arXiv subjects

G. Pappas

Publications and source records attributed to G. Pappas.

At least 19 recordsLinked to original sources

arXiv2026

Precision-Induced Irreversibility in non-Hermitian systems

Non-Hermitian evolution is mathematically invertible, yet finite dynamic range imposes a sharp operational limit on reversibility. We identify Precision-Induced Irreversibility (PIR): amplification, mode mixing (as warranted by non-normality), and a finite resolution floor -- whether set by numerical precision, detector noise, or environmental fluctuations -- conspire to produce a quantitative predictability horizon $T_{\mathrm{of}}$, beyond which distinct states collapse onto identical representations. Within the effective non-Hermitian description, the mechanism requires neither environmental decoherence nor nonlinear dynamics; remove any ingredient and reversibility can be restored. Echo-fidelity tests confirm this transition across arbitrary-precision arithmetic and hardware, revealing where formal invertibility and physical reversibility diverge.

quant-ph↗

arXiv2022

Black hole mass and spin measurements through the Relativistic Precession Model: XTE J1859+226

The X-ray light curves of accreting black holes and neutron stars in binary systems show various types of quasi-periodic oscillations (QPOs), the origin of which is still debated. The Relativistic Precession Model identifies the QPO frequencies with fundamental time scales from General Relativity, and has been proposed as a possible explanation of certain types of such oscillations. Under specific conditions (i.e., the detection of a particular QPOs triplet) such a model can be used to obtain self-consistent measurements of the mass and spin of the compact object. So far this has been possible only in the black hole binary GRO J1655-40. In the RXTE/PCA data from the 1999-2000 outburst of the black hole transient XTE J1859+226 we found a QPO triplet, and used the the Relativistic Precession Model to obtain high-precision measurements of the black hole mass and spin - M = (7.85+/-0.46) Msun, a* = 0.149+/-0.005 - the former being consistent with the most recent dynamical mass determination from optical measurements. Similarly to what has been already observed in other black hole systems, the frequencies of the QPOs and broad-band noise components match the general relativistic frequencies of particle motion close to the compact object predicted by the model. Our findings confirm previous results and further support the validity of the Relativistic Precession Model, which is the only electromagnetic-measurement-based method that so far has consistently yielded spins close to those from the gravitational waves produced by merging binary black holes.

astro-ph.HE↗

arXiv2020

Volume and symplectic structure for l-adic local systems

We introduce a notion of volume for an l-adic local system over an algebraic curve and, under some conditions, give a symplectic form on the rigid analytic deformation space of the corresponding geometric local system. These constructions can be viewed as arithmetic analogues of the volume and the Chern-Simons invariants of a representation of the fundamental group of a 3-manifold which fibers over the circle and of the symplectic form on the character varieties of a Riemann surface. We show that the absolute Galois group acts on the deformation space by conformal symplectomorphisms which extend to an l-adic analytic flow. We also prove that the locus of the deformation space over which the local system suitably descends is the critical set of a collection of rigid analytic functions. The vanishing cycles of these functions give additional invariants.

math.AG↗

arXiv2020

On integral models of Shimura varieties

We show how to characterize integral models of Shimura varieties over places of the reflex field where the level subgroup is parahoric by formulating a definition of a "canonical" integral model. We then prove that in Hodge type cases and under a tameness hypothesis, the integral models constructed by the author and Kisin in previous work are canonical and, in particular, independent of choices. A main tool is a theory of displays with parahoric structure that we develop in this paper.

math.AG↗

arXiv2018

Good and semi-stable reductions of Shimura varieties

We study variants of the local models constructed by the second author and Zhu and consider corresponding integral models of Shimura varieties of abelian type. We determine all cases of good, resp. of semi-stable, reduction under tame ramification hypotheses.

math.AG↗

arXiv2017

(G, \mu)-displays and Rapoport-Zink spaces

Let (G, \mu) be a pair of a reductive group G over the p-adic integers and a minuscule cocharacter {\mu} of G defined over an unramified extension. We introduce and study "(G, \mu)-displays" which generalize Zink's Witt vector displays. We use these to define certain Rapoport-Zink formal schemes purely group theoretically, i.e. without p-divisible groups.

math.AG↗

arXiv2016

Non-local Lagrangians: a variational approach to non-local conservation laws for wave mechanics

We introduce a class of non-local Lagrangians which allow for the variational derivation of non-local conser- vation laws in a self-consistent manner. The formalism developed here generalizes previous approaches, used in the context of $\mathcal{PT}$ symmetric quantum mechanics and optics in the paraxial approximation in a twofold way: firstly it is valid for a larger set of linear symmetry transforms and secondly it enables the derivation of additional non-local conservation laws for general higher dimensional wave mechanical systems.

quant-ph↗

arXiv2015

Integral models of Shimura varieties with parahoric level structure

For an odd prime p, we construct integral models over p for Shimura varieties with parahoric level structure, attached to Shimura data (G,X) of abelian type, such that G splits over a tamely ramified extension of Q_p. The local structure of these integral models is related to certain "local models", which are defined group theoretically. Under some additional assumptions, we show that these integral models satisfy a conjecture of Kottwitz which gives an explicit description for the trace of Frobenius action on their sheaf of nearby cycles.

