Weight Multiplicity Free Representations, g-Endomorphism Algebras, and Dynkin Polynomials

Throughout this paper, G is a connected semisimple algebraicgroup defined over an algebraically closed field k of characteristiczero, and g is its Lie algebra.     

Long Abelian ideals

We study Abelian ideals of a Borel subalgebra consisting of long roots. It is shown that methods of Cellini and Papi can be extended to this situation. A uniform expression for the number of long Abelian ideals is given. We also show that there is a one-to-one correspondence between the long Abelian ideals and B-stable commutative subalgebras in the little adjoint representation of the Langlands dual Lie algebra.     

Reflection groups on Riemannian manifolds

We investigate discrete groups G of isometries of a complete connected Riemannian manifold M which are generated by reflections, in particular those generated by disecting reflections. We show that these are Coxeter groups, and that the orbit space M/G is isometric to a Weyl chamber C which is a Riemannian manifold with corners and certain angle conditions along intersections of faces. We can also reconstruct the manifold and its action from the Riemannian chamber and its equipment of isotropy group data along the faces. We also discuss these results from the point of view of Riemannian orbifolds. Mathematics Subject Classification Primary 51F15, 53C20, 20F55, 22E40     

Observation of size-dependent thermalization in CdSe nanocrystals using time-resolved photoluminescence spectroscopy

We report heat dissipation times in semiconductor nanocrystals of CdSe. Specifically, a previously unresolved, subnanosecond decay component in the low-temperature photoluminescence decay dynamics exhibits longer decay lifetimes (tens to hundreds of picoseconds) for larger nanocrystals as well as a size-independent, ~25-meV spectral shift. We attribute the fast relaxation to transient phonon-mediated relaxation arising from nonequilibrium acoustic phonons. Following acoustic phonon dissipation, the dark exciton state recombines more slowly via LO-phonon assistance resulting in the observed spectral shift. The measured relaxation time scales agree with classical calculations of thermal diffusion, indicating that interfacial thermal conductivity does not limit thermal transport in these semiconductor nanocrystal dispersions.     

Counting statistics and detector properties of quantum point contacts

Quantum detector properties of the quantum point contact (QPC) are analyzed for an arbitrary electron transparency and coupling strength to the measured system and are shown to be determined by the electron counting statistics. Conditions of the quantum-limited operation of the QPC detector, which prevent information loss through the scattering time and scattering phases, are found for arbitrary coupling. We show that the phase information can be restored and used for the quantum-limited detection by inclusion of the QPC detector in the electronic Mach-Zehnder interferometer.     

Optical tailoring of electron spin coherence in quantum dots

We address the precession of an ensemble of electron spins, each confined in a (In, Ga)As/GaAs self-assembled quantum dot. The quantum dot inhomogeneity is directly reflected in the precession of the optically oriented electron spins about an external magnetic field, which is subject to fast dephasing on a nanoseconds time scale. Proper periodic laser excitation allows synchronization of the electron spin precessions with the excitation cycle. The experimental conditions can be tailored such that eventually all (about a million) electron spins that are excited by the laser precess with a single frequency. In this regime the ensemble can be exploited during the single electron spin coherence times being in the microseconds range.     

Density functional and spectroscopic studies of nitrogen inversion in substituted dizocilpines

While developing a synthesis towards tagged dizocilpine (MK‐801) analogues, we observed highly restricted inversion of a nitrogen centre in a number hydroxylamines obtained as key intermediates. These compounds are shown to possess some of the structural elements which are expected to significantly hinder the nitrogen inversion, potentially leading to hydroxylamines with a chiral nitrogen centre. Free energy barriers (ΔG^≠) of the nitrogen inversion were estimated to be ca. 22 kcal mol^?1 at temperatures near 420 K using variable temperature NMR measurements in DMSO‐d₆. Further density functional studies of a number model systems were undertaken in order to better rationalize the measured inversion barriers and follow the role of various structural factors in raising the barrier height of the nitrogen inversion process. Copyright © 2008 John Wiley & Sons, Ltd.     

Area Spaces: First Steps

We show that a Riemannian manifold of dimension at least 3 can be recovered from the space of boundaries of rectifiable integral 2-currents (the “lcycles”) equipped with the filling area distance, and discuss possible approaches to “spaces with area structures”.     

Nonlocal anomaly of the axial-vector current for bound states

We argue that the amplitude does not vanish in the limit of zero quark masses. This represents a new kind of violation of the classical equation of motion for the axial current and should be interpreted as the axial anomaly for bound states. The anomaly emerges in spite of the fact that the one loop integrals are ultraviolet finite as guaranteed by the finite size of bound-state wave functions. As a result, the amplitude behaves like approximately 1/p(2) in the limit of a large momentum p of the current. The observed effect requires the modification of the classical equation of motion of the axial-vector current by nonlocal operators.