1,684,952 research outputs found
A note on quantum chaology and gamma approximations to eigenvalue spacings for infinite random matrices
Quantum counterparts of certain simple classical systems can exhibit chaotic
behaviour through the statistics of their energy levels and the irregular
spectra of chaotic systems are modelled by eigenvalues of infinite random
matrices. We use known bounds on the distribution function for eigenvalue
spacings for the Gaussian orthogonal ensemble (GOE) of infinite random real
symmetric matrices and show that gamma distributions, which have an important
uniqueness property, can yield an approximation to the GOE distribution. That
has the advantage that then both chaotic and non chaotic cases fit in the
information geometric framework of the manifold of gamma distributions, which
has been the subject of recent work on neighbourhoods of randomness for general
stochastic systems. Additionally, gamma distributions give approximations, to
eigenvalue spacings for the Gaussian unitary ensemble (GUE) of infinite random
hermitian matrices and for the Gaussian symplectic ensemble (GSE) of infinite
random hermitian matrices with real quaternionic elements, except near the
origin. Gamma distributions do not precisely model the various analytic systems
discussed here, but some features may be useful in studies of qualitative
generic properties in applications to data from real systems which manifestly
seem to exhibit behaviour reminiscent of near-random processes.Comment: 9 pages, 5 figures, 2 tables, 27 references. Updates version 1 with
data and references from feedback receive
Low error measurement-free phase gates for qubus computation
We discuss the desired criteria for a two-qubit phase gate and present a
method for realising such a gate for quantum computation that is
measurement-free and low error. The gate is implemented between qubits via an
intermediate bus mode. We take a coherent state as the bus and use cross-Kerr
type interactions between the bus and the qubits. This new method is robust
against parameter variations and is thus low error. It fundamentally improves
on previous methods due its deterministic nature and the lack of approximations
used in the geometry of the phase rotations. This interaction is applicable
both to solid state and photonic qubit systems.Comment: 6 pages, 4 figures. Published versio
Some recent work in Frechet geometry
Some recent work in Frechet geometry is briefly reviewed. In particular an
earlier result on the structure of second tangent bundles in the finite
dimensional case was extended to infinite dimensional Banach manifolds and
Frechet manifolds that could be represented as projective limits of Banach
manifolds. This led to further results concerning the characterization of
second tangent bundles and differential equations in the more general Frechet
structure needed for applications. A summary is given of recent results on
hypercyclicity of operators on Frechet spaces.Comment: 14 pages 48 reference
Flow Induced by the Impulsive Motion of an Infinite Flat Plate in a Dusty Gas
Flow Induced by the Impulsive Motion of an Immite Flat Plate in a Dusty Gas. The problem of
flow induced by an infinite flat plate suddenly set into motion parallel to its own plane in an incompressible
dusty gas is of considerable physical interest in its own right as well as because of its close relation to the
non-linear, steady (constant-pressure) laminar boundary layer. Its solution provides complete and exact
information about modifications of the boundary layer growth and skin friction due to particle-fluid
interaction. Moreover, it provides a basis for judging the accuracy of approximations which have been
employed in more complex problems of viscous fluid-particle motion. The uncoupled thermal Rayleigh
problem for small relative temperature differences is directly inferred and this answers questions about the
modifications of the surface heat transfer rate and about the possibility of similarity with the velocity
boundary layer. Similarity is possible when, in addition to a Prandtl number of unity, the streamwise
relaxation processes are also similar
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On the entropy flows to disorder
Gamma distributions, which contain the exponential as a special case, have a
distinguished place in the representation of near-Poisson randomness for
statistical processes; typically, they represent distributions of spacings
between events or voids among objects. Here we look at the properties of the
Shannon entropy function and calculate its corresponding flow curves. We
consider univariate and bivariate gamma, as well as Weibull distributions which
also include exponential distributions.Comment: Enlarged version of original. 11 pages, 6 figures, 15 reference
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