math.AG↗

arXiv2015

Higher Chern classes in Iwasawa theory

We begin a study of m-th Chern classes and m-th characteristic symbols for Iwasawa modules which are supported in codimension at least m. This extends the classical theory of characteristic ideals and their generators for Iwasawa modules which are torsion, i.e., supported in codimension at least 1. We apply this to an Iwasawa module constructed from an inverse limit of p-parts of ideal class groups of abelian extensions of an imaginary quadratic field. When this module is pseudo-null, which is conjecturally always the case, we determine its second Chern class and show that it has a characteristic symbol given by the Steinberg symbol of two Katz p-adic L-functions.

math.NT↗

arXiv2015

Rapoport-Zink spaces for spinor groups

We develop a theory of Hodge type Rapoport-Zink formal schemes, which uniformize certain formal completions of the canonical integral models of Shimura varieties of Hodge type at primes of good reduction. We then apply the general theory to the special case of Shimura varieties associated with groups of spinor similitudes, and, in the basic case, determine explicitly the reduced scheme underlying the Rapoport-Zink formal scheme.

math.AG↗

arXiv2015

Systematic pathway to ${\mathcal{PT}}$ symmetry breaking in scattering systems

Recently [Phys. Rev. Lett. {\bf 106}, 093902 (2011)] it has been shown that $\mathcal{PT}$-symmetric scattering systems with balanced gain and loss, undergo a transition from $\mathcal{PT}$-symmetric scattering eigenstates, which are norm preserving, to symmetry broken pairs of eigenstates exhibiting net amplification and loss. In the present work we derive the existence of an invariant non-local current which can be directly associated with the observed transition playing the role of an "order parameter". The use of this current for the description of the $\mathcal{PT}$-symmetry breaking allows the extension of the known phase diagram to higher dimensions incorporating scattering states which are not eigenstates of the scattering matrix.

physics.optics↗

arXiv2015

Higher adeles and non-abelian Riemann-Roch

We show a Riemann-Roch theorem for group ring bundles over an arithmetic surface; this is expressed using the higher adeles of Beilinson-Parshin and the tame symbol via a theory of adelic equivariant Chow groups and Chern classes. The theorem is obtained by combining a group ring coefficient version of the local Riemann-Roch formula as in Kapranov-Vasserot with results on K-groups of group rings and an explicit description of group ring bundles over P^1. Our set-up provides an extension of several aspects of the classical Fr"ohlich theory of the Galois module structure of rings of integers of number fields to arithmetic surfaces.

math.AG↗

arXiv2015

Adams operations and Galois structure

We present a new method for determining the Galois module structure of the cohomology of coherent sheaves on varieties over the integers with a tame action of a finite group. This uses a novel Adams-Riemann-Roch type theorem obtained by combining the Kunneth formula with localization in equivariant K-theory and classical results about cyclotomic fields. As an application, we show two conjectures of Chinburg-Pappas-Taylor, in the case of curves.

math.AG↗

arXiv2014

K_1 of a p-adic group ring II. The determinantal kernel SK_1

We describe the group SK_1(R[G]) for group rings R[G] where G is an arbitrary finite group and where the coefficient ring R is a p-adically complete Noetherian integral domain of characteristic zero which admits a lift of Frobenius and which also satisfies a number of further mild conditions. Our results extend previous work of R. Oliver who obtained such results for the valuation rings of finite extensions of the p-adic field.

math.KT↗

arXiv2012

Local models of Shimura varieties and a conjecture of Kottwitz

We give a group theoretic definition of "local models" as sought after in the theory of Shimura varieties. These are projective schemes over the integers of a $p$-adic local field that are expected to model the singularities of integral models of Shimura varieties with parahoric level structure. Our local models are certain mixed characteristic degenerations of Grassmannian varieties; they are obtained by extending constructions of Beilinson, Drinfeld, Gaitsgory and the second-named author to mixed characteristics and to the case of general (tamely ramified) reductive groups. We study the singularities of local models and hence also of the corresponding integral models of Shimura varieties. In particular, we study the monodromy (inertia) action and show a commutativity property for the sheaves of nearby cycles. As a result, we prove a conjecture of Kottwitz which asserts that the semi-simple trace of Frobenius on the nearby cycles gives a function which is central in the parahoric Hecke algebra.

math.AG↗

arXiv2011

Local models of Shimura varieties, I. Geometry and combinatorics

We survey the theory of local models of Shimura varieties. In particular, we discuss their definition and illustrate it by examples. We give an overview of the results on their geometry and combinatorics obtained in the last 15 years. We also exhibit their connections to other classes of algebraic varieties such as nilpotent orbit closures, affine Schubert varieties, quiver Grassmannians and wonderful completions of symmetric spaces.

math.AG↗

arXiv2009

K_1 of a p-adic group ring I. The determinantal image

We study the K-group K_1 of the group ring of a finite group over a coefficient ring which is p-adically complete and admits a lift of Frobenius. In this paper, we consider the image of K_1 under the determinant map; the central tool is the group logarithm which we can define using the Frobenius lift. Using this we prove a fixed point theorem for the determinantal image of K_1.

math.KT↗

arXiv2009

Finite morphisms from curves over Dedekind rings to $P^1$

A theorem of B. Green states that if A is a Dedekind ring whose fraction field is a local or global field, every normal projective curve over Spec(A) has a finite morphism to P^1_A. We give a different proof of a variant of this result using intersection theory and work of Moret-Bailly.

math.AG↗