Solvable models of Bose-Einstein condensates: a new algebraic Bethe ansatz scheme

A new algebraic Bethe ansatz scheme is proposed to diagonalise classes of integrable models relevant to the description of Bose-Einstein condensates in dilute alkali gases. This is achieved by introducing the notion of Z-graded representations of the Yang-Baxter algebra.Comment: 14 pages, latex, no figure

Randomness Concerns When Deploying Differential Privacy

The U.S. Census Bureau is using differential privacy (DP) to protect confidential respondent data collected for the 2020 Decennial Census of Population & Housing. The Census Bureau's DP system is implemented in the Disclosure Avoidance System (DAS) and requires a source of random numbers. We estimate that the 2020 Census will require roughly 90TB of random bytes to protect the person and household tables. Although there are critical differences between cryptography and DP, they have similar requirements for randomness. We review the history of random number generation on deterministic computers, including von Neumann's "middle-square" method, Mersenne Twister (MT19937) (previously the default NumPy random number generator, which we conclude is unacceptable for use in production privacy-preserving systems), and the Linux /dev/urandom device. We also review hardware random number generator schemes, including the use of so-called "Lava Lamps" and the Intel Secure Key RDRAND instruction. We finally present our plan for generating random bits in the Amazon Web Services (AWS) environment using AES-CTR-DRBG seeded by mixing bits from /dev/urandom and the Intel Secure Key RDSEED instruction, a compromise of our desire to rely on a trusted hardware implementation, the unease of our external reviewers in trusting a hardware-only implementation, and the need to generate so many random bits.Comment: 12 pages plus 2 pages bibliograph

Location of crossings in the Floquet spectrum of a driven two-level system

Calculation of the Floquet quasi-energies of a system driven by a time-periodic field is an efficient way to understand its dynamics. In particular, the phenomenon of dynamical localization can be related to the presence of close approaches between quasi-energies (either crossings or avoided crossings). We consider here a driven two-level system, and study how the locations of crossings in the quasi-energy spectrum alter as the field parameters are changed. A perturbational scheme provides a direct connection between the form of the driving field and the quasi-energies which is exact in the limit of high frequencies. We firstly obtain relations for the quasi-energies for some common types of applied field in the high-frequency limit. We then show how the locations of the crossings drift as the frequency is reduced, and find a simple empirical formula which describes this drift extremely well in general, and appears to be exact for the specific case of square-wave driving.Comment: 6 pages, 6 figures. Minor changes to text, this version to be published in Physical Review

Algebraic Bethe ansatz method for the exact calculation of energy spectra and form factors: applications to models of Bose-Einstein condensates and metallic nanograins

In this review we demonstrate how the algebraic Bethe ansatz is used for the calculation of the energy spectra and form factors (operator matrix elements in the basis of Hamiltonian eigenstates) in exactly solvable quantum systems. As examples we apply the theory to several models of current interest in the study of Bose-Einstein condensates, which have been successfully created using ultracold dilute atomic gases. The first model we introduce describes Josephson tunneling between two coupled Bose-Einstein condensates. It can be used not only for the study of tunneling between condensates of atomic gases, but for solid state Josephson junctions and coupled Cooper pair boxes. The theory is also applicable to models of atomic-molecular Bose-Einstein condensates, with two examples given and analysed. Additionally, these same two models are relevant to studies in quantum optics. Finally, we discuss the model of Bardeen, Cooper and Schrieffer in this framework, which is appropriate for systems of ultracold fermionic atomic gases, as well as being applicable for the description of superconducting correlations in metallic grains with nanoscale dimensions. In applying all of the above models to physical situations, the need for an exact analysis of small scale systems is established due to large quantum fluctuations which render mean-field approaches inaccurate.Comment: 49 pages, 1 figure, invited review for J. Phys. A., published version available at http://stacks.iop.org/JPhysA/36/R6

Observation of associated near-side and away-side long-range correlations in √sNN=5.02 TeV proton-lead collisions with the ATLAS detector

Two-particle correlations in relative azimuthal angle (Δϕ) and pseudorapidity (Δη) are measured in √sNN=5.02  TeV p+Pb collisions using the ATLAS detector at the LHC. The measurements are performed using approximately 1  μb-1 of data as a function of transverse momentum (pT) and the transverse energy (ΣETPb) summed over 3.1<η<4.9 in the direction of the Pb beam. The correlation function, constructed from charged particles, exhibits a long-range (2<|Δη|<5) “near-side” (Δϕ∼0) correlation that grows rapidly with increasing ΣETPb. A long-range “away-side” (Δϕ∼π) correlation, obtained by subtracting the expected contributions from recoiling dijets and other sources estimated using events with small ΣETPb, is found to match the near-side correlation in magnitude, shape (in Δη and Δϕ) and ΣETPb dependence. The resultant Δϕ correlation is approximately symmetric about π/2, and is consistent with a dominant cos⁡2Δϕ modulation for all ΣETPb ranges and particle pT

