639 research outputs found
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 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 , where
and 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
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