6,315 research outputs found
Signatures of hermitian forms and the Knebusch Trace Formula
Signatures of quadratic forms have been generalized to hermitian forms over
algebras with involution. In the literature this is done via Morita theory,
which causes sign ambiguities in certain cases. In this paper, a hermitian
version of the Knebusch Trace Formula is established and used as a main tool to
resolve these ambiguities.
The last page is an erratum for the published version. We inadvertently (I)
gave an incorrect definition of adjoint involutions; (II) omitted dealing with
the case . As , the
omission does not affect our reasoning or our results. For the sake of
completeness we point out where some small changes should be made in the
published version.Comment: This is the final version before publication. The last page is an
updated erratum for the published versio
Division, adjoints, and dualities of bilinear maps
The distributive property can be studied through bilinear maps and various
morphisms between these maps. The adjoint-morphisms between bilinear maps
establish a complete abelian category with projectives and admits a duality.
Thus the adjoint category is not a module category but nevertheless it is
suitably familiar. The universal properties have geometric perspectives. For
example, products are orthogonal sums. The bilinear division maps are the
simple bimaps with respect to nondegenerate adjoint-morphisms. That formalizes
the understanding that the atoms of linear geometries are algebraic objects
with no zero-divisors. Adjoint-isomorphism coincides with principal isotopism;
hence, nonassociative division rings can be studied within this framework.
This also corrects an error in an earlier pre-print; see Remark 2.11
Spin coherence of holes in GaAs/AlGaAs quantum wells
The carrier spin coherence in a p-doped GaAs/(Al,Ga)As quantum well with a
diluted hole gas has been studied by picosecond pump-probe Kerr rotation with
an in-plane magnetic field. For resonant optical excitation of the positively
charged exciton the spin precession shows two types of oscillations. Fast
oscillating electron spin beats decay with the radiative lifetime of the
charged exciton of 50 ps. Long lived spin coherence of the holes with dephasing
times up to 650 ps. The spin dephasing time as well as the in-plane hole g
factor show strong temperature dependence, underlining the importance of hole
localization at cryogenic temperatures.Comment: 5 pages, 4 figures in PostScript forma
Spin dynamics and magnetic-field-induced polarization of excitons in ultrathin GaAs/AlAs quantum wells with indirect band gap and type-II band alignment
The exciton spin dynamics are investigated both experimentally and
theoretically in two-monolayer-thick GaAs/AlAs quantum wells with an indirect
band gap and a type-II band alignment. The magnetic-field-induced circular
polarization of photoluminescence, , is studied as function of the
magnetic field strength and direction as well as sample temperature. The
observed nonmonotonic behaviour of these functions is provided by the interplay
of bright and dark exciton states contributing to the emission. To interpret
the experiment, we have developed a kinetic master equation model which
accounts for the dynamics of the spin states in this exciton quartet, radiative
and nonradiative recombination processes, and redistribution of excitons
between these states as result of spin relaxation. The model offers
quantitative agreement with experiment and allows us to evaluate, for the
studied structure, the heavy-hole factor, , and the spin
relaxation times of electron, s, and hole, s, bound in the exciton.Comment: 17 pages, 16 figure
Longitudinal and transversal spin dynamics of donor-bound electrons in fluorine-doped ZnSe: spin inertia versus Hanle effect
The spin dynamics of the strongly localized, donor-bound electrons in
fluorine-doped ZnSe epilayers is studied by pump-probe Kerr rotation
techniques. A method exploiting the spin inertia is developed and used to
measure the longitudinal spin relaxation time, , in a wide range of
magnetic fields, temperatures, and pump densities. The time of the
donor-bound electron spin of about 1.6 s remains nearly constant for
external magnetic fields varied from zero up to 2.5 T (Faraday geometry) and in
a temperature range K. The inhomogeneous spin dephasing time,
ns, is measured using the resonant spin amplification and Hanle
effects under pulsed and steady-state pumping, respectively. These findings
impose severe restrictions on possible spin relaxation mechanisms.Comment: 10 pages, 7 figure
Level Eulerian Posets
The notion of level posets is introduced. This class of infinite posets has
the property that between every two adjacent ranks the same bipartite graph
occurs. When the adjacency matrix is indecomposable, we determine the length of
the longest interval one needs to check to verify Eulerianness. Furthermore, we
show that every level Eulerian poset associated to an indecomposable matrix has
even order. A condition for verifying shellability is introduced and is
automated using the algebra of walks. Applying the Skolem--Mahler--Lech
theorem, the -series of a level poset is shown to be a rational
generating function in the non-commutative variables and .
In the case the poset is also Eulerian, the analogous result holds for the
-series. Using coalgebraic techniques a method is developed to
recognize the -series matrix of a level Eulerian poset
Optical control of electron spin coherence in CdTe/(Cd,Mg)Te quantum wells
Optical control of the spin coherence of quantum well electrons by short
laser pulses with circular or linear polarization is studied experimentally and
theoretically. For that purpose the coherent electron spin dynamics in a
n-doped CdTe/(Cd,Mg)Te quantum well structure was measured by time-resolved
pump-probe Kerr rotation, using resonant excitation of the negatively charged
exciton (trion) state. The amplitude and phase shifts of the electron spin beat
signal in an external magnetic field, that are induced by laser control pulses,
depend on the pump-control delay and polarization of the control relative to
the pump pulse. Additive and non-additive contributions to pump-induced signal
due to the control are isolated experimentally. These contributions can be well
described in the framework of a two-level model for the optical excitation of
the resident electron to the trion.Comment: 15 pages, 18 figure
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