Flooding of Regular Phase Space Islands by Chaotic States

We investigate systems with a mixed phase space, where regular and chaotic dynamics coexist. Classically, regions with regular motion, the regular islands, are dynamically not connected to regions with chaotic motion, the chaotic sea. Typically, this is also reflected in the quantum properties, where eigenstates either concentrate on the regular or the chaotic regions. However, it was shown that quantum mechanically, due to the tunneling process, a coupling is induced and flooding of regular islands may occur. This happens when the Heisenberg time, the time needed to resolve the discrete spectrum, is larger than the tunneling time from the regular region to the chaotic sea. In this case the regular eigenstates disappear. We study this effect by the time evolution of wave packets initially started in the chaotic sea and find increasing probability in the regular island. Using random matrix models a quantitative prediction is derived. We find excellent agreement with numerical data obtained for quantum maps and billiards systems. For open systems we investigate the phenomenon of flooding and disappearance of regular states, where the escape time occurs as an additional time scale. We discuss the reappearance of regular states in the case of strongly opened systems. This is demonstrated numerically for quantum maps and experimentally for a mushroom shaped microwave resonator. The reappearance of regular states is explained qualitatively by a matrix model.Untersucht werden Systeme mit gemischtem Phasenraum, in denen sowohl reguläre als auch chaotische Dynamik auftritt. In der klassischen Mechanik sind Gebiete regulärer Bewegung, die sogenannten regulären Inseln, dynamisch nicht mit den Gebieten chaotischer Bewegung, der chaotischen See, verbunden. Dieses Verhalten spiegelt sich typischerweise auch in den quantenmechanischen Eigenschaften wider, so dass Eigenfunktionen entweder auf chaotischen oder regulären Gebieten konzentriert sind. Es wurde jedoch gezeigt, dass aufgrund des Tunneleffektes eine Kopplung auftritt und reguläre Inseln geflutet werden können. Dies geschieht wenn die Heisenbergzeit, das heißt die Zeit die das System benötigt, um das diskrete Spektrum aufzulösen, größer als die Tunnelzeit vom Regulären ins Chaotische ist, wobei reguläre Eigenzustände verschwinden. Dieser Effekt wird über eine Zeitentwicklung von Wellenpaketen, die in der chaotischen See gestartet werden, untersucht. Es kommt zu einer ansteigenden Wahrscheinlichkeit in der regulären Insel. Mithilfe von Zufallsmatrixmodellen wird eine quantitative Vorhersage abgeleitet, welche die numerischen Daten von Quantenabbildungen und Billardsystemen hervorragend beschreibt. Der Effekt des Flutens und das Verschwinden regulärer Zustände wird ebenfalls mit offenen Systemen untersucht. Hier tritt die Fluchtzeit als zusätzliche Zeitskala auf. Das Wiederkehren regulärer Zustände im Falle stark geöffneter Systeme wird qualitativ mithilfe eines Matrixmodells erklärt und numerisch für Quantenabbildungen sowie experimentell für einen pilzförmigen Mikrowellenresonator belegt

Field-Tunable 0-π-Transitions in SnTe Topological Crystalline Insulator SQUIDs

The manifestation of spin-orbit interactions, long known to dramatically affect the band structure of heavy-element compounds, governs the physics in the surging class of topological matter. A particular example is found in the new family of topological crystalline insulators. In this systems transport occurs at the surfaces and spin-momentum locking yields crystal-symmetry protected spin-polarized transport. We investigated the current-phase relation of SnTe thin films connected to superconducting electrodes to form SQUID devices. Our results demonstrate that an assisting in-plane magnetic field component can induce 0-π-transitions. We attribute these findings to giant g-factors and large spinorbit coupling of SnTe topological crystalline insulator, which provides a new platform for investigation of the interplay between spin-orbit physics and topological transport

Coagulation equations with gelation

Smoluchowski's equation for rapid coagulation is used to describe the kinetics of gelation, in which the coagulation kernel K ij models the bonding mechanism. For different classes of kernels we derive criteria for the occurrence of gelation, and obtain critical exponents in the pre- and postgelation stage in terms of the model parameters; we calculate bounds on the time of gelation t c , and give an exact postgelation solution for the model K ij =( ij ω ) (ω>1/2) and K ij =a i+j ( a >1). For the model K ij = i ω + j ω ( ω <1, without gelation) initial solutions are given. It is argued that the kernel K ij ∼ ij ω with ω≃1−1/d ( d is dimensionality) effectively models the sol-gel transformation in polymerizing systems and approximately accounts for the effects of cross-linking and steric hindrance neglected in the classical theory of Flory and Stockmayer ( Ω =1). For all Ω the exponents, t=Ω +3/2 and σ=Ω −1/2, γ =(3/2− Ω)/(Ω − 1/2) and Β =1, characterize the size distribution, at and slightly below the gel point, under the assumption that scaling is valid.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45146/1/10955_2005_Article_BF01019497.pd

WW Domains of the Yes-Kinase-Associated-Protein (YAP) Transcriptional Regulator Behave as Independent Units with Different Binding Preferences for PPxY Motif-Containing Ligands

YAP is a WW domain-containing effector of the Hippo tumor suppressor pathway, and the object of heightened interest as a potent oncogene and stemness factor. YAP has two major isoforms that differ in the number of WW domains they harbor. Elucidating the degree of co-operation between these WW domains is important for a full understanding of the molecular function of YAP. We present here a detailed biophysical study of the structural stability and binding properties of the two YAP WW domains aimed at investigating the relationship between both domains in terms of structural stability and partner recognition. We have carried out a calorimetric study of the structural stability of the two YAP WW domains, both isolated and in a tandem configuration, and their interaction with a set of functionally relevant ligands derived from PTCH1 and LATS kinases. We find that the two YAP WW domains behave as independent units with different binding preferences, suggesting that the presence of the second WW domain might contribute to modulate target recognition between the two YAP isoforms. Analysis of structural models and phage-display studies indicate that electrostatic interactions play a critical role in binding specificity. Together, these results are relevant to understand of YAP function and open the door to the design of highly specific ligands of interest to delineate the functional role of each WW domain in YAP signaling.This work was supported by the Spanish Ministry of Education and Science [grant BIO2009-13261-CO2], the Spanish Ministry of Economy and Competitivity [grant BIO2012-39922-CO2] including FEDER (European Funds for Regional Development) funds and the Governement of Andalusia [grant CVI-5915]. Marius Sudol was supported by PA Breast Cancer Coalition Grants (#60707 and #920093) plus the Geisinger Clinic