SO) coupling and
electron-electron interaction in a numerically exact way. Noninteracting
electrons exchange orientations of their spins in a manner that can be
understood by interdot tunneling associated with spin precession in an
effective SO magnetic field that results in anisotropy of the spin swap. The
Coulomb interaction blocks the electron transfer between the dots but the spin
transfer and spin precession due to SO coupling is still observed. The
electron-electron interaction additionally induces an appearance of spin
components in the direction of the effective SO magnetic field which are
opposite in both dots. Simulations indicate that the isotropy of the spin swap
is restored for equal Dresselhaus and Rashba constants and properly oriented
dots
Emergence of order in selection-mutation dynamics
We characterize the time evolution of a d-dimensional probability
distribution by the value of its final entropy. If it is near the
maximally-possible value we call the evolution mixing, if it is near zero we
say it is purifying. The evolution is determined by the simplest non-linear
equation and contains a d times d matrix as input. Since we are not interested
in a particular evolution but in the general features of evolutions of this
type, we take the matrix elements as uniformly-distributed random numbers
between zero and some specified upper bound. Computer simulations show how the
final entropies are distributed over this field of random numbers. The result
is that the distribution crowds at the maximum entropy, if the upper bound is
unity. If we restrict the dynamical matrices to certain regions in matrix
space, for instance to diagonal or triangular matrices, then the entropy
distribution is maximal near zero, and the dynamics typically becomes
purifying.Comment: 8 pages, 8 figure
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