Hydrodynamic synchronization of flagellar oscillators

We survey the theory synchronization in collections of noisy oscillators. This framework is applied to flagellar synchronization by hydrodynamic interactions. The time-reversibility of hydrodynamics at low Reynolds numbers prompts swimming strokes that break symmetry to facilitate hydrodynamic synchronization. We discuss different physical mechanisms for flagellar synchronization, which break this symmetry in different ways.Comment: 15 pages, 3 figures; accepted for publication in EPJ Special Topics Issue,Lecture Notes of the Summer School "Microswimmers -- From Single Particle Motion to Collective Behaviour'', organised by the DFG Priority Programme SPP 1726 (Forschungszentrum J\"ulich, J\"ulich, 2015

Spectral properties of Bunimovich mushroom billiards

Properties of a quantum mushroom billiard in the form of a superconducting microwave resonator have been investigated. They reveal unexpected nonuniversal features such as, e.g., a supershell effect in the level density and a dip in the nearest-neighbor spacing distribution. Theoretical predictions for the quantum properties of mixed systems rely on the sharp separability of phase space - an unusual property met by mushroom billiards. We however find deviations which are ascribed to the presence of dynamic tunneling.Comment: 4 pages, 7 .eps-figure

The Energy-Momentum tensor on SpincSpin^c manifolds

On $Spin^c$ manifolds, we study the Energy-Momentum tensor associated with a spinor field. First, we give a spinorial Gauss type formula for oriented hypersurfaces of a $Spin^c$ manifold. Using the notion of generalized cylinders, we derive the variationnal formula for the Dirac operator under metric deformation and point out that the Energy-Momentum tensor appears naturally as the second fundamental form of an isometric immersion. Finally, we show that generalized $Spin^c$ Killing spinors for Codazzi Energy-Momentum tensor are restrictions of parallel spinors.Comment: To appear in IJGMMP (International Journal of Geometric Methods in Modern Physics), 22 page

Much Polyphony but Little Harmony: Otto Sackur's Groping for a Quantum Theory of Gases

The endeavor of Otto Sackur (1880-1914) was driven, on the one hand, by his interest in Nernst’s theorem, statistical mechanics, and the problem of chemical equilibrium, and, on the other, his goal to shed light on classical mechanics from the quantum vantage point. Inspired by the interplay between classical physics and quantum theory, Sackur chanced to expound his personal take on the role of the quantum in the changing landscape of physics in the turbulent 1910s. In this paper, we tell the story of this enthusiastic practitioner of the old quantum theory and early contributor to quantum statistical mechanics, whose scientific ontogenesis provides a telling clue about the phylogeny of his contemporaries

Collisions of paramagnetic molecules in magnetic fields: An analytic model based on Fraunhofer diffraction of matter waves

We investigate the effects of a magnetic field on the dynamics of rotationally inelastic collisions of open-shell molecules (² Σ, ³Σ, and ²Π) with closed-shell atoms. Our treatment makes use of the Fraunhofer model of matter wave scattering and its recent extension to collisions in electric [M. Lemeshko and B. Friedrich, J. Chem. Phys. 129, 024301 (2008)] and radiative fields [M. Lemeshko and B. Friedrich, Int. J. Mass. Spec. in press (2008)]. A magnetic field aligns the molecule in the space-fixed frame and thereby alters the effective shape of the diffraction target. This significantly affects the differential and integral scattering cross sections. We exemplify our treatment by evaluating the magnetic-field-dependent scattering characteristics of the He – CaH (X² Σ⁺), He – O₂ (X³Σ⁻) and He – OH (X²ΠΩ ) systems at thermal collision energies. Since the cross sections can be obtained fordifferent orientations of the magnetic field with respect to the relative velocity vector, the model also offers predictions about the frontal-versus-lateral steric asymmetry of the collisions. The steric asymmetry is found to be almost negligible for the He – OH system, weak for the He – CaH collisions, and strong for the He – O₂ . While odd ∆M transitions dominate the He – OH (J = 3/2, f → J′ , e/f ) integral cross sections in a magnetic field parallel to the relative velocity vector, even ∆M transitions prevail in the case of the He – CaH (X²Σ⁺) and He – O₂ (X³Σ⁻) collision systems. For the latter system, the magnetic field opens inelastic channels that are closed in the absence of the field. These involve the transitions N = 1, J = 0 → N′, J′ with J′ = N′

An analytic model of the stereodynamics of rotationally inelastic molecular collisions

We develop an analytic model of vector correlations in rotationally inelastic atom-diatom collisions and test it against the much examined Ar--NO (X²Π) system. Based on the Fraunhofer scattering of matter waves, the model furnishes complex scattering amplitudes needed to evaluate the polarization moments characterizing the quantum stereodynamics. The analytic polarization moments are found to be in an excellent agreement with experimental results and with close-coupling calculations available at thermal energies. The model reveals that the stereodynamics is governed by diffraction from the repulsive core of the Ar--NO potential, which can be characterized by a single Legendre moment