Local Casimir Energies for a Thin Spherical Shell

The local Casimir energy density for a massless scalar field associated with step-function potentials in a 3+1 dimensional spherical geometry is considered. The potential is chosen to be zero except in a shell of thickness $\delta$, where it has height $h$, with the constraint $h\delta=1$. In the limit of zero thickness, an ideal $\delta$-function shell is recovered. The behavior of the energy density as the surface of the shell is approached is studied in both the strong and weak coupling regimes. The former case corresponds to the well-known Dirichlet shell limit. New results, which shed light on the nature of surface divergences and on the energy contained within the shell, are obtained in the weak coupling limit, and for a shell of finite thickness. In the case of zero thickness, the energy has a contribution not only from the local energy density, but from an energy term residing entirely on the surface. It is shown that the latter coincides with the integrated local energy density within the shell. We also study the dependence of local and global quantities on the conformal parameter. In particular new insight is provided on the reason for the divergence in the global Casimir energy in third order in the coupling.Comment: 16 pages, revtex 4, no figures. Major additions, clarifications, and corections, references adde

PT-Symmetric Versus Hermitian Formulations of Quantum Mechanics

A non-Hermitian Hamiltonian that has an unbroken PT symmetry can be converted by means of a similarity transformation to a physically equivalent Hermitian Hamiltonian. This raises the following question: In which form of the quantum theory, the non-Hermitian or the Hermitian one, is it easier to perform calculations? This paper compares both forms of a non-Hermitian $ix^3$ quantum-mechanical Hamiltonian and demonstrates that it is much harder to perform calculations in the Hermitian theory because the perturbation series for the Hermitian Hamiltonian is constructed from divergent Feynman graphs. For the Hermitian version of the theory, dimensional continuation is used to regulate the divergent graphs that contribute to the ground-state energy and the one-point Green's function. The results that are obtained are identical to those found much more simply and without divergences in the non-Hermitian PT-symmetric Hamiltonian. The $\mathcal{O}(g^4)$ contribution to the ground-state energy of the Hermitian version of the theory involves graphs with overlapping divergences, and these graphs are extremely difficult to regulate. In contrast, the graphs for the non-Hermitian version of the theory are finite to all orders and they are very easy to evaluate.Comment: 13 pages, REVTeX, 10 eps figure

AC Stark shift noise in QND measurement arising from quantum fluctuations of light polarization

In a recent letter [Auzinsh {\it{et. al.}} (physics/0403097)] we have analyzed the noise properties of an idealized atomic magnetometer that utilizes spin squeezing induced by a continuous quantum nondemolition measurement. Such a magnetometer measures spin precession of $N$ atomic spins by detecting optical rotation of far-detuned probe light. Here we consider maximally squeezed probe light, and carry out a detailed derivation of the contribution to the noise in a magnetometric measurement due to the differential AC Stark shift between Zeeman sublevels arising from quantum fluctuations of the probe polarization.Comment: This is a companion note to physics/040309

Can a quantum nondemolition measurement improve the sensitivity of an atomic magnetometer?

Noise properties of an idealized atomic magnetometer that utilizes spin squeezing induced by a continuous quantum nondemolition measurement are considered. Such a magnetometer measures spin precession of $N$ atomic spins by detecting optical rotation of far-detuned light. Fundamental noise sources include the quantum projection noise and the photon shot-noise. For measurement times much shorter than the spin-relaxation time observed in the absence of light ($\tau_{\rm rel}$) divided by $\sqrt{N}$, the optimal sensitivity of the magnetometer scales as $N^{-3/4}$, so an advantage over the usual sensitivity scaling as $N^{-1/2}$ can be achieved. However, at longer measurement times, the optimized sensitivity scales as $N^{-1/2}$, as for a usual shot-noise limited magnetometer. If strongly squeezed probe light is used, the Heisenberg uncertainty limit may, in principle, be reached for very short measurement times. However, if the measurement time exceeds $\tau_{\rm rel}/N$, the $N^{-1/2}$ scaling is again restored.Comment: Some details of calculations can be found in a companion note: physics/040712

FoxP2 isoforms delineate spatiotemporal transcriptional networks for vocal learning in the zebra finch.

