Condensate fluctuations of a trapped, ideal Bose gas

For a non-self-interacting Bose gas with a fixed, large number of particles confined to a trap, as the ground state occupation becomes macroscopic, the condensate number fluctuations remain micrscopic. However, this is the only significant aspect in which the grand canonical description differs from canonical or microcanonical in the thermodynamic limit. General arguments and estimates including some vanishingly small quantities are compared to explicit, fixed-number calculations for 10^2 to 10^6 particles.Comment: 16 pages (REVTeX) plus 4 figures (ps), revision includes brief comparison of repulsive-interaction vs. fixed-N fluctuation damping. To be published in Phys. Rev.

Importance of Compton scattering to radiation spectra of isolated neutron stars

Model atmospheres of isolated neutron stars with low magnetic field are calculated with Compton scattering taking into account. Models with effective temperatures 1, 3 and 5 MK, with two values of surface gravity log(g)g = 13.9 and 14.3), and different chemical compositions are calculated. Radiation spectra computed with Compton scattering are softer than the computed with Thomson scattering at high energies (E > 5 keV) for hot (T_eff > 1 MK) atmospheres with hydrogen-helium composition. Compton scattering is more significant to hydrogen models with low surface gravity. The emergent spectra of the hottest (T_eff > 3 MK) model atmospheres can be described by diluted blackbody spectra with hardness factors ~ 1.6 - 1.9. Compton scattering is less important for models with solar abundance of heavy elements.Comment: Proceedings of the 363. WE-Heraeus Seminar on: Neutron Stars and Pulsars (Posters and contributed talks) Physikzentrum Bad Honnef, Germany, May.14-19, 2006, eds. W.Becker, H.H.Huang, MPE Report 291, pp.173-17

Introduction to Holographic Superconductors

These lectures give an introduction to the theory of holographic superconductors. These are superconductors that have a dual gravitational description using gauge/gravity duality. After introducing a suitable gravitational theory, we discuss its properties in various regimes: the probe limit, the effects of backreaction, the zero temperature limit, and the addition of magnetic fields. Using the gauge/gravity dictionary, these properties reproduce many of the standard features of superconductors. Some familiarity with gauge/gravity duality is assumed. A list of open problems is included at the end.Comment: 34 pages, 10 figures, to appear in the proceedings of the 5th Aegean Summer School, "From Gravity to Thermal Gauge Theories: the AdS/CFT Correspondence"; v2: references adde

Natural Orbitals and BEC in traps, a diffusion Monte Carlo analysis

We investigate the properties of hard core Bosons in harmonic traps over a wide range of densities. Bose-Einstein condensation is formulated using the one-body Density Matrix (OBDM) which is equally valid at low and high densities. The OBDM is calculated using diffusion Monte Carlo methods and it is diagonalized to obtain the "natural" single particle orbitals and their occupation, including the condensate fraction. At low Boson density, $na^3 < 10^{-5}$, where $n = N/V$ and $a$ is the hard core diameter, the condensate is localized at the center of the trap. As $na^3$ increases, the condensate moves to the edges of the trap. At high density it is localized at the edges of the trap. At $na^3 \leq 10^{-4}$ the Gross-Pitaevskii theory of the condensate describes the whole system within 1%. At $na^3 \approx 10^{-3}$ corrections are 3% to the GP energy but 30% to the Bogoliubov prediction of the condensate depletion. At $na^3 \gtrsim 10^{-2}$, mean field theory fails. At $na^3 \gtrsim 0.1$, the Bosons behave more like a liquid $^4$He droplet than a trapped Boson gas.Comment: 13 pages, 14 figures, submitted Phys. Rev.

