A Free-Algebraic Solution for the Planar Approximation

An explicit solution for the generating functional of n-point functions in the planar approximation is given in terms of two sets of free-algebraic annihilation and creation operators.Comment: 15 pages, added referenc

Interactions of the magnetospheres of stars and close-in giant planets

Since the first discovery of an extrasolar planetary system more than a decade ago, hundreds more have been discovered. Surprisingly, many of these systems harbor Jupiter-class gas giants located close to the central star, at distances of 0.1 AU or less. Observations of chromospheric 'hot spots' that rotate in phase with the planetary orbit, and elevated stellar X-ray luminosities,suggest that these close-in planets significantly affect the structure of the outer atmosphere of the star through interactions between the stellar magnetic field and the planetary magnetosphere. Here we carry out the first detailed three-dimensional MagnetoHydroHynamics (MHD) simulation containing the two magnetic bodies and explore the consequences of such interactions on the steady-state coronal structure. The simulations reproduce the observable features of 1) increase in the total X-ray luminosity, 2) appearance of coronal hot spots, and 3) phase shift of these spots with respect to the direction of the planet. The proximate cause of these is an increase in the density of coronal plasma in the direction of the planet, which prevents the corona from expanding and leaking away this plasma via a stellar wind. The simulations produce significant low temperature heating. By including dynamical effects, such as the planetary orbital motion, the simulation should better reproduce the observed coronal heating

Chromosphere of K giant stars Geometrical extent and spatial structure detection

We aim to constrain the geometrical extent of the chromosphere of non-binary K giant stars and detect any spatial structures in the chromosphere. We performed observations with the CHARA interferometer and the VEGA beam combiner at optical wavelengths. We observed seven non-binary K giant stars. We measured the ratio of the radii of the photosphere to the chromosphere using the interferometric measurements in the Halpha and the Ca II infrared triplet line cores. For beta Ceti, spectro-interferometric observations are compared to an non-local thermal equilibrium (NLTE) semi-empirical model atmosphere including a chromosphere. The NLTE computations provide line intensities and contribution functions that indicate the relative locations where the line cores are formed and can constrain the size of the limb-darkened disk of the stars with chromospheres. We measured the angular diameter of seven K giant stars and deduced their fundamental parameters: effective temperatures, radii, luminosities, and masses. We determined the geometrical extent of the chromosphere for four giant stars. The chromosphere extents obtained range between 16% to 47% of the stellar radius. The NLTE computations confirm that the Ca II/849 nm line core is deeper in the chromosphere of ? Cet than either of the Ca II/854 nm and Ca II/866 nm line cores. We present a modified version of a semi-empirical model atmosphere derived by fitting the Ca II triplet line cores of this star. In four of our targets, we also detect the signature of a differential signal showing the presence of asymmetries in the chromospheres. Conclusions. It is the first time that geometrical extents and structure in the chromospheres of non-binary K giant stars are determined by interferometry. These observations provide strong constrains on stellar atmosphere models.Comment: 10 pages, 12 figure

The Dynamics of Stellar Coronae Harboring Hot-jupiters II. A Space Weather Event on A Hot-jupiter

We carry out a numerical simulation depicting the effects of a Coronal Mass Ejection (CME) event on a close-in giant planet in an extrasolar system. We drive the CME in a similar manner as in simulations of space weather events on Earth. The simulation includes the planetary orbital motion, which leads to the forming of a comet-like planetary magnetotail which is oriented almost perpendicular to the direction of propagation of the CME. The combination of this feature and the fact that the CME does not expand much by the time it reaches the planet leads to a unique CME-magnetosphere interaction, where the CME itself is highly affected by the presence of the planetary magnetosphere. We find that the planet is well-shielded from CME penetration, even for a relatively weak internal magnetic field. The planetary angular momentum loss associated with such an event is negligible compared to the total planetary angular momentum. We also find that the energy which is deposited in the magnetosphere is much higher than in the case of the Earth, and our simulation suggests there is a large-scale change in the orientation of the magnetosphere-ionosphere current system during the CME event.Comment: 16 pages, 10 figures, accepted to Ap

Radon--Nikodym representations of Cuntz--Krieger algebras and Lyapunov spectra for KMS states

We study relations between $(H,\beta)$--KMS states on Cuntz--Krieger algebras and the dual of the Perron--Frobenius operator $\mathcal{L}_{-\beta H}^{*}$. Generalising the well--studied purely hyperbolic situation, we obtain under mild conditions that for an expansive dynamical system there is a one--one correspondence between $(H,\beta)$--KMS states and eigenmeasures of $\mathcal{L}_{-\beta H}^{*}$ for the eigenvalue 1. We then consider representations of Cuntz--Krieger algebras which are induced by Markov fibred systems, and show that if the associated incidence matrix is irreducible then these are $\ast$--isomorphic to the given Cuntz--Krieger algebra. Finally, we apply these general results to study multifractal decompositions of limit sets of essentially free Kleinian groups $G$ which may have parabolic elements. We show that for the Cuntz--Krieger algebra arising from $G$ there exists an analytic family of KMS states induced by the Lyapunov spectrum of the analogue of the Bowen--Series map associated with $G$. Furthermore, we obtain a formula for the Hausdorff dimensions of the restrictions of these KMS states to the set of continuous functions on the limit set of $G$. If $G$ has no parabolic elements, then this formula can be interpreted as the singularity spectrum of the measure of maximal entropy associated with $G$.Comment: 30 pages, minor changes in the proofs of Theorem 3.9 and Fact

