High-field optically detected nuclear magnetic resonance in GaAs

A method for high-field optically detected nuclear magnetic resonance (ODNMR) is developed sensitive to 10**8 nuclei. Nuclear spin transitions are induced using a radio frequency coil and detected through Faraday rotation spectroscopy. Unlike conventional ODNMR, which is limited to low fields and relies on the measurement of time-averaged luminescence polarization, this technique monitors nuclear polarization through time-resolved measurements of electron spin dynamics. Measurements in a (110) GaAs quantum well reveal Ga-69, Ga-71, and As-75 resonances and their quadrupolar splittings while resolving changes in nuclear polarization of 0.02%.Comment: 4 pages, 3 figure

Functional integral over velocities for a spinning particle with and without anomalous magnetic moment in a constant electromagnetic field

The technique of functional integration over velocities is applied to the calculation of the propagator of a spinning particle with and without anomalous magnetic moment. A representation for the spin factor is obtained in this context for the particle in a constant electromagnetic field. As a by-product, we also obtain a Schwinger representation for the first case.Comment: latex, 19 page

The Infrared Jet In 3C66B

We present images of infrared emission from the radio jet in 3C66B. Data at three wavelengths (4.5, 6.75 and 14.5 microns) were obtained using the Infrared Space Observatory. The 6.75 micron image clearly shows an extension aligned with the radio structure. The jet was also detected in the 14.5 micron image, but not at 4.5 micron. The radio-infrared-optical spectrum of the jet can be interpreted as synchrotron emission from a population of electrons with a high-energy break of 4e11 eV. We place upper limits on the IR flux from the radio counter-jet. A symmetrical, relativistically beamed twin-jet structure is consistent with our results if the jets consist of multiple components.Comment: 7 pages, 4 figure

Analysis of electric-field-induced spin splitting in wide modulation-doped quantum wells

We analyze the proper inclusion of electric-field-induced spin splittings in the framework of the envelope function approximation. We argue that the Rashba effect should be included in the form of a macroscopic potential as diagonal terms in a multiband approach rather than the commonly used Rashba term dependent on k and electric field. It is pointed out that the expectation value of the electric field in a subband is sometimes not unique because the expectation values can even have opposite signs for the spin-split subband components. Symmetric quantum wells with Dresselhaus terms and the influence of the interfaces on the spin splitting are also discussed. We apply a well established multiband approach to wide modulation-doped InGaSb quantum wells with strong built-in electric fields in the interface regions. We demonstrate an efficient mechanism for switching on and off the Rashba splitting with an electric field being an order of magnitude smaller than the local built-in field that determines the Rashba splitting. The implications of our findings for spintronic devices, in particular the Datta-Das spin transistor and proposed modifications of it, are discussed.Comment: Modified version, now published. 10 pages, 3 figures, 2 table

Minimality and irreducibility of symplectic four-manifolds

We prove that all minimal symplectic four-manifolds are essentially irreducible. We also clarify the relationship between holomorphic and symplectic minimality of K\"ahler surfaces. This leads to a new proof of the deformation-invariance of holomorphic minimality for complex surfaces with even first Betti number which are not Hirzebruch surfaces.Comment: final version; cosmetic changes only; to appear in International Mathematics Research Notice

Quasimodularity and large genus limits of Siegel-Veech constants

Quasimodular forms were first studied in the context of counting torus coverings. Here we show that a weighted version of these coverings with Siegel-Veech weights also provides quasimodular forms. We apply this to prove conjectures of Eskin and Zorich on the large genus limits of Masur-Veech volumes and of Siegel-Veech constants. In Part I we connect the geometric definition of Siegel-Veech constants both with a combinatorial counting problem and with intersection numbers on Hurwitz spaces. We introduce modified Siegel-Veech weights whose generating functions will later be shown to be quasimodular. Parts II and III are devoted to the study of the quasimodularity of the generating functions arising from weighted counting of torus coverings. The starting point is the theorem of Bloch and Okounkov saying that q-brackets of shifted symmetric functions are quasimodular forms. In Part II we give an expression for their growth polynomials in terms of Gaussian integrals and use this to obtain a closed formula for the generating series of cumulants that is the basis for studying large genus asymptotics. In Part III we show that the even hook-length moments of partitions are shifted symmetric polynomials and prove a formula for the q-bracket of the product of such a hook-length moment with an arbitrary shifted symmetric polynomial. This formula proves quasimodularity also for the (-2)-nd hook-length moments by extrapolation, and implies the quasimodularity of the Siegel-Veech weighted counting functions. Finally, in Part IV these results are used to give explicit generating functions for the volumes and Siegel-Veech constants in the case of the principal stratum of abelian differentials. To apply these exact formulas to the Eskin-Zorich conjectures we provide a general framework for computing the asymptotics of rapidly divergent power series.Comment: 107 pages, final version, to appear in J. of the AM