arXiv subjects

Tobias Schmidt

Publications and source records attributed to Tobias Schmidt.

54 records · Page 3Linked to original sources

arXiv2015

Effect of ensemble generalization on the highest-occupied Kohn-Sham eigenvalue

There are several approximations to the exchange-correlation functional in density-functional theory that accurately predict total energy-related properties of many-electron systems, such as binding energies, bond lengths, and crystal structures. Other approximations are designed to describe potential-related processes, such as charge transfer and photoemission. However, the development of a functional which can serve the two purposes simultaneously is a long-standing challenge. Trying to address it, we employ in the current work the ensemble generalization procedure proposed in Phys. Rev. Lett. 110, 126403 (2013). Focusing on the prediction of the ionization potential via the highest occupied Kohn-Sham eigenvalue, we examine a variety of exchange-correlation approximations: the local spin-density approximation, semi-local generalized gradient approximations, and global and local hybrid functionals. Results for a test set of 26 diatomic molecules and single atoms are presented. We find that the aforementioned ensemble generalization systematically improves the prediction of the ionization potential, for various systems and exchange-correlation functionals, without compromising the accuracy of total energy-related properties. We specifically examine hybrid functionals. These depend on a parameter controlling the ratio of semi-local to non-local functional components. The ionization potential obtained with ensemble-generalized functionals is found to depend only weakly on the parameter value, contrary to common experience with non-generalized hybrids, thus eliminating one aspect of the so-called `parameter dilemma' of hybrid functionals.

physics.chem-ph↗

arXiv2015

Locally analytic representations of ${\rm GL}(2,L)$ via semistable models of ${\mathbb P}^1$

In this paper we study certain sheaves of $p$-adically complete rings of differential operators on semistable models of the projective line over the ring of integers in a finite extension $L$ of ${\mathbb Q}_p$. The global sections of these sheaves can be identified with (central reductions of) analytic distribution algebras of wide open congruence subgroups. It is shown that the global sections functor furnishes an equivalence between the categories of coherent module sheaves and finitely presented modules over the distribution algebras. Using work of M. Emerton, we then describe admissible representations of ${\rm GL}(2,L)$ in terms of sheaves on the projective limit of these formal schemes.

math.RT↗

arXiv2015

The companion candidate near Fomalhaut - a background neutron star?

The directly detected planetary mass companion candidate close to the young, nearby star Fomalhaut is a subject of intense discussion. While the detection of common proper motion led to the interpretation as Jovian-mass companion, later non-detections in the infrared raised doubts. Recent astrometric measurements indicate a belt crossing or highly eccentric orbit for the object, if a companion, making the planetary interpretation potentially even more problematic. In this study we discuss the possibility of Fomalhaut\,b being a background object with a high proper motion. By analysing the available photometric and astrometric data of the object, we show that they are fully consistent with a neutron star: Neutron stars are faint, hot (blue), and fast moving. Neutron stars with an effective temperature of the whole surface area being 112,000 K to 126,500 K (with small to negligible extinction) at a distance of roughly 11 pc (best fit) would be consistent with all observables, namely with the photometric detections in the optical, with the upper limits in the infrared and X-rays, as well as with the astrometry (consistent with a distances of 11 pc or more and high proper motion as typical for neutron stars) as well as with non-detection of pulsation (not beamed). We consider the probability of finding an unrelated object or even a neutron star nearby and mostly co-aligned in proper motion with Fomalhaut A and come to the conclusion that this is definitely well possible.

astro-ph.SR↗

arXiv2014

Forms of an affinoid disc and ramification

Let $k$ be a complete nonarchimedean field and let $X$ be an affinoid closed disc over $k$. We classify the tamely ramified twisted forms of $X$. Generalizing work of P. Russell on inseparable forms of the affine line we construct explicit families of wildly ramified forms of $X$. We compute the class group and the Grothendieck group of forms of $X$ in certain cases.

math.RA↗

arXiv2014

Arithmetic differential operators on a semistable model of ${\mathbb P}^1$

In this paper we study sheaves of logarithmic arithmetic differential operators on a particular semistable model of the projective line. The main result here is that the first cohomology group of these sheaves is non-torsion. We also consider a refinement of the order filtration on the sheaf of level zero (before taking the p-adic completion). The associated graded sheaf, which we explicitly determine, explains to some extent the occurrence of the cohomology classes in degree one.

math.RT↗

arXiv2014

Dimensions of some locally analytic representations

Let $G$ be the group of points of a split reductive group over a finite extension of ${\mathbb Q}_p$. In this paper, we compute the dimensions of certain classes of locally analytic $G$-representations. This includes principal series representations and certain representations coming from homogeneous line bundles on $p$-adic symmetric spaces. As an application, we compute the dimensions in Colmez' unitary principal series of ${\rm GL}_2({\mathbb Q}_p)$.

