Witnessing eigenstates for quantum simulation of Hamiltonian spectra

The efficient calculation of Hamiltonian spectra, a problem often intractable on classical machines, can find application in many fields, from physics to chemistry. Here, we introduce the concept of an "eigenstate witness" and through it provide a new quantum approach which combines variational methods and phase estimation to approximate eigenvalues for both ground and excited states. This protocol is experimentally verified on a programmable silicon quantum photonic chip, a mass-manufacturable platform, which embeds entangled state generation, arbitrary controlled-unitary operations, and projective measurements. Both ground and excited states are experimentally found with fidelities >99%, and their eigenvalues are estimated with 32-bits of precision. We also investigate and discuss the scalability of the approach and study its performance through numerical simulations of more complex Hamiltonians. This result shows promising progress towards quantum chemistry on quantum computers.Comment: 9 pages, 4 figures, plus Supplementary Material [New version with minor typos corrected.

Perturbative approach to the hydrogen atom in strong magnetic field

The states of hydrogen atom with principal quantum number n <= 3 and zero magnetic quantum number in constant homogeneous magnetic field H are considered. The perturbation theory series is summed with the help of Borel transformation and conformal mapping of the Borel variable. Convergence of approximate energy eigenvalues and their agreement with corresponding existing results are observed for external fields up to n^3 H ~ 5. The possibility of restoring the asymptotic behaviour of energy levels using perturbation theory coefficients is also discussed.Comment: LaTeX, 8 pages with 5 eps figure

Resummation of the Divergent Perturbation Series for a Hydrogen Atom in an Electric Field

We consider the resummation of the perturbation series describing the energy displacement of a hydrogenic bound state in an electric field (known as the Stark effect or the LoSurdo-Stark effect), which constitutes a divergent formal power series in the electric field strength. The perturbation series exhibits a rich singularity structure in the Borel plane. Resummation methods are presented which appear to lead to consistent results even in problematic cases where isolated singularities or branch cuts are present on the positive and negative real axis in the Borel plane. Two resummation prescriptions are compared: (i) a variant of the Borel-Pade resummation method, with an additional improvement due to utilization of the leading renormalon poles (for a comprehensive discussion of renormalons see [M. Beneke, Phys. Rep. vol. 317, p. 1 (1999)]), and (ii) a contour-improved combination of the Borel method with an analytic continuation by conformal mapping, and Pade approximations in the conformal variable. The singularity structure in the case of the LoSurdo-Stark effect in the complex Borel plane is shown to be similar to (divergent) perturbative expansions in quantum chromodynamics.Comment: 14 pages, RevTeX, 3 tables, 1 figure; numerical accuracy of results enhanced; one section and one appendix added and some minor changes and additions; to appear in phys. rev.

Are Debris Disks and Massive Planets Correlated?

Using data from the Spitzer Space Telescope Legacy Science Program ``Formation and Evolution of Planetary Systems'' (FEPS), we have searched for debris disks around 9 FGK stars (2-10 Gyr), known from radial velocity (RV) studies to have one or more massive planets. Only one of the sources, HD 38529, has excess emission above the stellar photosphere; at 70 micron the signal-to-noise ratio in the excess is 4.7 while at wavelengths < 30 micron there is no evidence of excess. The remaining sources show no excesses at any Spitzer wavelengths. Applying survival tests to the FEPS sample and the results for the FGK survey published in Bryden et al. (2006), we do not find a significant correlation between the frequency and properties of debris disks and the presence of close-in planets. We discuss possible reasons for the lack of a correlation.Comment: 24 pages, 3 figures. Accepted to Astrophysical Journa

Formation and Evolution of Planetary Systems: Cold Outer Disks Associated with Sun-like stars

We present the discovery of debris systems around three solar mass stars based upon observations performed with the Spitzer Space Telescope as part of a Legacy Science Program, ``the Formation and Evolution of Planetary Systems'' (FEPS). We also confirm the presence of debris around two other stars. All the stars exhibit infrared emission in excess of the expected photospheres in the 70 micron band, but are consistent with photospheric emission at <= 33 micron. This restricts the maximum temperature of debris in equilibrium with the stellar radiation to T < 70 K. We find that these sources are relatively old in the FEPS sample, in the age range 0.7 - 3 Gyr. Based on models of the spectral energy distributions, we suggest that these debris systems represent materials generated by collisions of planetesimal belts. We speculate on the nature of these systems through comparisons to our own Kuiper Belt, and on the likely planet(s) responsible for stirring the system and ultimately releasing dust through collisions. We further report observations of a nearby star HD 13974 (d =11 pc) that is indistinguishable from a bare photosphere at both 24 micron and 70 micron. The observations place strong upper limits on the presence of any cold dust in this nearby system (L_IR/L_* < 10^{-5.2}).Comment: 31 pages, 9 figures, accepted for publication in Ap

"Ordinary, the same as anywhere else": notes on the management of spoiled identity in 'marginal' middle class neighbourhoods

Urban sociologists are becoming increasingly interested in neighbourhood as a source of middle-class identity. Particular emphasis is currently being given to two types of middle-class neighbourhood; gentrified urban neighbourhoods of ‘distinction’ and inconspicuous ‘suburban landscapes of privilege’. However, there has been a dearth of work on ‘marginal’ middle-class neighbourhoods that are similarly ‘inconspicuous’ rather than distinctive, but less exclusive, thus containing sources of ‘spoiled identity’. This article draws on data gathered from two ‘marginal’ middleclass neighbourhoods that contained a particular source of ‘spoiled identity’: social renters. Urban sociological analyses of neighbour responses to these situations highlight a process of dis-identification with the maligned object, which exacerbates neighbour differences. Our analysis of data from the ‘marginal’ middle-class neighbourhoods suggests something entirely different and Goffmanesque. This entailed the management of spoiled identity, which emphasized similarities rather than differences between neighbours.</p

Mediating the Presence of Others: Reconceptualising Co-Presence as Mediated Intimacy

Drawing insight from queer and media studies, this article analyses data from the UK study Adults’ Media Lives. The authors claim that this study reveals the significance of people’s intimate relationships to their media practices, highlighting in particular how people’s media practices mediate the ‘presence’ of others. The authors put forward the concept of mediated intimacy to capture both the cultural intimacy people have with media and the mediation of intimacy by media practices. Mediating intimacy has implications for normative conceptions of intimate life, including the significance of ‘time’ to the values of ‘home’ and ‘work’