A new geometric description for Igusa's modular form (azy)5(azy)_5

The modular form $(azy)_5$ notably appears in one of Igusa's classic structure theorems as a generator of the ring of full modular forms in genus 2, being exhibited by means of a complicated algebraic expression. In this work a different description for this modular form is provided by resorting to a peculiar geometrical approach.Comment: 10 page

On `maximal' poles of zeta functions, roots of b-functions and monodromy Jordan blocks

The main objects of study in this paper are the poles of several local zeta functions: the Igusa, topological and motivic zeta function associated to a polynomial or (germ of) holomorphic function in n variables. We are interested in poles of maximal possible order n. In all known cases (curves, non-degenerate polynomials) there is at most one pole of maximal order n which is then given by the log canonical threshold of the function at the corresponding singular point. For an isolated singular point we prove that if the log canonical threshold yields a pole of order n of the corresponding (local) zeta function, then it induces a root of the Bernstein-Sato polynomial of the given function of multiplicity n (proving one of the cases of the strongest form of a conjecture of Igusa-Denef-Loeser). For an arbitrary singular point we show under the same assumption that the monodromy eigenvalue induced by the pole has a Jordan block of size n on the (perverse) complex of nearby cycles.Comment: 8 pages, to be published in Journal of Topolog

Ultrafast control of inelastic tunneling in a double semiconductor quantum

In a semiconductor-based double quantum well (QW) coupled to a degree of freedom with an internal dynamics, we demonstrate that the electronic motion is controllable within femtoseconds by applying appropriately shaped electromagnetic pulses. In particular, we consider a pulse-driven AlxGa1-xAs based symmetric double QW coupled to uniformly distributed or localized vibrational modes and present analytical results for the lowest two levels. These predictions are assessed and generalized by full-fledged numerical simulations showing that localization and time-stabilization of the driven electron dynamics is indeed possible under the conditions identified here, even with a simultaneous excitations of vibrational modes.Comment: to be published in Appl.Phys.Let

Global analysis by hidden symmetry

Hidden symmetry of a G'-space X is defined by an extension of the G'-action on X to that of a group G containing G' as a subgroup. In this setting, we study the relationship between the three objects: (A) global analysis on X by using representations of G (hidden symmetry); (B) global analysis on X by using representations of G'; (C) branching laws of representations of G when restricted to the subgroup G'. We explain a trick which transfers results for finite-dimensional representations in the compact setting to those for infinite-dimensional representations in the noncompact setting when $X_C$ is $G_C$-spherical. Applications to branching problems of unitary representations, and to spectral analysis on pseudo-Riemannian locally symmetric spaces are also discussed.Comment: Special volume in honor of Roger Howe on the occasion of his 70th birthda

Torons and black hole entropy

We consider a supersymmetric system of D-5-branes compactified on a 5-torus with a self-dual background field strength on a 4-torus and carrying left-moving momentum along a circle. The corresponding supergravity solution describes a 5-dimensional black hole with a regular horizon. The entropy of this black hole may be explained in terms of the Landau degeneracy for open strings stretching between different branes. In the gauge theory approximation this D-5-brane system is described by a super Yang-Mills theory with a t'Hooft twist. By choosing a supersymmetric branch of the theory we obtain perfect agreement with the entropy formula. The result relies on the number of massless torons associated with the gauge field components that obey twisted boundary conditions.Comment: 31 pages, latex. Some equations corrected. Final version to be published in Nuclear Physics

Dirac Operator Zero-modes on a Torus

We study Dirac operator zero-modes on a torus for gauge background with uniform field strengths. Under the basic translations of the torus coordinates the wave functions are subject to twisted periodic conditions. In a suitable torus coordinates the zero-mode wave functions can be related to holomorphic functions of the complex torus coordinates. We construct the zero-mode wave functions that satisfy the twisted periodic conditions. The chirality and the degeneracy of the zero-modes are uniquely determined by the gauge background and are consistent with the index theorem.Comment: 28 pages, 2 figure

On the Whitehead spectrum of the circle

The seminal work of Waldhausen, Farrell and Jones, Igusa, and Weiss and Williams shows that the homotopy groups in low degrees of the space of homeomorphisms of a closed Riemannian manifold of negative sectional curvature can be expressed as a functor of the fundamental group of the manifold. To determine this functor, however, it remains to determine the homotopy groups of the topological Whitehead spectrum of the circle. The cyclotomic trace of B okstedt, Hsiang, and Madsen and a theorem of Dundas, in turn, lead to an expression for these homotopy groups in terms of the equivariant homotopy groups of the homotopy fiber of the map from the topological Hochschild T-spectrum of the sphere spectrum to that of the ring of integers induced by the Hurewicz map. We evaluate the latter homotopy groups, and hence, the homotopy groups of the topological Whitehead spectrum of the circle in low degrees. The result extends earlier work by Anderson and Hsiang and by Igusa and complements recent work by Grunewald, Klein, and Macko.Comment: 52 page

Temperature dependency of the emission properties from positioned In(Ga)As/GaAs quantum dots

The authors gratefully acknowledge funding by the state of Bavaria and the bilateral project of the Deutsche Forschungsgemeinschaft (DFG) and the Japan Science and Technology Agency (JST) (project ‘single quantum dot lasers’).In this letter we study the influence of temperature and excitation power on the emission linewidth from site-controlled InGaAs/GaAs quantum dots grown on nanoholes defined by electron beam lithography and wet chemical etching. We identify thermal electron activation as well as direct exciton loss as the dominant intensity quenching channels. Additionally, we carefully analyze the effects of optical and acoustic phonons as well as close-by defects on the emission linewidth by means of temperature and power dependent micro-photoluminescence on single quantum dots with large pitches.Publisher PDFPeer reviewe

Interfacing Building Response with Human Behavior Under Seismic Events

The goal of this paper is to model the interaction of humans with their built environment during and immediately following a natural disaster. The study uses finite element simulations to evaluate the response of buildings under input ground motions and agent-based dynamic modeling to model the subsequent evacuation of building occupants in the study area immediately following the seismic event. The structural model directly captures building damage and collapse, as well as floor accelerations and displacements to determine nonstructural damage, injuries and fatalities. The goal of this research is to make connections between building damage and occupant injuries, with geographic automata as the information handler for the agent-based platform. This research demonstrates that human behavior and evacuation patterns can be evaluated in the context of realistic structural and nonstructural damage assessments, and that prior knowledge of evacuation patterns is critical for adequate preparedness of cities to severe earthquakes

Interfacing Building Response with Human Behavior Under Seismic Events

The goal of this paper is to model the interaction of humans with their built environment during and immediately following a natural disaster. The study uses finite element simulations to evaluate the response of buildings under input ground motions and agent-based dynamic modeling to model the subsequent evacuation of building occupants in the study area immediately following the seismic event. The structural model directly captures building damage and collapse, as well as floor accelerations and displacements to determine nonstructural damage, injuries and fatalities. The goal of this research is to make connections between building damage and occupant injuries, with geographic automata as the information handler for the agent-based platform. This research demonstrates that human behavior and evacuation patterns can be evaluated in the context of realistic structural and nonstructural damage assessments, and that prior knowledge of evacuation patterns is critical for adequate preparedness of cities to severe earthquakes