Uncovering Ramanujan's "Lost" Notebook: An Oral History

Here we weave together interviews conducted by the author with three prominent figures in the world of Ramanujan's mathematics, George Andrews, Bruce Berndt and Ken Ono. The article describes Andrews's discovery of the "lost" notebook, Andrews and Berndt's effort of proving and editing Ramanujan's notes, and recent breakthroughs by Ono and others carrying certain important aspects of the Indian mathematician's work into the future. Also presented are historical details related to Ramanujan and his mathematics, perspectives on the impact of his work in contemporary mathematics, and a number of interesting personal anecdotes from Andrews, Berndt and Ono

Hamiltonian Analysis of Non-Linear Sigma Model on Supercoset Target

This paper is devoted to the study of the Hamiltonian formulation of non-linear sigma models on supercoset targets. We calculate the Poisson brackets of left-invariant currents. Then we introduce the Hamiltonian of the system and determine the equations of motion for left-invariant currents. We also determine the charge corresponding to the invariance of the action under global left multiplication.Comment: 17. pages,v2: references added, v3: references added, minor correction

Nonlocal charges of T-dual strings

We obtain sets of infinite number of conserved nonlocal charges of strings in a flat space and pp-wave backgrounds, and compare them before and after T-duality transformation. In the flat background the set of nonlocal charges is the same before and after the T-duality transformation with interchanging odd and even-order charges. In the IIB pp-wave background an infinite number of nonlocal charges are independent, contrast to that in a flat background only the zero-th and first order charges are independent. In the IIA pp-wave background, which is the T-dualized compactified IIB pp-wave background, the zero-th order charges are included as a part of the set of nonlocal charges in the IIB background. To make this correspondence complete a variable conjugate to the winding number is introduced as a Lagrange multiplier in the IIB action a la Buscher's transformation.Comment: 23 pages, 1 figur

Integrability of Type II Superstrings on Ramond-Ramond Backgrounds in Various Dimensions

We consider type II superstrings on AdS backgrounds with Ramond-Ramond flux in various dimensions. We realize the backgrounds as supercosets and analyze explicitly two classes of models: non-critical superstrings on AdS_{2d} and critical superstrings on AdS_p\times S^p\times CY. We work both in the Green--Schwarz and in the pure spinor formalisms. We construct a one-parameter family of flat currents (a Lax connection) leading to an infinite number of conserved non-local charges, which imply the classical integrability of both sigma-models. In the pure spinor formulation, we use the BRST symmetry to prove the quantum integrability of the sigma-model. We discuss how classical \kappa-symmetry implies one-loop conformal invariance. We consider the addition of space-filling D-branes to the pure spinor formalism.Comment: LaTeX2e, 56 pages, 1 figure, JHEP style; v2: references added, typos fixed in some equations; v3: typos fixed to match the published versio

Mineral exploration in the Cockermouth area, Cumbria. Part 2: follow-up surveys

This report describes the results of geochemical, geological and geophysical surveys across three small areas of Carboniferous and Lower Palaeozoic rocks along the northern margin of the English Lake District. The areas were chosen from the appraisal of regional-scale survey data described by Cooper et al. (1991). In two of the areas, Ruthwaite and Tallentire, the objective was to provide more information on the extent and magnitude of fracture-controlled epigenetic baryte and base metal mineralisation. In the third area, at Whitrigg, brief surveys were carried out to aid the interpretation of unexplained geochemical and geophysical anomalies found during two projects carried out under the Mineral Exploration and Investment Grants Act (MEIGA). At Ruthwaite, where a mine formerly worked baryte from a fault separating Lower Palaeozoic and Carboniferous rocks, surface indications of further baryte mineralisation were found. Soil analyses indicated that mineralisation may be present along the continuation of the faultline worked at Ruthwaite and in the Eycott Volcanic Group rocks to the south of it. In this area relatively small, but in some circumstances perhaps economically attractive, deposits of baryte may be present under drift cover. In the Tallentire Hill area, geological mapping followed by traverse-based soil sampling showed that fracture-controlled mineralisation is widespread in the Carboniferous (Dinantian and Namurian) rocks. The fracture fillings consist dominantly of baryte, often accompanied by carbonate, with traces of copper and mercury. Where seen at surface the fracture fillings are too small, patchy and low-grade to be of any economic importance. Baryte mineralisation also occurs locally as patchy impregnations in sandstones. These are considered to be epigenetic deposits related to the fracture-controlled mineralisation. Trial geophysical surveys suggested that electrical methods may be useful in determining the extent of the mineralised sandstone. There is a possibility that more extensive baryte deposits may be present in the limestone succession underlying the mineralised sandstones. In the Whitrigg area, Carboniferous rocks are separated from Lower Palaeozoic rocks of the Eycott Volcanic Group by the easterly-trending Boundary Fault and north-westerly-trending Bothel Fault. Evidence from an old mineral working and the results of a soil survey indicate that patchy, epigenetic, fracture-controlled baryte and base metal mineralisation occurs along the Bothel Fault and, locally, in the adjacent rocks. A feature of this mineralisation is the presence of mercury, which is most abundant in a sample of brecciated and altered rock from the Eycott Volcanic Group. Prominent base metal in soil anomalies discovered by MEIGA-funded projects near Stangerhill are not associated with barium anomalies. It was concluded that these soil anomalies are most likely to be caused by secondary concentration in overburden, and that the source of metals may be a sub-cropping metalliferous horizon within the Carboniferous succession or, more probably, fracture-controlled mineralisation. Trial geophysical surveys carried out in all three areas indicated that in ground free of artificial sources the VLF(EM) and conductivity mapping methods could be useful for tracing faults beneath drift and providing information on drift thickness. Closely-spaced soil sampling proved effective for detecting mineralisation in areas where the drift cover is thin, and a trial soil-gas survey showed that this technique could also be useful for tracing faults beneath drift

