Long range order for lattice dipoles

We consider a system of classical Heisenberg spins on a cubic lattice in dimensions three or more, interacting via the dipole-dipole interaction. We prove that at low enough temperature the system displays orientational long range order, as expected by spin wave theory. The proof is based on reflection positivity methods. In particular, we demonstrate a previously unproven conjecture on the dispersion relation of the spin waves, first proposed by Froehlich and Spencer, which allows one to apply infrared bounds for estimating the long distance behavior of the spin-spin correlation functions.Comment: 9 page

KMS, etc

A general form of the ``Wick rotation'', starting from imaginary-time Green functions of quantum-mechanical systems in thermal equilibrium at positive temperature, is established. Extending work of H. Araki, the role of the KMS condition and of an associated anti-unitary symmetry operation, the ``modular conjugation'', in constructing analytic continuations of Green functions from real- to imaginary times, and back, is clarified. The relationship between the KMS condition for the vacuum with respect to Lorentz boosts, on one hand, and the spin-statistics connection and the PCT theorem, on the other hand, in local, relativistic quantum field theory is recalled. General results on the reconstruction of local quantum theories in various non-trivial gravitational backgrounds from ``Euclidian amplitudes'' are presented. In particular, a general form of the KMS condition is proposed and applied, e.g., to the Unruh- and the Hawking effects. This paper is dedicated to Huzihiro Araki on the occasion of his seventieth birthday, with admiration, affection and best wishes.Comment: 56 pages, submitted to J. Math. Phy

Spectral Geometry of Heterotic Compactifications

The structure of heterotic string target space compactifications is studied using the formalism of the noncommutative geometry associated with lattice vertex operator algebras. The spectral triples of the noncommutative spacetimes are constructed and used to show that the intrinsic gauge field degrees of freedom disappear in the low-energy sectors of these spacetimes. The quantum geometry is thereby determined in much the same way as for ordinary superstring target spaces. In this setting, non-abelian gauge theories on the classical spacetimes arise from the K-theory of the effective target spaces.Comment: 14 pages LaTe

Ellipsoidal Coulomb Crystals in a Linear Radiofrequency Trap

A static quadrupole potential breaks the cylindrical symmetry of the effective potential of a linear rf trap. For a one-component fluid plasma at low temperature, the resulting equilibrium charge distribution is predicted to be an ellipsoid. We have produced laser-cooled Be$^+$ ellipsoidal ion crystals and found good agreement between their shapes and the cold fluid prediction. In two-species mixtures, containing Be$^+$ and sympathetically cooled ions of lower mass, a sufficiently strong static quadrupole potential produces a spatial separation of the species.Comment: 4 pages, 3 figure

Infraparticle Scattering States in Non-Relativistic QED: II. Mass Shell Properties

We study the infrared problem in the usual model of QED with non-relativistic matter. We prove spectral and regularity properties characterizing the mass shell of an electron and one-electron infraparticle states of this model. Our results are crucial for the construction of infraparticle scattering states, which are treated in a separate paper.Comment: AMS Latex, 45 pages, 2 figure

The Anderson Model as a Matrix Model

In this paper we describe a strategy to study the Anderson model of an electron in a random potential at weak coupling by a renormalization group analysis. There is an interesting technical analogy between this problem and the theory of random matrices. In d=2 the random matrices which appear are approximately of the free type well known to physicists and mathematicians, and their asymptotic eigenvalue distribution is therefore simply Wigner's law. However in d=3 the natural random matrices that appear have non-trivial constraints of a geometrical origin. It would be interesting to develop a general theory of these constrained random matrices, which presumably play an interesting role for many non-integrable problems related to diffusion. We present a first step in this direction, namely a rigorous bound on the tail of the eigenvalue distribution of such objects based on large deviation and graphical estimates. This bound allows to prove regularity and decay properties of the averaged Green's functions and the density of states for a three dimensional model with a thin conducting band and an energy close to the border of the band, for sufficiently small coupling constant.Comment: 23 pages, LateX, ps file available at http://cpth.polytechnique.fr/cpth/rivass/articles.htm

Expression and alternative splicing of the neural cell adhesion molecule NCAM in human granulosa cells during luteinization

Freshly aspirated human granulosa cells from pre-ovulatory follicles and granulosa cells luteinized in culture possess the neural cell adhesion molecule (NCAM) of approximate molecular mass of 140,000 and NCAM mRNA as confirmed by S1-nuclease protection assays and RT-PCR. Moreover, in the process of luteinization the NCAM isoform pattern is modified. Isoforms containing an insert of 10 amino acids (termed VASE) in the extracellular domain of NCAM were supplemented by alternatively spliced isoforms without this insert. NCAM immunoreactivity, at light and electron microscope levels, was associated with the cell membrane of most granulosa cells which formed clusters. During time in culture an increasing subpopulation of granulosa cells, devoid of NCAM immunoreactivity, spread out and formed monolayers. This differential expression and the alternative splicing of NCAM during luteinization of granulosa cells raise the possibility that NCAM could be involved in folliculogenesis and the formation of the corpus luteum in the human

Response-theory for nonresonant hole burning: Stochastic dynamics

Using non-linear response theory the time signals relevant for nonresonant spectral hole burning are calculated. The step-reponse function following the application of a high amplitude ac field (pump) and an intermediate waiting period is shown to be the sum of the equilibrium integrated response and a modification due to the preparation via ac irradiation. Both components are calculated for a class of stochastic dipole reorientation models. The results indicate that the method can be used for a clearcut distinction of homogeneously and heterogeneously broadened susceptibilities as they occur in the relaxation of supercooled liquids or other disordered materials. This is because only in the heterogeneous case is a frequency selective modification of the response possible.Comment: revised version, 7 pages, 2 figure