A parabolic free boundary problem with Bernoulli type condition on the free boundary

Consider the parabolic free boundary problem $$\Delta u - \partial_t u = 0 \textrm{in} \{u>0\}, |\nabla u|=1 \textrm{on} \partial\{u>0\} .$$ For a realistic class of solutions, containing for example {\em all} limits of the singular perturbation problem $$\Delta u_\epsilon - \partial_t u_\epsilon = \beta_\epsilon(u_\epsilon) \textrm{as} \epsilon\to 0,$$ we prove that one-sided flatness of the free boundary implies regularity. In particular, we show that the topological free boundary $\partial\{u>0\}$ can be decomposed into an {\em open} regular set (relative to $\partial\{u>0\}$) which is locally a surface with H\"older-continuous space normal, and a closed singular set. Our result extends the main theorem in the paper by H.W. Alt-L.A. Caffarelli (1981) to more general solutions as well as the time-dependent case. Our proof uses methods developed in H.W. Alt-L.A. Caffarelli (1981), however we replace the core of that paper, which relies on non-positive mean curvature at singular points, by an argument based on scaling discrepancies, which promises to be applicable to more general free boundary or free discontinuity problems

Discontinuous shear modulus determines the glass transition temperature

A solid - amorphous or crystalline - is defined by a finite shear modulus while a fluid lacks such. We thus experimentally investigate the elastic properties of a colloidal glass former near the glass transition: spectroscopy of vibrational excitations yields the dispersion relations of longitudinal and transverse phonons in the glassy state. From the long wavelength limit of the dispersion relation we extract the bulk and the shear modulus. As expected, the latter disappear in a fluid and we measure a clearly resolved discontinuous behaviour of the elastic moduli at the glass transition. This not only determines the transition temperature T_G of the system but also directly addresses recent discussions about elasticity during vitrification. We show that low frequency excitations in our system are plane waves such that continuum elasticity theory can be used to describe the macroscopic behaviour.Comment: 8 pages, 6 figure

Retrospective Analysis of Wood Anatomical Traits Reveals a Recent Extension in Tree Cambial Activity in Two High-Elevation Conifers

The study of xylogenesis or wood formation is a powerful, yet labor intensive monitoring approach to investigate intra-annual tree growth responses to environmental factors. However, it seldom covers more than a few growing seasons, so is in contrast to the much longer lifespan of woody plants and the time scale of many environmental processes. Here we applied a novel retrospective approach to test the long-term (1926–2012) consistency in the timing of onset and ending of cambial activity, and in the maximum cambial cell division rate in two conifer species, European larch and Norway spruce at high-elevation in the Alps. We correlated daily temperature with time series of cell number and lumen area partitioned into intra-annual sectors. For both species, we found a good correspondence (1–10 days offset) between the periods when anatomical traits had significant correlations with temperature in recent decades (1969–2012) and available xylogenesis data (1996–2005), previously collected at the same site. Yet, results for the 1926–1968 period indicate a later onset and earlier ending of the cambial activity by 6–30 days. Conversely, the peak in the correlation between annual cell number and temperature, which should correspond to the peak in secondary growth rate, was quite stable over time, with just a minor advance of 4–5 days in the recent decades. Our analyses on time series of wood anatomical traits proved useful to infer on past long-term changes in xylogenetic phases. Combined with intensive continuous monitoring, our approach will improve the understanding of tree responses to climate variability in both the short- and long-term context

A simple minimax estimator for quantum states

Quantum tomography requires repeated measurements of many copies of the physical system, all prepared by a source in the unknown state. In the limit of very many copies measured, the often-used maximum-likelihood (ML) method for converting the gathered data into an estimate of the state works very well. For smaller data sets, however, it often suffers from problems of rank deficiency in the estimated state. For many systems of relevance for quantum information processing, the preparation of a very large number of copies of the same quantum state is still a technological challenge, which motivates us to look for estimation strategies that perform well even when there is not much data. In this article, we review the concept of minimax state estimation, and use minimax ideas to construct a simple estimator for quantum states. We demonstrate that, for the case of tomography of a single qubit, our estimator significantly outperforms the ML estimator for small number of copies of the state measured. Our estimator is always full-rank, and furthermore, has a natural dependence on the number of copies measured, which is missing in the ML estimator.Comment: 26 pages, 3 figures. v2 contains minor improvements to the text, and an additional appendix on symmetric measurement

Quantum control of electron--phonon scatterings in artificial atoms

The phonon-induced dephasing dynamics in optically excited semiconductor quantum dots is studied within the frameworks of the independent Boson model and optimal control. We show that appropriate tailoring of laser pulses allows a complete control of the optical excitation despite the phonon dephasing, a finding in marked contrast to other environment couplings.Comment: to appear in Phys. Rev. Let

Adiabatic Faraday effect in a two-level Hamiltonian formalism

The helicity of a photon traversing a magnetized plasma can flip when the B-field along the trajectory slowly reverses. Broderick and Blandford have recently shown that this intriguing effect can profoundly change the usual Faraday effect for radio waves. We study this phenomenon in a formalism analogous to neutrino flavor oscillations: the evolution is governed by a Schroedinger equation for a two-level system consisting of the two photon helicities. Our treatment allows for a transparent physical understanding of this system and its dynamics. In particular, it allows us to investigate the nature of transitions at intermediate adiabaticities.Comment: 8 pages, 2 eps figures, and a note added. Title changed. Matches published versio

Pulsar Bound on the Photon Electric Charge Reexamined

If photons had a small electric charge $Q_\gamma$ their path in the galactic magnetic field would be curved, leading to a time delay between photons of different frequency from a distant source. Cocconi's previous application of this argument led to a limit which is too restrictive by a factor of about 200; the corrected bound is Q_\gamma/e\lapprox10^{-29}.Comment: 3 pages, LaTe

High-resolution antenna near-field imaging and sub-THz measurements with a small atomic vapor-cell sensing element

Atomic sensing and measurement of millimeter-wave (mmW) and THz electric fields using quantum-optical EIT spectroscopy of Rydberg states in atomic vapors has garnered significant interest in recent years towards the development of atomic electric-field standards and sensor technologies. Here we describe recent work employing small atomic vapor cell sensing elements for near-field imaging of the radiation pattern of a K$_u$-band horn antenna at 13.49 GHz. We image fields at a spatial resolution of $\lambda/10$ and measure over a 72 to 240 V/m field range using off-resonance AC-Stark shifts of a Rydberg resonance. The same atomic sensing element is used to measure sub-THz electric fields at 255 GHz, an increase in mmW-frequency by more than one order of magnitude. The sub-THz field is measured over a continuous $\pm$100 MHz frequency band using a near-resonant mmW atomic transition