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 $E^n$ for each $n\in\N$. Our theory is analogous to, but distinct from, an existing theory of `operator spaces'; it is designed to relate to general spaces $L^p$ for $p\in [1,\infty]$, and in particular to $L^1$-spaces, rather than to $L^2$-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 ${\mathcal M}(E,F)$ 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

Two-mode heterodyne phase detection

We present an experimental scheme that achieves ideal phase detection on a two-mode field. The two modes $a$ and $b$ are the signal and image band modes of an heterodyne detector, with the field approaching an eigenstate of the photocurrent $\hat{Z}=a+b^{\dag}$. 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

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

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 $0.1 {\rm M_{\odot}}$ which is nearly independent of the equation of state, and a maximum mass between $1.47 {\rm M_{\odot}}$ and $1.98 {\rm M_{\odot}}$ 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