Testrun results from prototype fiber detectors for high rate particle tracking

A fiber detector concept has been realized allowing to registrate particles within less than 100 nsec with a space point precision of about 0.1 mm at low occupancy. Three full size prototypes have been build by different producers and tested at a 3 GeV electron beam at DESY. After 3 m of light guides 8-10 photoelectrons were registrated by multichannel photomultipliers providing an efficiency of more than 99%. Using all available data a resolution of 0.086 mm was measured.Comment: 18 pages, 17 figure

Integrable Discretizations of Chiral Models

A construction of conservation laws for chiral models (generalized sigma-models on a two-dimensional space-time continuum using differential forms is extended in such a way that it also comprises corresponding discrete versions. This is achieved via a deformation of the ordinary differential calculus. In particular, the nonlinear Toda lattice results in this way from the linear (continuum) wave equation. The method is applied to several further examples. We also construct Lax pairs and B\"acklund transformations for the class of models considered in this work.Comment: 14 pages, Late

Differential Calculi on Commutative Algebras

A differential calculus on an associative algebra A is an algebraic analogue of the calculus of differential forms on a smooth manifold. It supplies A with a structure on which dynamics and field theory can be formulated to some extent in very much the same way we are used to from the geometrical arena underlying classical physical theories and models. In previous work, certain differential calculi on a commutative algebra exhibited relations with lattice structures, stochastics, and parametrized quantum theories. This motivated the present systematic investigation of differential calculi on commutative and associative algebras. Various results about their structure are obtained. In particular, it is shown that there is a correspondence between first order differential calculi on such an algebra and commutative and associative products in the space of 1-forms. An example of such a product is provided by the Ito calculus of stochastic differentials. For the case where the algebra A is freely generated by `coordinates' x^i, i=1,...,n, we study calculi for which the differentials dx^i constitute a basis of the space of 1-forms (as a left A-module). These may be regarded as `deformations' of the ordinary differential calculus on R^n. For n < 4 a classification of all (orbits under the general linear group of) such calculi with `constant structure functions' is presented. We analyse whether these calculi are reducible (i.e., a skew tensor product of lower-dimensional calculi) or whether they are the extension (as defined in this article) of a one dimension lower calculus. Furthermore, generalizations to arbitrary n are obtained for all these calculi.Comment: 33 pages, LaTeX. Revision: A remark about a quasilattice and Penrose tiling was incorrect in the first version of the paper (p. 14

Genuine Counterfactual Communication with a Nanophotonic Processor

In standard communication information is carried by particles or waves. Counterintuitively, in counterfactual communication particles and information can travel in opposite directions. The quantum Zeno effect allows Bob to transmit a message to Alice by encoding information in particles he never interacts with. The first suggested protocol not only required thousands of ideal optical components, but also resulted in a so-called "weak trace" of the particles having travelled from Bob to Alice, calling the scalability and counterfactuality of previous proposals and experiments into question. Here we overcome these challenges, implementing a new protocol in a programmable nanophotonic processor, based on reconfigurable silicon-on-insulator waveguides that operate at telecom wavelengths. This, together with our telecom single-photon source and highly-efficient superconducting nanowire single-photon detectors, provides a versatile and stable platform for a high-fidelity implementation of genuinely trace-free counterfactual communication, allowing us to actively tune the number of steps in the Zeno measurement, and achieve a bit error probability below 1%, with neither post-selection nor a weak trace. Our demonstration shows how our programmable nanophotonic processor could be applied to more complex counterfactual tasks and quantum information protocols.Comment: 6 pages, 4 figure

Flow Phase Diagram for the Helium Superfluids

The flow phase diagram for He II and $^3$He-B is established and discussed based on available experimental data and the theory of Volovik [JETP Letters {\bf{78}} (2003) 553]. The effective temperature - dependent but scale - independent Reynolds number $Re_{eff}=1/q=(1+\alpha')/\alpha$, where $\alpha$ and $\alpha'$ are the mutual friction parameters and the superfluid Reynolds number characterizing the circulation of the superfluid component in units of the circulation quantum are used as the dynamic parameters. In particular, the flow diagram allows identification of experimentally observed turbulent states I and II in counterflowing He II with the turbulent regimes suggested by Volovik.Comment: 2 figure

Soliton equations and the zero curvature condition in noncommutative geometry

Familiar nonlinear and in particular soliton equations arise as zero curvature conditions for GL(1,R) connections with noncommutative differential calculi. The Burgers equation is formulated in this way and the Cole-Hopf transformation for it attains the interpretation of a transformation of the connection to a pure gauge in this mathematical framework. The KdV, modified KdV equation and the Miura transformation are obtained jointly in a similar setting and a rather straightforward generalization leads to the KP and a modified KP equation. Furthermore, a differential calculus associated with the Boussinesq equation is derived from the KP calculus.Comment: Latex, 10 page