math.RT↗

arXiv2014

A self-interaction-free local hybrid functional: Accurate binding energies vis-à-vis accurate ionization potentials from Kohn-Sham eigenvalues

We present and test a new approximation for the exchange-correlation (xc) energy of Kohn-Sham density functional theory. It combines exact exchange with a compatible non-local correlation functional. The functional is by construction free of one-electron self-interaction, respects constraints derived from uniform coordinate scaling, and has the correct asymptotic behavior of the xc energy density. It contains one parameter that is not determined ab initio. We investigate whether it is possible to construct a functional that yields accurate binding energies and affords other advantages, specifically Kohn-Sham eigenvalues that reliably reflect ionization potentials. Tests for a set of atoms and small molecules show that within our local-hybrid form accurate binding energies can be achieved by proper optimization of the free parameter in our functional, along with an improvement in dissociation energy curves and in Kohn-Sham eigenvalues. However, the correspondence of the latter to experimental ionization potentials is not yet satisfactory, and if we choose to optimize their prediction, a rather different value of the functional's parameter is obtained. We put this finding in a larger context by discussing similar observations for other functionals and possible directions for further functional development that our findings suggest.

physics.chem-ph↗

arXiv2013

Integral models of P^1 and analytic distribution algebras for GL_2

In the first part of the paper we show that the ring of global sections of arithmetic differential operators on the formal projective line over Zp is isomorphic to the analytic distribution algebra of the 'wide open' congruence subgroup of level zero of GL(2,Zp). In the second part we study rings of logarithmic differential operators on semistable integral models of the projective line over Zp and we relate these to analytic distribution algebra of 'wide open' congruence subgroups of higher level.

math.RT↗

arXiv2013

Picard groups in $p$-adic Fourier theory

Let $L$ be a proper finite extension of the field of $p$-adic numbers and let $o\subset L$ be its integers, viewed as an abelian locally $L$-analytic group. Let $\hat{o}$ be the rigid analytic group variety parametrizing the locally analytic characters of o. We study the Picard group and the Grothendieck group of this variety. This preprint is in final version, replaces the former preprint 'Vector bundles over analytic character varieties' and appears in Manuscripta Mathematica.

math.RT↗

arXiv2013

Verma modules over p-adic Arens-Michael envelopes of reductive Lie algebras

Let K be a locally compact nonarchimedean field, g a split reductive Lie algebra over K and U(g) its universal enveloping algebra. We study the category C_g of coadmissible modules over the nonarchimedean Arens-Michael envelope of U(g). Let p be a parabolic subalgebra of g. The main result identifies a certain explicitly given highest weight category inside C_g with the classical parabolic BGG category of g relative to p. This paper is in final form, replaces and expands the former preprint 'BGG reciprocity for p-adic Arens-Michael envelopes of semisimple Lie algebras' and appears in Journal of Algebra.

math.RT↗

arXiv2013

On locally analytic Beilinson-Bernstein localization and the canonical dimension

Let G be a connected split reductive group over a p-adic field. In the first part of the paper we prove, under certain assumptions on G and the prime p, a localization theorem of Beilinson-Bernstein type for admissible locally analytic representations of principal congruence subgroups in the rational points of G. In doing so we take up and extend some recent methods and results of Ardakov-Wadsley on completed universal enveloping algebras to a locally analytic setting. As an application we prove, in the second part of the paper, a locally analytic version of Smith's theorem on the canonical dimension. This paper is in final form, is an expanded version of the former preprint 'On the dimension of locally analytic representations of semisimple p-adic groups' and has appeared in Mathematische Zeitschrift.

math.RT↗

arXiv2012

Stable flatness of nonarchimedean hyperenveloping algebras

Let L be a p-adic local field and g a finite dimensional Lie algebra over L. We show that its hyperenveloping algebra F(g) is a stably flat completion of its universal enveloping algebra. As a consequence the relative cohomology for the locally convex algebra F(g) coincides with the underlying Lie algebra cohomology. Final version. Some minor items corrected. Appeared in Journal of Algebra (2010).

math.RT↗

arXiv2012

On unitary deformations of smooth modular representations

Let G be a locally analytic group. We use deformation theory and Emerton's 'augmented' Iwasawa modules to study the possible liftings of a given absolutely irreducible smooth modular representation of G to a unitary Banach space representation. Final version. Some minor items changed. Appears in Israel J. Math.

math.RT↗

arXiv2012

Auslander Regularity of p-adic Distribution Algebras

Given a compact p-adic Lie group we show that its distribution algebra is Frechet-Stein with Auslander regular Banach algebras. As an application, we show that nonzero coadmissible modules coming from smooth or, more general, U(g)-finite representations have maximal codimension.

