Quantum Black Holes, Elliptic Genera and Spectral Partition Functions

We study M-theory and D-brane quantum partition functions for microscopic black hole ensembles within the context of the AdS/CFT correspondence in terms of highest weight representations of infinite-dimensional Lie algebras, elliptic genera, and Hilbert schemes, and describe their relations to elliptic modular forms. The common feature in our examples lie in the modular properties of the characters of certain representations of the pertinent affine Lie algebras, and in the role of spectral functions of hyperbolic three-geometry associated with q-series in the calculation of elliptic genera. We present new calculations of supergravity elliptic genera on local Calabi-Yau threefolds in terms of BPS invariants and spectral functions, and also of equivariant D-brane elliptic genera on generic toric singularities. We use these examples to conjecture a link between the black hole partition functions and elliptic cohomology.Comment: 42 page

Characterisation of the Etching Quality in Micro-Electro-Mechanical Systems by Thermal Transient Methodology

Our paper presents a non-destructive thermal transient measurement method that is able to reveal differences even in the micron size range of MEMS structures. Devices of the same design can have differences in their sacrificial layers as consequence of the differences in their manufacturing processes e.g. different etching times. We have made simulations examining how the etching quality reflects in the thermal behaviour of devices. These simulations predicted change in the thermal behaviour of MEMS structures having differences in their sacrificial layers. The theory was tested with measurements of similar MEMS devices prepared with different etching times. In the measurements we used the T3Ster thermal transient tester equipment. The results show that deviations in the devices, as consequence of the different etching times, result in different temperature elevations and manifest also as shift in time in the relevant temperature transient curves.Comment: Submitted on behalf of TIMA Editions (http://irevues.inist.fr/tima-editions

Adaptive finite element analysis based on p-convergence

The results of numerical experiments are presented in which a posteriori estimators of error in strain energy were examined on the basis of a typical problem in linear elastic fracture mechanics. Two estimators were found to give close upper and lower bounds for the strain energy error. The potential significance of this is that the same estimators may provide a suitable basis for adaptive redistribution of the degrees of freedom in finite element models

Localized spectral asymptotics for boundary value problems and correlation effects in the free Fermi gas in general domains

We rigorously derive explicit formulae for the pair correlation function of the ground state of the free Fermi gas in the thermodynamic limit for general geometries of the macroscopic regions occupied by the particles and arbitrary dimension. As a consequence we also establish the asymptotic validity of the local density approximation for the corresponding exchange energy. At constant density these formulae are universal and do not depend on the geometry of the underlying macroscopic domain. In order to identify the correlation effects in the thermodynamic limit, we prove a local Weyl law for the spectral asymptotics of the Laplacian for certain quantum observables which are themselves dependent on a small parameter under very general boundary conditions

Quantum complex scalar fields and noncommutativity

In this work we analyze complex scalar fields using a new framework where the object of noncommutativity $\theta^{\mu\nu}$ represents independent degrees of freedom. In a first quantized formalism, $\theta^{\mu\nu}$ and its canonical momentum $\pi_{\mu\nu}$ are seen as operators living in some Hilbert space. This structure is compatible with the minimal canonical extension of the Doplicher-Fredenhagen-Roberts (DFR) algebra and is invariant under an extended Poincar\'e group of symmetry. In a second quantized formalism perspective, we present an explicit form for the extended Poincar\'e generators and the same algebra is generated via generalized Heisenberg relations. We also introduce a source term and construct the general solution for the complex scalar fields using the Green's function technique.Comment: 13 pages. Latex. Final version to appear in Physical Review

3D-2D crossover in the naturally layered superconductor (LaSe)1.14(NbSe2)

The temperature and angular dependencies of the resistive upper critical magnetic field $B_{c2}$ reveal a dimensional crossover of the superconducting state in the highly anisotropic misfit-layer single crystal of (LaSe)$_{1.14}$(NbSe$_2$) with the critical temperature $T_c$ of 1.23 K. The temperature dependence of the upper critical field $B_{c2\parallel ab}(T)$ for a field orientation along the conducting $(ab)$-planes displays a characteristic upturn at 1.1 K and below this temperature the angular dependence of $B_{c2}$ has a cusp around the parallel field orientation. Both these typical features are observed for the first time in a naturally crystalline layered system.Comment: 7 pages incl. 3 figure