Validity of the Adiabatic Approximation

We analyze the validity of the adiabatic approximation, and in particular the reliability of what has been called the "standard criterion" for validity of this approximation. Recently, this criterion has been found to be insufficient. We will argue that the criterion is sufficient only when it agrees with the intuitive notion of slowness of evolution of the Hamiltonian. However, it can be insufficient in cases where the Hamiltonian varies rapidly but only by a small amount. We also emphasize the distinction between the adiabatic {\em theorem} and the adiabatic {\em approximation}, two quite different although closely related ideas.Comment: 4 pages, 1 figur

A homomorphism between link and XXZ modules over the periodic Temperley-Lieb algebra

We study finite loop models on a lattice wrapped around a cylinder. A section of the cylinder has N sites. We use a family of link modules over the periodic Temperley-Lieb algebra EPTL_N(\beta, \alpha) introduced by Martin and Saleur, and Graham and Lehrer. These are labeled by the numbers of sites N and of defects d, and extend the standard modules of the original Temperley-Lieb algebra. Beside the defining parameters \beta=u^2+u^{-2} with u=e^{i\lambda/2} (weight of contractible loops) and \alpha (weight of non-contractible loops), this family also depends on a twist parameter v that keeps track of how the defects wind around the cylinder. The transfer matrix T_N(\lambda, \nu) depends on the anisotropy \nu and the spectral parameter \lambda that fixes the model. (The thermodynamic limit of T_N is believed to describe a conformal field theory of central charge c=1-6\lambda^2/(\pi(\lambda-\pi)).) The family of periodic XXZ Hamiltonians is extended to depend on this new parameter v and the relationship between this family and the loop models is established. The Gram determinant for the natural bilinear form on these link modules is shown to factorize in terms of an intertwiner i_N^d between these link representations and the eigenspaces of S^z of the XXZ models. This map is shown to be an isomorphism for generic values of u and v and the critical curves in the plane of these parameters for which i_N^d fails to be an isomorphism are given.Comment: Replacement of "The Gram matrix as a connection between periodic loop models and XXZ Hamiltonians", 31 page

From solar-like to anti-solar differential rotation in cool stars

Stellar differential rotation can be separated into two main regimes: solar-like when the equator rotates faster than the poles and anti-solar when the polar regions rotate faster than the equator. We investigate the transition between these two regimes with 3-D numerical simulations of rotating spherical shells. We conduct a systematic parameter study which also includes models from different research groups. We find that the direction of the differential rotation is governed by the contribution of the Coriolis force in the force balance, independently of the model setup (presence of a magnetic field, thickness of the convective layer, density stratification). Rapidly-rotating cases with a small Rossby number yield solar-like differential rotation, while weakly-rotating models sustain anti-solar differential rotation. Close to the transition, the two kinds of differential rotation are two possible bistable states. This study provides theoretical support for the existence of anti-solar differential rotation in cool stars with large Rossby numbers.Comment: 5 pages, 6 figures, accepted for publication in MNRA

What controls the magnetic geometry of M dwarfs?

Context: observations of rapidly rotating M dwarfs show a broad variety of large-scale magnetic fields encompassing dipole-dominated and multipolar geometries. In dynamo models, the relative importance of inertia in the force balance -- quantified by the local Rossby number -- is known to have a strong impact on the magnetic field geometry. Aims: we aim to assess the relevance of the local Rossby number in controlling the large-scale magnetic field geometry of M dwarfs. Methods: we explore the similarities between anelastic dynamo models in spherical shells and observations of active M-dwarfs, focusing on field geometries derived from spectropolarimetric studies. To do so, we construct observation-based quantities aimed to reflect the diagnostic parameters employed in numerical models. Results: the transition between dipole-dominated and multipolar large-scale fields in early to mid M dwarfs is tentatively attributed to a Rossby number threshold. We interpret late M dwarfs magnetism to result from a dynamo bistability occurring at low Rossby number. By analogy with numerical models, we expect different amplitudes of differential rotation on the two dynamo branches.Comment: 4 pages, 4 figures, accepted for publication in A&

A universal optical all-fiber omnipolarizer

Wherever the polarization properties of a light beam are of concern, polarizers and polarizing beamsplitters (PBS) are indispensable devices in linear-, nonlinear-and quantum-optical schemes. By the very nature of their operation principle, transformation of incoming unpolarized or partially polarized beams through these devices introduces large intensity variations in the fully polarized outcoming beam(s). Such intensity fluctuations are often detrimental, particularly when light is post-processed by nonlinear crystals or other polarization-sensitive optic elements. Here we demonstrate the unexpected capability of light to self-organize its own state-of-polarization, upon propagation in optical fibers, into universal and environmentally robust states, namely right and left circular polarizations. We experimentally validate a novel polarizing device-the Omnipolarizer, which is understood as a nonlinear dual-mode polarizing optical element capable of operating in two modes-as a digital PBS and as an ideal polarizer. Switching between the two modes of operation requires changing beam's intensity

