491 research outputs found
Special symplectic Lie groups and hypersymplectic Lie groups
A special symplectic Lie group is a triple such that
is a finite-dimensional real Lie group and is a left invariant
symplectic form on which is parallel with respect to a left invariant
affine structure . In this paper starting from a special symplectic Lie
group we show how to ``deform" the standard Lie group structure on the
(co)tangent bundle through the left invariant affine structure such
that the resulting Lie group admits families of left invariant hypersymplectic
structures and thus becomes a hypersymplectic Lie group. We consider the affine
cotangent extension problem and then introduce notions of post-affine structure
and post-left-symmetric algebra which is the underlying algebraic structure of
a special symplectic Lie algebra. Furthermore, we give a kind of double
extensions of special symplectic Lie groups in terms of post-left-symmetric
algebras.Comment: 32 page
Quantum dots based on spin properties of semiconductor heterostructures
The possibility of a novel type of semiconductor quantum dots obtained by
spatially modulating the spin-orbit coupling intensity in III-V
heterostructures is discussed. Using the effective mass model we predict
confined one-electron states having peculiar spin properties. Furthermore, from
mean field calculations (local-spin-density and Hartree-Fock) we find that even
two electrons could form a bound state in these dots.Comment: 9 pages, 3 figures. Accepted in PRB (Brief Report) (2004
Shot noise and spin-orbit coherent control of entangled and spin polarized electrons
We extend our previous work on shot noise for entangled and spin polarized
electrons in a beam-splitter geometry with spin-orbit (\textit{s-o})
interaction in one of the incoming leads (lead 1). Besides accounting for both
the Dresselhaus and the Rashba spin-orbit terms, we present general formulas
for the shot noise of singlet and triplets states derived within the scattering
approach. We determine the full scattering matrix of the system for the case of
leads with \textit{two} orbital channels coupled via weak \textit{s-o}
interactions inducing channel anticrossings. We show that this interband
coupling coherently transfers electrons between the channels and gives rise to
an additional modulation angle -- dependent on both the Rashba and Dresselhaus
interaction strengths -- which allows for further independent coherent control
of the electrons traversing the incoming leads. We derive explicit shot noise
formulas for a variety of correlated pairs (e.g., Bell states) and lead spin
polarizations. Interestingly, the singlet and \textit{each} of the triplets
defined along the quantization axis perpendicular to lead 1 (with the local
\textit{s-o} interaction) and in the plane of the beam splitter display
distinctive shot noise for injection energies near the channel anticrossings;
hence, one can tell apart all the triplets, in addition to the singlet, through
noise measurements. We also find that spin-orbit induced backscattering within
lead 1 reduces the visibility of the noise oscillations, due to the additional
partition noise in this lead. Finally, we consider injection of two-particle
wavepackets into leads with multiple discrete states and find that two-particle
entanglement can still be observed via noise bunching and antibunching.Comment: 30 two-column pages and 7 figure
Anisotropic splitting of intersubband spin plasmons in quantum wells with bulk and structural inversion asymmetry
In semiconductor heterostructures, bulk and structural inversion asymmetry
and spin-orbit coupling induce a k-dependent spin splitting of valence and
conduction subbands, which can be viewed as being caused by momentum-dependent
crystal magnetic fields. This paper studies the influence of these effective
magnetic fields on the intersubband spin dynamics in an asymmetric n-type
GaAs/AlGaAs quantum well. We calculate the dispersions of intersubband spin
plasmons using linear response theory. The so-called D'yakonov-Perel'
decoherence mechanism is inactive for collective intersubband excitations,
i.e., crystal magnetic fields do not lead to decoherence of spin plasmons.
Instead, we predict that the main signature of bulk and structural inversion
asymmetry in intersubband spin dynamics is a three-fold, anisotropic splitting
of the spin plasmon dispersion. The importance of many-body effects is pointed
out, and conditions for experimental observation with inelastic light
scattering are discussed.Comment: 8 pages, 6 figure
- âŠ