Determining Reheating Temperature at Colliders with Axino or Gravitino Dark Matter

After a period of inflationary expansion, the Universe reheated and reached full thermal equilibrium at the reheating temperature T_R. In this work we point out that, in the context of effective low-energy supersymmetric models, LHC measurements may allow one to determine T_R as a function of the mass of the dark matter particle assumed to be either an axino or a gravitino. An upper bound on their mass may also be derived.Comment: 19 pages, some improvements, JHEP versio

Rms-flux relation in the optical fast variability data of BL Lacertae object S5 0716+714

The possibility that BL Lac S5 0716+714 exhibits a linear root mean square (rms)-flux relation in its IntraDay Variability (IDV) is analysed. The results may be used as an argument in the existing debate regarding the source of optical IDV in Active Galactic Nuclei. 63 time series in different optical bands were used. A linear rms-flux relation at a confidence level higher than 65% was recovered for less than 8% of the cases. We were able to check if the magnitude is log-normally distributed for eight timeseries and found, with a confidence > 95%, that this is not the case.Comment: Accepted by Astrophysics and Space Scienc

Optical fibers with interferometric path length stability by controlled heating for transmission of optical signals and as components in frequency standards

We present a simple method to stabilize the optical path length of an optical fiber to an accuracy of about 1/100 of the laser wavelength. We study the dynamic response of the path length to modulation of an electrically conductive heater layer of the fiber. The path length is measured against the laser wavelength by use of the Pound-Drever-Hall method; negative feedback is applied via the heater. We apply the method in the context of a cryogenic resonator frequency standard.Comment: Expanded introduction and outlook. 9 pages, 5 figure

The Hubble Space Telescope Wide Field Camera 3 Early Release Science data: Panchromatic Faint Object Counts for 0.2-2 microns wavelength

We describe the Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3) Early Release Science (ERS) observations in the Great Observatories Origins Deep Survey (GOODS) South field. The new WFC3 ERS data provide calibrated, drizzled mosaics in the UV filters F225W, F275W, and F336W, as well as in the near-IR filters F098M (Ys), F125W (J), and F160W (H) with 1-2 HST orbits per filter. Together with the existing HST Advanced Camera for Surveys (ACS) GOODS-South mosaics in the BViz filters, these panchromatic 10-band ERS data cover 40-50 square arcmin at 0.2-1.7 {\mu}m in wavelength at 0.07-0.15" FWHM resolution and 0.090" Multidrizzled pixels to depths of AB\simeq 26.0-27.0 mag (5-{\sigma}) for point sources, and AB\simeq 25.5-26.5 mag for compact galaxies. In this paper, we describe: a) the scientific rationale, and the data taking plus reduction procedures of the panchromatic 10-band ERS mosaics; b) the procedure of generating object catalogs across the 10 different ERS filters, and the specific star-galaxy separation techniques used; and c) the reliability and completeness of the object catalogs from the WFC3 ERS mosaics. The excellent 0.07-0.15" FWHM resolution of HST/WFC3 and ACS makes star- galaxy separation straightforward over a factor of 10 in wavelength to AB\simeq 25-26 mag from the UV to the near-IR, respectively.Comment: 51 pages, 71 figures Accepted to ApJS 2011.01.2

A high stability semiconductor laser system for a 88^{88}Sr-based optical lattice clock

We describe a frequency stabilized diode laser at 698 nm used for high resolution spectroscopy of the 1S0-3P0 strontium clock transition. For the laser stabilization we use state-of-the-art symmetrically suspended optical cavities optimized for very low thermal noise at room temperature. Two-stage frequency stabilization to high finesse optical cavities results in measured laser frequency noise about a factor of three above the cavity thermal noise between 2 Hz and 11 Hz. With this system, we demonstrate high resolution remote spectroscopy on the 88Sr clock transition by transferring the laser output over a phase-noise-compensated 200 m-long fiber link between two separated laboratories. Our dedicated fiber link ensures a transfer of the optical carrier with frequency stability of 7 \cdot 10^{-18} after 100 s integration time, which could enable the observation of the strontium clock transition with an atomic Q of 10^{14}. Furthermore, with an eye towards the development of transportable optical clocks, we investigate how the complete laser system (laser+optics+cavity) can be influenced by environmental disturbances in terms of both short- and long-term frequency stability.Comment: 9 pages, 9 figures, submitted to Appl. Phys.