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

Two-Electron Photon Emission From Metallic Quantum Wells

Unusual emission of visible light is observed in scanning tunneling microscopy of the quantum well system Na on Cu(111). Photons are emitted at energies exceeding the energy of the tunneling electrons. Model calculations of two-electron processes which lead to quantum well transitions reproduce the experimental fluorescence spectra, the quantum yield, and the power-law variation of the intensity with the excitation current.Comment: revised version, as published; 4 pages, 3 figure

q-Newton binomial: from Euler to Gauss

A counter-intuitive result of Gauss (formulae (1.6), (1.7) below) is made less mysterious by virtue of being generalized through the introduction of an additional parameter

Phase operators, phase states and vector phase states for SU(3) and SU(2,1)

This paper focuses on phase operators, phase states and vector phase states for the sl(3) Lie algebra. We introduce a one-parameter generalized oscillator algebra A(k,2) which provides a unified scheme for dealing with su(3) (for k < 0), su(2,1) (for k > 0) and h(4) x h(4) (for k = 0) symmetries. Finite- and infinite-dimensional representations of A(k,2) are constructed for k < 0 and k > 0 or = 0, respectively. Phase operators associated with A(k,2) are defined and temporally stable phase states (as well as vector phase states) are constructed as eigenstates of these operators. Finally, we discuss a relation between quantized phase states and a quadratic discrete Fourier transform and show how to use these states for constructing mutually unbiased bases

New limits on "odderon" amplitudes from analyticity constraints

In studies of high energy $pp$ and $\bar pp$ scattering, the odd (under crossing) forward scattering amplitude accounts for the difference between the $pp$ and $\bar pp$ cross sections. Typically, it is taken as $f_-=-\frac{p}{4\pi}Ds^{\alpha-1}e^{i\pi(1-\alpha)/2}$ ($\alpha\sim 0.5$), which has $\Delta\sigma, \Delta\rho\to0$ as $s\to\infty$, where $\rho$ is the ratio of the real to the imaginary portion of the forward scattering amplitude. However, the odd-signatured amplitude can have in principle a strikingly different behavior, ranging from having $\Delta\sigma\to$non-zero constant to having $\Delta\sigma \to \ln s/s_0$ as $s\to\infty$, the maximal behavior allowed by analyticity and the Froissart bound. We reanalyze high energy $pp$ and $\bar pp$ scattering data, using new analyticity constraints, in order to put new and precise limits on the magnitude of ``odderon'' amplitudes.Comment: 13 pages LaTex, 6 figure