Local and Global Casimir Energies: Divergences, Renormalization, and the Coupling to Gravity

From the beginning of the subject, calculations of quantum vacuum energies or Casimir energies have been plagued with two types of divergences: The total energy, which may be thought of as some sort of regularization of the zero-point energy, $\sum\frac12\hbar\omega$, seems manifestly divergent. And local energy densities, obtained from the vacuum expectation value of the energy-momentum tensor, $\langle T_{00}\rangle$, typically diverge near boundaries. The energy of interaction between distinct rigid bodies of whatever type is finite, corresponding to observable forces and torques between the bodies, which can be unambiguously calculated. The self-energy of a body is less well-defined, and suffers divergences which may or may not be removable. Some examples where a unique total self-stress may be evaluated include the perfectly conducting spherical shell first considered by Boyer, a perfectly conducting cylindrical shell, and dilute dielectric balls and cylinders. In these cases the finite part is unique, yet there are divergent contributions which may be subsumed in some sort of renormalization of physical parameters. The divergences that occur in the local energy-momentum tensor near surfaces are distinct from the divergences in the total energy, which are often associated with energy located exactly on the surfaces. However, the local energy-momentum tensor couples to gravity, so what is the significance of infinite quantities here? For the classic situation of parallel plates there are indications that the divergences in the local energy density are consistent with divergences in Einstein's equations; correspondingly, it has been shown that divergences in the total Casimir energy serve to precisely renormalize the masses of the plates, in accordance with the equivalence principle.Comment: 53 pages, 1 figure, invited review paper to Lecture Notes in Physics volume in Casimir physics edited by Diego Dalvit, Peter Milonni, David Roberts, and Felipe da Ros

From problems in the North to the problematic North : Northern devolution through the lens of history

Current debates about Northern English cities and their role in national economic strategies cannot be read simply through the lens of contemporary politics. We therefore take the Northern Powerhouse as our starting point in a chapter which traces a long history of policy and planning discourses about the North of England. We use David Russell’s chronology of key historical moments in which Northern English cities hold a particular charge in cultural narratives of the nation to guide our analysis of contemporaneous tensions in debates about planning and governance. A focus on representations about the North of England over the course of the last two centuries reveals four interlocking themes: namely the role of London in directing debates about the North; a tension between political and spatial approaches to planning; the characterisation of cities in the North of England as intrinsically problematic places; and the continued issue of poverty in these cities

CP Asymmetries in B_s Decays and Spontaneous CP violation

We study possible effects of new physics in CP asymmetries in two-body $B_s$ decays in left-right models with spontaneous CP violation. Considering the contributions of new CP phases to the $B_s$ mixing as well as to the penguin dominated decay amplitudes we show that, with the present constraints, large deviations from the standard model predictions in CP asymmetries are allowed in both cases. Detection of the new physics can be done by measuring non-zero asymmetries which are predicted to vanish in the standard model or by comparing two measurements which are predicted to be equal in the standard model. In particular, we show that the measurement of the CKM angle $\gamma$ in electroweak penguin dominated processes $B_s^0\to\rho^0\eta^{(')}, \rho^0\phi$ can largely be affected by the new physics.Comment: References and discussion added, version to be published in PR

Meta-analysis of exome array data identifies six novel genetic loci for lung function

Background: Over 90 regions of the genome have been associated with lung function to date, many of which have also been implicated in chronic obstructive pulmonary disease. Methods: We carried out meta-analyses of exome array data and three lung function measures: forced expiratory volume in one second (FEV1), forced vital capacity (FVC) and the ratio of FEV1 to FVC (FEV1/FVC). These analyses by the SpiroMeta and CHARGE consortia included 60,749 individuals of European ancestry from 23 studies, and 7,721 individuals of African Ancestry from 5 studies in the discovery stage, with follow-up in up to 111,556 independent individuals. Results: We identified significant (P<2·8x10-7) associations with six SNPs: a nonsynonymous variant in RPAP1, which is predicted to be damaging, three intronic SNPs (SEC24C, CASC17 and UQCC1) and two intergenic SNPs near to LY86 and FGF10. Expression quantitative trait loci analyses found evidence for regulation of gene expression at three signals and implicated several genes, including TYRO3 and PLAU. Conclusions: Further interrogation of these loci could provide greater understanding of the determinants of lung function and pulmonary disease