Coherent States of the q--Canonical Commutation Relations

For the $q$-deformed canonical commutation relations $a(f)a^\dagger(g) = (1-q)\,\langle f,g\rangle{\bf1}+q\,a^\dagger(g)a(f)$ for $f,g$ in some Hilbert space ${\cal H}$ we consider representations generated from a vector $\Omega$ satisfying $a(f)\Omega=\langle f,\phi\rangle\Omega$, where $\phi\in{\cal H}$. We show that such a representation exists if and only if $\Vert\phi\Vert\leq1$. Moreover, for $\Vert\phi\Vert<1$ these representations are unitarily equivalent to the Fock representation (obtained for $\phi=0$). On the other hand representations obtained for different unit vectors $\phi$ are disjoint. We show that the universal C*-algebra for the relations has a largest proper, closed, two-sided ideal. The quotient by this ideal is a natural $q$-analogue of the Cuntz algebra (obtained for $q=0$). We discuss the Conjecture that, for $d<\infty$, this analogue should, in fact, be equal to the Cuntz algebra itself. In the limiting cases $q=\pm1$ we determine all irreducible representations of the relations, and characterize those which can be obtained via coherent states.Comment: 19 pages, Plain Te

The Highly Eccentric Pre-Main Sequence Spectroscopic Binary RX J0529.3+1210

The young system RX J0529.3+1210 was initially identified as a single-lined spectroscopic binary. Using high-resolution infrared spectra, acquired with NIRSPEC on Keck II, we measured radial velocities for the secondary. The method of using the infrared regime to convert single-lined spectra into double-lined spectra, and derive the mass ratio for the binary system, has been successfully used for a number of young, low-mass binaries. For RX J0529.3+1210, a long- period(462 days) and highly eccentric(0.88) binary system, we determine the mass ratio to be 0.78+/-0.05 using the infrared double-lined velocity data alone, and 0.73+/-0.23 combining visible light and infrared data in a full orbital solution. The large uncertainty in the latter is the result of the sparse sampling in the infrared and the high eccentricity: the stars do not have a large velocity separation during most of their ~1.3 year orbit. A mass ratio close to unity, consistent with the high end of the one sigma uncertainty for this mass ratio value, is inconsistent with the lack of a visible light detection of the secondary component. We outline several scenarios for a color difference in the two stars, such as one heavily spotted component, higher order multiplicity, or a unique evolutionary stage, favoring detection of only the primary star in visible light, even in a mass ratio ~1 system. However, the evidence points to a lower ratio. Although RX J0529.3+1210 exhibits no excess at near-infrared wavelengths, a small 24 micron excess is detected, consistent with circumbinary dust. The properties of this binary and its membership in Lambda Ori versus a new nearby stellar moving group at ~90 pc are discussed. We speculate on the origin of this unusual system and on the impact of such high eccentricity on the potential for planet formation.Comment: 4 Figure

Models of Star-Planet Magnetic Interaction

Magnetic interactions between a planet and its environment are known to lead to phenomena such as aurorae and shocks in the solar system. The large number of close-in exoplanets that were discovered triggered a renewed interest in magnetic interactions in star-planet systems. Multiple other magnetic effects were then unveiled, such as planet inflation or heating, planet migration, planetary material escape, and even modification of the host star properties. We review here the recent efforts in modelling and understanding magnetic interactions between stars and planets in the context of compact systems. We first provide simple estimates of the effects of magnetic interactions and then detail analytical and numerical models for different representative scenarii. We finally lay out a series of future developments that are needed today to better understand and constrain these fascinating interactions.Comment: 23 pages, 10 figures, accepted as a chapter in the Handbook of Exoplanet

Kitaev's quantum double model from a local quantum physics point of view

A prominent example of a topologically ordered system is Kitaev's quantum double model $\mathcal{D}(G)$ for finite groups $G$ (which in particular includes $G = \mathbb{Z}_2$, the toric code). We will look at these models from the point of view of local quantum physics. In particular, we will review how in the abelian case, one can do a Doplicher-Haag-Roberts analysis to study the different superselection sectors of the model. In this way one finds that the charges are in one-to-one correspondence with the representations of $\mathcal{D}(G)$, and that they are in fact anyons. Interchanging two of such anyons gives a non-trivial phase, not just a possible sign change. The case of non-abelian groups $G$ is more complicated. We outline how one could use amplimorphisms, that is, morphisms $A \to M_n(A)$ to study the superselection structure in that case. Finally, we give a brief overview of applications of topologically ordered systems to the field of quantum computation.Comment: Chapter contributed to R. Brunetti, C. Dappiaggi, K. Fredenhagen, J. Yngvason (eds), Advances in Algebraic Quantum Field Theory (Springer 2015). Mainly revie

Generalized Fock Spaces, New Forms of Quantum Statistics and their Algebras

We formulate a theory of generalized Fock spaces which underlies the different forms of quantum statistics such as ``infinite'', Bose-Einstein and Fermi-Dirac statistics. Single-indexed systems as well as multi-indexed systems that cannot be mapped into single-indexed systems are studied. Our theory is based on a three-tiered structure consisting of Fock space, statistics and algebra. This general formalism not only unifies the various forms of statistics and algebras, but also allows us to construct many new forms of quantum statistics as well as many algebras of creation and destruction operators. Some of these are : new algebras for infinite statistics, q-statistics and its many avatars, a consistent algebra for fractional statistics, null statistics or statistics of frozen order, ``doubly-infinite'' statistics, many representations of orthostatistics, Hubbard statistics and its variations.Comment: This is a revised version of the earlier preprint: mp_arc 94-43. Published versio