Search for direct production of charginos and neutralinos in events with three leptons and missing transverse momentum in √s = 7 TeV pp collisions with the ATLAS detector

A search for the direct production of charginos and neutralinos in final states with three electrons or muons and missing transverse momentum is presented. The analysis is based on 4.7 fb−1 of proton–proton collision data delivered by the Large Hadron Collider and recorded with the ATLAS detector. Observations are consistent with Standard Model expectations in three signal regions that are either depleted or enriched in Z-boson decays. Upper limits at 95% confidence level are set in R-parity conserving phenomenological minimal supersymmetric models and in simplified models, significantly extending previous results

Measurement of χ c1 and χ c2 production with s√ = 7 TeV pp collisions at ATLAS

The prompt and non-prompt production cross-sections for the χ c1 and χ c2 charmonium states are measured in pp collisions at s√ = 7 TeV with the ATLAS detector at the LHC using 4.5 fb−1 of integrated luminosity. The χ c states are reconstructed through the radiative decay χ c → J/ψγ (with J/ψ → μ + μ −) where photons are reconstructed from γ → e + e − conversions. The production rate of the χ c2 state relative to the χ c1 state is measured for prompt and non-prompt χ c as a function of J/ψ transverse momentum. The prompt χ c cross-sections are combined with existing measurements of prompt J/ψ production to derive the fraction of prompt J/ψ produced in feed-down from χ c decays. The fractions of χ c1 and χ c2 produced in b-hadron decays are also measured

Measurements of fiducial and differential cross sections for Higgs boson production in the diphoton decay channel at s√=8 TeV with ATLAS

Measurements of fiducial and differential cross sections are presented for Higgs boson production in proton-proton collisions at a centre-of-mass energy of s√=8 TeV. The analysis is performed in the H → γγ decay channel using 20.3 fb−1 of data recorded by the ATLAS experiment at the CERN Large Hadron Collider. The signal is extracted using a fit to the diphoton invariant mass spectrum assuming that the width of the resonance is much smaller than the experimental resolution. The signal yields are corrected for the effects of detector inefficiency and resolution. The pp → H → γγ fiducial cross section is measured to be 43.2 ±9.4(stat.) − 2.9 + 3.2 (syst.) ±1.2(lumi)fb for a Higgs boson of mass 125.4GeV decaying to two isolated photons that have transverse momentum greater than 35% and 25% of the diphoton invariant mass and each with absolute pseudorapidity less than 2.37. Four additional fiducial cross sections and two cross-section limits are presented in phase space regions that test the theoretical modelling of different Higgs boson production mechanisms, or are sensitive to physics beyond the Standard Model. Differential cross sections are also presented, as a function of variables related to the diphoton kinematics and the jet activity produced in the Higgs boson events. The observed spectra are statistically limited but broadly in line with the theoretical expectations

Search for squarks and gluinos in events with isolated leptons, jets and missing transverse momentum at s√=8 TeV with the ATLAS detector

The results of a search for supersymmetry in final states containing at least one isolated lepton (electron or muon), jets and large missing transverse momentum with the ATLAS detector at the Large Hadron Collider are reported. The search is based on proton-proton collision data at a centre-of-mass energy s√=8 TeV collected in 2012, corresponding to an integrated luminosity of 20 fb−1. No significant excess above the Standard Model expectation is observed. Limits are set on supersymmetric particle masses for various supersymmetric models. Depending on the model, the search excludes gluino masses up to 1.32 TeV and squark masses up to 840 GeV. Limits are also set on the parameters of a minimal universal extra dimension model, excluding a compactification radius of 1/R c = 950 GeV for a cut-off scale times radius (ΛR c) of approximately 30

Measurement of the production of a W boson in association with a charm quark in pp collisions at √s = 7 TeV with the ATLAS detector

The production of a W boson in association with a single charm quark is studied using 4.6 fb−1 of pp collision data at s√ = 7 TeV collected with the ATLAS detector at the Large Hadron Collider. In events in which a W boson decays to an electron or muon, the charm quark is tagged either by its semileptonic decay to a muon or by the presence of a charmed meson. The integrated and differential cross sections as a function of the pseudorapidity of the lepton from the W-boson decay are measured. Results are compared to the predictions of next-to-leading-order QCD calculations obtained from various parton distribution function parameterisations. The ratio of the strange-to-down sea-quark distributions is determined to be 0.96+0.26−0.30 at Q 2 = 1.9 GeV2, which supports the hypothesis of an SU(3)-symmetric composition of the light-quark sea. Additionally, the cross-section ratio σ(W + +c¯¯)/σ(W − + c) is compared to the predictions obtained using parton distribution function parameterisations with different assumptions about the s−s¯¯¯ quark asymmetry