1,720,407 research outputs found
Multi-normed spaces
We modify the very well known theory of normed spaces (E, \norm) within
functional analysis by considering a sequence (\norm_n : n\in\N) of norms,
where \norm_n is defined on the product space for each .
Our theory is analogous to, but distinct from, an existing theory of
`operator spaces'; it is designed to relate to general spaces for , and in particular to -spaces, rather than to -spaces.
After recalling in Chapter 1 some results in functional analysis, especially
in Banach space, Hilbert space, Banach algebra, and Banach lattice theory that
we shall use, we shall present in Chapter 2 our axiomatic definition of a
`multi-normed space' ((E^n, \norm_n) : n\in \N), where (E, \norm) is a
normed space. Several different, equivalent, characterizations of multi-normed
spaces are given, some involving the theory of tensor products; key examples of
multi-norms are the minimum and maximum multi-norm based on a given space.
Multi-norms measure `geometrical features' of normed spaces, in particular by
considering their `rate of growth'. There is a strong connection between
multi-normed spaces and the theory of absolutely summing operators.
A substantial number of examples of multi-norms will be presented.
Following the pattern of standard presentations of the foundations of
functional analysis, we consider generalizations to `multi-topological linear
spaces' through `multi-null sequences', and to `multi-bounded' linear
operators, which are exactly the `multi-continuous' operators. We define a new
Banach space of multi-bounded operators, and show that it
generalizes well-known spaces, especially in the theory of Banach lattices.
We conclude with a theory of `orthogonal decompositions' of a normed space
with respect to a multi-norm, and apply this to construct a `multi-dual' space.Comment: Many update
The meaning of S-D dominance
The dominance of S and D pairs in the description of deformed nuclei is one
of the facts that provided sustain to the Interacting Boson Approximation. In
Ref.(J. Dukelsky and S. Pittel, Phys. Rev. Lett. 86, 4791, 2001.), using an
exactly solvable model with a repulsive pairing interaction between bosons it
has been shown that the ground state is described almost completely in terms of
S and D bosons. In the present paper we study the excited states obtained
within this exactly solvable hamiltonian and show that in order to obtain a
rotational spectra all the other degrees of freedom are needed.Comment: Are S and D pairs enough to describe deformed nuclei
Two-mode heterodyne phase detection
We present an experimental scheme that achieves ideal phase detection on a
two-mode field. The two modes and are the signal and image band modes
of an heterodyne detector, with the field approaching an eigenstate of the
photocurrent . The field is obtained by means of a
high-gain phase-insensitive amplifier followed by a high-transmissivity
beam-splitter with a strong local oscillator at the frequency of one of the two
modes.Comment: 3 pages, 1 figur
Wormhole Effect in a Strong Topological Insulator
An infinitely thin solenoid carrying magnetic flux Phi (a `Dirac string')
inserted into an ordinary band insulator has no significant effect on the
spectrum of electrons. In a strong topological insulator, remarkably, such a
solenoid carries protected gapless one-dimensional fermionic modes when
Phi=hc/2e. These modes are spin-filtered and represent a distinct bulk
manifestation of the topologically non-trivial insulator. We establish this
`wormhole' effect by both general qualitative considerations and by numerical
calculations within a minimal lattice model. We also discuss the possibility of
experimental observation of a closely related effect in artificially engineered
nanostructures.Comment: 4 pages, 3 figures. For related work and info visit
http://www.physics.ubc.ca/~fran
Cork-resin ablative insulation for complex surfaces and method for applying the same
A method of applying cork-resin ablative insulation material to complex curved surfaces is disclosed. The material is prepared by mixing finely divided cork with a B-stage curable thermosetting resin, forming the resulting mixture into a block, B-stage curing the resin-containing block, and slicing the block into sheets. The B-stage cured sheet is shaped to conform to the surface being insulated, and further curing is then performed. Curing of the resins only to B-stage before shaping enables application of sheet material to complex curved surfaces and avoids limitations and disadvantages presented in handling of fully cured sheet material
Pairwise entanglement and readout of atomic-ensemble and optical wave-packet modes in traveling-wave Raman interactions
We analyze quantum entanglement of Stokes light and atomic electronic
polarization excited during single-pass, linear-regime, stimulated Raman
scattering in terms of optical wave-packet modes and atomic-ensemble spatial
modes. The output of this process is confirmed to be decomposable into multiple
discrete, bosonic mode pairs, each pair undergoing independent evolution into a
two-mode squeezed state. For this we extend the Bloch-Messiah reduction
theorem, previously known for discrete linear systems (S. L. Braunstein, Phys.
Rev. A, vol. 71, 055801 (2005)). We present typical mode functions in the case
of one-dimensional scattering in an atomic vapor. We find that in the absence
of dispersion, one mode pair dominates the process, leading to a simple
interpretation of entanglement in this continuous-variable system. However,
many mode pairs are excited in the presence of dispersion-induced temporal
walkoff of the Stokes, as witnessed by the photon-count statistics. We also
consider the readout of the stored atomic polarization using the anti-Stokes
scattering process. We prove that the readout process can also be decomposed
into multiple mode pairs, each pair undergoing independent evolution analogous
to a beam-splitter transformation. We show that this process can have unit
efficiency under realistic experimental conditions. The shape of the output
light wave packet can be predicted. In case of unit readout efficiency it
contains only excitations originating from a specified atomic excitation mode
Topological Anderson Insulator in Three Dimensions
Disorder, ubiquitously present in solids, is normally detrimental to the
stability of ordered states of matter. In this letter we demonstrate that not
only is the physics of a strong topological insulator robust to disorder but,
remarkably, under certain conditions disorder can become fundamentally
responsible for its existence. We show that disorder, when sufficiently strong,
can transform an ordinary metal with strong spin-orbit coupling into a strong
topological `Anderson' insulator, a new topological phase of quantum matter in
three dimensions.Comment: 5 pages, 2 figures. For related work and info visit
http://www.physics.ubc.ca/~franz
Computation of Neutron Star Structure Using Modern Equation of State
Using the modern equations of state derived from microscopic calculations, we
have calculated the neutron star structure. For the neutron star, we have
obtained a minimum mass about which is nearly independent
of the equation of state, and a maximum mass between and
which is strongly dependent on the equation of state. It
is shown that among the equations of state of neutron star matter which we have
used, the stiffest one leads to higher maximum mass and radius and lower
central density. It is seen that the given maximum mass for the Reid-93
equation of state shows a good consistency with the accurate observations of
radio pulsars. We have indicated that the thickness of neutron star crust is
very small compared to the predicted neutron star radius.Comment: 16 pages, 6 figure
Multichannel visible spectroscopy diagnostic for particle transport studies in the H-1 heliac
A multichannel spectroscopy diagnostic has been developed to study cross-field particle transport in the radiation-dominated low-temperature plasmas (Te<100 eV) in the H-1 heliac. The optical setup covers the full plasma minor radius in the poloidal plane collecting light from ten parallel chords arranged tangentially to the flux surfaces. The light collected from the plasma is coupled into optical fibers and through interference filters into photomultipliers. Two such ten-fiber arrays are aligned parallel to one another to allow the simultaneous monitoring of two different spectral lines. The net radial electron particle flux is determined from the continuity equation by integrating over the ionization source term in the steady-state partially ionized plasma. The diagnostic measures the neutral line intensities and their ratios (in case of helium using the line ratio technique) and also measures excited neutral and ion spectral lines (in case of the argon plasma transport studies). A comparative analysis of the radial particle transport in the low- and high-confinement regimes is presented
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