math.RT↗

arXiv2012

Analytic vectors in continuous p-adic representations

Given a compact p-adic Lie group G over a finite unramified extension L/Q_p let G_0 be the product over all Galois conjugates of G. We construct an exact and faithful functor from admissible G-Banach space representations to admissible locally L-analytic G_0-representations that coincides with passage to analytic vectors in case L=Q_p. On the other hand, we study the functor "passage to analytic vectors" and its derived functors over general basefields. As an application we determine the higher analytic vectors in certain locally analytic induced representations.

math.RT↗

arXiv2012

Locally analytic representations and sheaves on the Bruhat-Tits building

Let L be a finite field extension of Q_p and let G be the group of L-rational points of a split connected reductive group over L. We view G as a locally L-analytic group with Lie algebra g. We define a functor from admissible locally analytic G-representations with prescribed infinitesimal character to a category of equivariant sheaves on the Bruhat-Tits building of G. For smooth representations, the corresponding sheaves are closely related to the sheaves constructed by S. Schneider and U. Stuhler. The functor is also compatible, in a certain sense, with the localization of g-modules on the flag variety by A. Beilinson and J. Bernstein.

math.RT↗

arXiv2008

Astrometric and photometric monitoring of GQ Lup and its sub-stellar companion

Neuhaeuser et al. (2005) presented direct imaging evidence for a sub-stellar companion to the young T Tauri star GQ Lup. Common proper motion was highly significant, but no orbital motion was detected. Faint luminosity, low gravity, and a late-M/early-L spectral type indicated that the companion is either a planet or a brown dwarf. We have monitored GQ Lup and its companion in order to detect orbital and parallactic motion and variability in its brightness. We also search for closer and fainter companions. We have taken six more images with the VLT Adaptive Optics instrument NACO from May 2005 to Feb 2007, always with the same calibration binary from Hipparcos for both astrometric and photometric calibration. By adding up all the images taken so far, we search for additional companions. The position of GQ Lup A and its companion compared to a nearby non-moving background object varies as expected for parallactic motion by about one pixel (2 πwith parallax π). We could not find evidence for variability of the GQ Lup companion in the K-band (standard deviation being \pm 0.08 mag), which may be due to large error bars. No additional companions are found with deep imaging. There is now exceedingly high significance for common proper motion of GQ Lup A and its companion. In addition, we see for the first time an indication for orbital motion (about 2 to 3 mas/yr decrease in separation, but no significant change in the position angle), consistent with a near edge-on or highly eccentric orbit. We measured the parallax for GQ Lup A to be π= 6.4 \pm 1.9 mas (i.e. 156 \pm 50 pc) and for the GQ Lup companion to be 7.2 \pm 2.1 mas (i.e. 139 \pm 45 pc), both consistent with being in the Lupus I cloud and bound to each other.

astro-ph↗

arXiv2006

Direct detection of exoplanet host star companion gamma Cep B and revised masses for both stars and the sub-stellar object

The star gamma Cep is known as a single-lined spectroscopic triple system at a distance of 13.8 pc, composed of a K1 III-IV primary star with V = 3.2 mag, a stellar-mass companion in a 66--67 year orbit (Torres 2006), and a substellar companion with M_p sin i = 1.7 M_Jup that is most likely a planet (Hatzes et al. 2003). We aim to obtain a first direct detection of the stellar companion, to determine its current orbital position (for comparison with the spectroscopic and astrometric data), its infrared magnitude and, hence, mass. We use the Adaptive Optics camera CIAO at the Japanese 8m telescope Subaru on Mauna Kea, Hawaii, with the semi-transparent coronograph to block most of the light from the bright primary gamma Cep A, and to detect at the same time the faint companion B. In addition, we also used the IR camera Omega-Cass at the Calar Alto 3.5m telescope, Spain, to image gamma Cep A and B by adding up many very short integrations (without AO). gamma Cep B is clearly detected on our CIAO and Omega-Cass images. We use a photometric standard star to determine the magnitude of B after PSF subtraction in the Subaru image, and the magnitude difference between A and B in the Calar Alto images, and find an average value of K = 7.3 \pm 0.2 mag. The separations and position angles between A and B are measured on 15 July 2006 and 11 and 12 Sept 2006, B is slightly south of west of A. By combining the radial velocity, astrometric, and imaging data, we have refined the binary orbit and determined the dynamical masses of the two stars in the gamma Cep system, namely 1.40 \pm 0.12 M_sun for the primary and 0.409 \pm 0.018 M_sun for the secondary (consistent with being a M4 dwarf). We also determine the minimum mass of the sub-stellar companion to be M_p sin i = 1.60 \pm 0.13 M_Jup.

astro-ph↗