11,373 research outputs found
Vector constants of motion for time-dependent Kepler and isotropic harmonic oscillator potentials
A method of obtaining vector constants of motion for time-independent as well
as time-dependent central fields is discussed. Some well-established results
are rederived in this alternative way and new ones obtained.Comment: 18 pages, no figures, regular Latex article forma
On equivariant characteristic ideals of real classes
Let be an odd prime, an abelian totally real number field,
its cyclotomic -extension,
We give an explicit description of the equivariant characteristic ideal of
over for all odd by applying M. Witte's formulation of an equivariant main conjecture (or
"limit theorem") due to Burns and Greither. This could shed some light on
Greenberg's conjecture on the vanishing of the -invariant of
$F_\infty/F.
Quantum Channels and Representation Theory
In the study of d-dimensional quantum channels , an assumption
which is not very restrictive, and which has a natural physical interpretation,
is that the corresponding Kraus operators form a representation of a Lie
algebra. Physically, this is a symmetry algebra for the interaction
Hamiltonian. This paper begins a systematic study of channels defined by
representations; the famous Werner-Holevo channel is one element of this
infinite class. We show that the channel derived from the defining
representation of SU(n) is a depolarizing channel for all , but for most
other representations this is not the case. Since the Bloch sphere is not
appropriate here, we develop technology which is a generalization of Bloch's
technique. Our method works by representing the density matrix as a polynomial
in symmetrized products of Lie algebra generators, with coefficients that are
symmetric tensors. Using these tensor methods we prove eleven theorems, derive
many explicit formulas and show other interesting properties of quantum
channels in various dimensions, with various Lie symmetry algebras. We also
derive numerical estimates on the size of a generalized ``Bloch sphere'' for
certain channels. There remain many open questions which are indicated at
various points through the paper.Comment: 28 pages, 1 figur
Decoherence-protected memory for a single-photon qubit
The long-lived, efficient storage and retrieval of a qubit encoded on a
photon is an important ingredient for future quantum networks. Although systems
with intrinsically long coherence times have been demonstrated, the combination
with an efficient light-matter interface remains an outstanding challenge. In
fact, the coherence times of memories for photonic qubits are currently limited
to a few milliseconds. Here we report on a qubit memory based on a single atom
coupled to a high-finesse optical resonator. By mapping and remapping the qubit
between a basis used for light-matter interfacing and a basis which is less
susceptible to decoherence, a coherence time exceeding 100 ms has been measured
with a time-independant storage-and-retrieval efficiency of 22%. This
demonstrates the first photonic qubit memory with a coherence time that exceeds
the lower bound needed for teleporting qubits in a global quantum internet.Comment: 3 pages, 4 figure
Principal manifolds and graphs in practice: from molecular biology to dynamical systems
We present several applications of non-linear data modeling, using principal
manifolds and principal graphs constructed using the metaphor of elasticity
(elastic principal graph approach). These approaches are generalizations of the
Kohonen's self-organizing maps, a class of artificial neural networks. On
several examples we show advantages of using non-linear objects for data
approximation in comparison to the linear ones. We propose four numerical
criteria for comparing linear and non-linear mappings of datasets into the
spaces of lower dimension. The examples are taken from comparative political
science, from analysis of high-throughput data in molecular biology, from
analysis of dynamical systems.Comment: 12 pages, 9 figure
Determinationof oxidation induction time and temperature bY DSC: Results of round robin tests
Results obtained from three round robin tests, performed in 1998, 2000 and 2004, are summarized and presented. Oxidation Induction Time (OITtime) and Oxidation Induction Temperature (OITtemp) on six different grades of polyethylene were measured by DSC. The measured data were collected by Empa and evaluated using a robust statistical method concerning repeatability and reproducibility standard deviation. The results of the tests indicate that the determination of OITtime is associated with a high degree of uncertainty, especially for low OITtime values. Thus, OITtemp measurements could be a valuable alternative for testing less stabilized or non-stabilized polyolefin in particular. However, OITtemp data reveal that the ability to distinguish between different polymer samples decreases drastically as OITtemp values increas
Spin correlations and Dzyaloshinskii-Moriya interaction in CsCuCl
We report on electron spin resonance (ESR) studies of the spin relaxation in
CsCuCl. The main source of the ESR linewidth at temperatures K is attributed to the uniform Dzyaloshinskii-Moriya interaction. The
vector components of the Dzyaloshinskii-Moriya interaction are determined from
the angular dependence of the ESR spectra using a high-temperature
approximation. Both the angular and temperature dependence of the ESR linewidth
have been analyzed using a self-consistent quantum-mechanical approach. In
addition analytical expressions based on a quasi-classical picture for spin
fluctuations are derived, which show good agreement with the quantum-approach
for temperatures K. A small modulation of the
ESR linewidth observed in the -plane is attributed to the anisotropic
Zeeman interaction, which reflects the two magnetically nonequivalent Cu
positions
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