What is a quantum simulator?

Quantum simulators are devices that actively use quantum effects to answer questions about model systems and, through them, real systems. Here we expand on this definition by answering several fundamental questions about the nature and use of quantum simulators. Our answers address two important areas. First, the difference between an operation termed simulation and another termed computation. This distinction is related to the purpose of an operation, as well as our confidence in and expectation of its accuracy. Second, the threshold between quantum and classical simulations. Throughout, we provide a perspective on the achievements and directions of the field of quantum simulation.Comment: 13 pages, 2 figure

Intersection Graph of a Module

Let $V$ be a left $R$-module where $R$ is a (not necessarily commutative) ring with unit. The intersection graph \cG(V) of proper $R$-submodules of $V$ is an undirected graph without loops and multiple edges defined as follows: the vertex set is the set of all proper $R$-submodules of $V,$ and there is an edge between two distinct vertices $U$ and $W$ if and only if $U\cap W\neq 0.$ We study these graphs to relate the combinatorial properties of \cG(V) to the algebraic properties of the $R$-module $V.$ We study connectedness, domination, finiteness, coloring, and planarity for \cG (V). For instance, we find the domination number of \cG (V). We also find the chromatic number of \cG(V) in some cases. Furthermore, we study cycles in \cG(V), and complete subgraphs in \cG (V) determining the structure of $V$ for which \cG(V) is planar

The Effective Potential And Additional Large Radius Compactified Space-Time Dimensions

The consequences of large radius extra space-time compactified dimensions on the four dimensional one loop effective potential are investigated for a model which includes scalar self interactions and Yukawa coupling to fermions. The Kaluza-Klein tower of states associated with the extra compact dimensions shifts the location of the effective potential minimum and modifies its curvature. The dependence of these effects on the radius of the extra dimension is illustrated for various choices of coupling constants and masses. For large radii, the consequence of twisting the fermion boundary condition on the compactified dimensions is numerically found to produce but a negligible effect on the effective potential.Comment: 14 pages, LaTeX, 6 Postscript figure

Accuracy of adults’ recall of childhood social class: findings from the Aberdeen children of the 1950s study

<b>Background</b>: Although adult reported childhood socioeconomic position has been related to health outcomes in many studies, little is known about the validity of such distantly recalled information. This study evaluated the validity of adults’ reports of childhood paternal social class. <b>Methods</b>: Data are drawn from the Aberdeen children of the 1950s study, a cohort of 12 150 people born in Aberdeen (Scotland) who took part in a school based survey in 1962. In this survey, two indices of early life socioeconomic position were collected: occupational social class at birth (abstracted from maternity records) and occupational social class in childhood (reported during the 1962 survey by the study participants). Between 2000 and 2003, a questionnaire was mailed to traced middle aged cohort members in which inquiries were made about their fathers’ occupation when they were aged 12 years. The level of agreement between these reports and prospectively collected data on occupational social class was assessed. <b>Results</b>: In total, 7183 (63.7%) persons responded to the mid-life questionnaire. Agreement was moderate between social class of father recalled in adulthood and that measured in early life ( statistics were 0.47 for social class measured at birth, and 0.56 for social class reported by the child). The relation of occupational social class to birth weight and childhood intelligence was in the expected directions, although weaker for adults’ reports in comparison with prospectively gathered data. <b>Conclusions</b>: In studies of adult disease aetiology, associations between childhood social class based on adult recall of parental occupation and health outcomes are likely to underestimate real effects

The Akulov-Volkov Lagrangian, Symmetry Currents and Spontaneously Broken Extended Supersymmetry

A generalization of the Akulov-Volkov effective Lagrangian governing the self interactions of the Nambu-Goldstone fermions associated with spontaneously broken extended supersymmetry as well as their coupling to matter is presented and scrutinized. The resulting currents associated with R-symmetry, supersymmetry and space-time translations are constructed and seen to form a supermultiplet structure.Comment: 17 pages, LaTeX; Title, abstract and introduction changes, references adde

The Tunneling Hybrid Monte-Carlo algorithm

The hermitian Wilson kernel used in the construction of the domain-wall and overlap Dirac operators has exceptionally small eigenvalues that make it expensive to reach high-quality chiral symmetry for domain-wall fermions, or high precision in the case of the overlap operator. An efficient way of suppressing such eigenmodes consists of including a positive power of the determinant of the Wilson kernel in the Boltzmann weight, but doing this also suppresses tunneling between topological sectors. Here we propose a modification of the Hybrid Monte-Carlo algorithm which aims to restore tunneling between topological sectors by excluding the lowest eigenmodes of the Wilson kernel from the molecular-dynamics evolution, and correcting for this at the accept/reject step. We discuss the implications of this modification for the acceptance rate.Comment: improved discussion in appendix B, RevTeX, 19 page

The Arches cluster revisited: I. Data presentation and stellar census

Context. Located within the central region of the Galaxy, the Arches cluster appears to be one of the youngest, densest and most massive stellar aggregates within the Milky Way. As such it has the potential to be a uniquely instructive laboratory for the study of star formation in extreme environments and the physics of very massive stars. Aims. To realise this possibility, the fundamental physical properties of both cluster and constituent stars need to be robustly determined; tasks we attempt here. Methods. In order to accomplish these goals we provide and analyse new multi-epoch near-IR spectroscopic data obtained with the VLT/SINFONI and photometry from the HST/WFC3. We are able to stack multiple epochs of spectroscopy for individual stars in order to obtain the deepest view of the cluster members ever obtained. Results. We present spectral classifications for 88 cluster members, all of which are WNLh or O stars: a factor of three increase over previous studies. We find no further examples of Wolf-Rayet stars within the cluster; importantly no H-free examples were identified. The smooth and continuous progression in spectral morphologies from O super-/hypergiants through to the WNLh cohort implies a direct evolutionary connection. We identify candidate giant and main sequence O stars spectroscopically for the first time. No products of binary evolution may be unambiguously identified despite the presence of massive binaries within the Arches. Conclusions. Notwithstanding difficulties imposed by the highly uncertain (differential) reddening to the Arches, we infer a main sequence/luminosity class V turn-off mass of ∼ 30 − 38M⊙ via the distribution of spectral types. Analysis of the eclipsing binary F2 suggests current masses of ∼ 80M⊙ and ∼ 60M⊙ for the WNLh and O hypergiant cohorts, respectively; we conclude that all classified stars have masses > 20M⊙. An age of ∼ 2.0 − 3.3Myr is suggested by the turn-off between ∼O4-5 V; constraints imposed by the supergiant population and the lack of H-free WRs are consistent with this estimate. While the absence of highly evolved WC stars strongly argues against the prior occurrence of SNe within the Arches, the derived age does accommodate such events for exceptionally massive stars. Further progress will require quantitative analysis of multiple individual cluster members in addition to further spectroscopic observations to better constrain the binary and main sequence populations; nevertheless it is abundantly clear that the Arches offers an unprecedented insight into the formation, evolution and death of the most massive stars Nature allows to form

Collisional cooling of ultra-cold atom ensembles using Feshbach resonances

We propose a new type of cooling mechanism for ultra-cold fermionic atom ensembles, which capitalizes on the energy dependence of inelastic collisions in the presence of a Feshbach resonance. We first discuss the case of a single magnetic resonance, and find that the final temperature and the cooling rate is limited by the width of the resonance. A concrete example, based on a p-wave resonance of $^{40}$K, is given. We then improve upon this setup by using both a very sharp optical or radio-frequency induced resonance and a very broad magnetic resonance and show that one can improve upon temperatures reached with current technologies.Comment: 4 pages, 3 figure