Determination of the Antiferroquadrupolar Order Parameters in UPd3

By combining accurate heat capacity and X-ray resonant scattering results we have resolved the long standing question regarding the nature of the quadrupolar ordered phases in UPd_3. The order parameter of the highest temperature quadrupolar phase has been uniquely determined to be antiphase Q_{zx} in contrast to the previous conjecture of Q_{x^2-y^2} . The azimuthal dependence of the X-ray scattering intensity from the quadrupolar superlattice reflections indicates that the lower temperature phases are described by a superposition of order parameters. The heat capacity features associated with each of the phase transitions characterize their order, which imposes restrictions on the matrix elements of the quadrupolar operators.Comment: 4 pages, 5 figure

On the monitoring of surface displacement in connection with volcano reactivation in Tenerife, Canary Islands, using space techniques

Geodetic volcano monitoring in Tenerife has mainly focused on the Las Cañadas Caldera, where a geodetic micronetwork and a levelling profile are located. A sensitivity test of this geodetic network showed that it should be extended to cover the whole island for volcano monitoring purposes. Furthermore, InSAR allowed detecting two unexpected movements that were beyond the scope of the traditional geodetic network. These two facts prompted us to design and observe a GPS network covering the whole of Tenerife that was monitored in August 2000. The results obtained were accurate to one centimetre, and confirm one of the deformations, although they were not definitive enough to confirm the second one. Furthermore, new cases of possible subsidence have been detected in areas where InSAR could not be used to measure deformation due to low coherence. A first modelling attempt has been made using a very simple model and its results seem to indicate that the deformation observed and the groundwater level variation in the island may be related. Future observations will be necessary for further validation and to study the time evolution of the displacements, carry out interpretation work using different types of data (gravity, gases, etc) and develop models that represent the island more closely. The results obtained are important because they might affect the geodetic volcano monitoring on the island, which will only be really useful if it is capable of distinguishing between displacements that might be linked to volcanic activity and those produced by other causes. One important result in this work is that a new geodetic monitoring system based on two complementary techniques, InSAR and GPS, has been set up on Tenerife island. This the first time that the whole surface of any of the volcanic Canary Islands has been covered with a single network for this purpose. This research has displayed the need for further similar studies in the Canary Islands, at least on the islands which pose a greater risk of volcanic reactivation, such as Lanzarote and La Palma, where InSAR techniques have been used already

Layout of Graphs with Bounded Tree-Width

A \emph{queue layout} of a graph consists of a total order of the vertices, and a partition of the edges into \emph{queues}, such that no two edges in the same queue are nested. The minimum number of queues in a queue layout of a graph is its \emph{queue-number}. A \emph{three-dimensional (straight-line grid) drawing} of a graph represents the vertices by points in $\mathbb{Z}^3$ and the edges by non-crossing line-segments. This paper contributes three main results: (1) It is proved that the minimum volume of a certain type of three-dimensional drawing of a graph $G$ is closely related to the queue-number of $G$. In particular, if $G$ is an $n$-vertex member of a proper minor-closed family of graphs (such as a planar graph), then $G$ has a $O(1)\times O(1)\times O(n)$ drawing if and only if $G$ has O(1) queue-number. (2) It is proved that queue-number is bounded by tree-width, thus resolving an open problem due to Ganley and Heath (2001), and disproving a conjecture of Pemmaraju (1992). This result provides renewed hope for the positive resolution of a number of open problems in the theory of queue layouts. (3) It is proved that graphs of bounded tree-width have three-dimensional drawings with O(n) volume. This is the most general family of graphs known to admit three-dimensional drawings with O(n) volume. The proofs depend upon our results regarding \emph{track layouts} and \emph{tree-partitions} of graphs, which may be of independent interest.Comment: This is a revised version of a journal paper submitted in October 2002. This paper incorporates the following conference papers: (1) Dujmovic', Morin & Wood. Path-width and three-dimensional straight-line grid drawings of graphs (GD'02), LNCS 2528:42-53, Springer, 2002. (2) Wood. Queue layouts, tree-width, and three-dimensional graph drawing (FSTTCS'02), LNCS 2556:348--359, Springer, 2002. (3) Dujmovic' & Wood. Tree-partitions of $k$-trees with applications in graph layout (WG '03), LNCS 2880:205-217, 200