Human speech is one of the few examples of vocal learning among mammals yet ~half of avian species exhibit this ability. Its neurogenetic basis is largely unknown beyond a shared requirement for FoxP2 in both humans and zebra finches. We manipulated FoxP2 isoforms in Area X, a song-specific region of the avian striatopallidum analogous to human anterior striatum, during a critical period for song development. We delineate, for the first time, unique contributions of each isoform to vocal learning. Weighted gene coexpression network analysis of RNA-seq data revealed gene modules correlated to singing, learning, or vocal variability. Coexpression related to singing was found in juvenile and adult Area X whereas coexpression correlated to learning was unique to juveniles. The confluence of learning and singing coexpression in juvenile Area X may underscore molecular processes that drive vocal learning in young zebra finches and, by analogy, humans

Hyperpolarized xenon nuclear spins detected by optical atomic magnetometry

We report the use of an atomic magnetometer based on nonlinear magneto-optical rotation with frequency modulated light (FM NMOR) to detect nuclear magnetization of xenon gas. The magnetization of a spin-exchange-polarized xenon sample ($1.7$cm$^3$ at a pressure of $5$bar, natural isotopic abundance, polarization 1%), prepared remotely to the detection apparatus, is measured with an atomic sensor (which is insensitive to the leading field of 0.45 G applied to the sample; an independent bias field at the sensor is $140 \mu$G). An average magnetic field of $\sim 10$nG induced by the xenon sample on the 10-cm diameter atomic sensor is detected with signal-to-noise ratio $\sim 10$, limited by residual noise in the magnetic environment. The possibility of using modern atomic magnetometers as detectors of nuclear magnetic resonance and in magnetic resonance imaging is discussed. Atomic magnetometers appear to be ideally suited for emerging low-field and remote-detection magnetic resonance applications.Comment: 4 pages, 4 figure

A multi-dimensional energy-based analysis of neighbourhood sustainability assessment tools: are institutional indicators really missing?

Neighbourhood Sustainability Assessment Tools (NSATs) have become the modern day template for urban planners to achieve sustainable development in their communities, districts and cities. The popularity of the pioneering NSATs led to the creation of other tools in different regions. Also, with the popularity and replication of these tools came the replication of their limitations. The most notable limitation and motivation for this study is the inadequate recognition of the complexities of institutional dimensions (i.e. policies, laws and regulation) that contribute to mainstreaming and operationalising sustainable neighbourhood development. Studies that have investigated NSATs generally argue lack of coverage of the institutional dimension. However, there has been little consistent and explicit mention of the precise indicators and criteria sought out to make this claim. Also, there is a clear confusion as to what institutional indicators actually are, what characteristics they possess and how best they can be identified. This study, via the lens of energy-based indicators, expands on the role of the institutional indicator and its associated dimensions. This study also utilises a multi-dimensional approach to indicator analysis and draws out current trend or characteristics of institutional indicators in 15 currently existing NSATs. The results show a limited view on the classification of institutional indicators. The study also demonstrates that there are more institutional indicators than previously reported in prior studies. Additionally, this study confirms that an institutional indicator cannot be a single entity or identity but rather it must operate under the linkage of the other dimensions (environment, social and economic). Finally, this study, based on the analysis of 15 NSATs provides a definition of what can be considered an institutional indicator. In conclusion, it is recommended that future development of NSATs should ensure a constant institutional link to indicators, as this could provide an enhanced alternative to the development of NSATs, particularly for regions that are looking into developing their own assessment tools

Velocity-selective direct frequency-comb spectroscopy of atomic vapors

We present an experimental and theoretical investigation of two-photon direct frequency-comb spectroscopy performed through velocity-selective excitation. In particular, we explore the effect of repetition rate on the $\textrm{5S}_{1/2}\rightarrow \textrm{5D}_{3/2, 5/2}$ two-photon transitions excited in a rubidium atomic vapor cell. The transitions occur via step-wise excitation through the $\textrm{5P}_{1/2, 3/2}$ states by use of the direct output of an optical frequency comb. Experiments were performed with two different frequency combs, one with a repetition rate of $\approx 925$ MHz and one with a repetition rate of $\approx 250$ MHz. The experimental spectra are compared to each other and to a theoretical model.Comment: 10 pages, 7 figure