Higgs Bundles, Gauge Theories and Quantum Groups

The appearance of the Bethe Ansatz equation for the Nonlinear Schr\"{o}dinger equation in the equivariant integration over the moduli space of Higgs bundles is revisited. We argue that the wave functions of the corresponding two-dimensional topological U(N) gauge theory reproduce quantum wave functions of the Nonlinear Schr\"{o}dinger equation in the $N$-particle sector. This implies the full equivalence between the above gauge theory and the $N$-particle sub-sector of the quantum theory of Nonlinear Schr\"{o}dinger equation. This also implies the explicit correspondence between the gauge theory and the representation theory of degenerate double affine Hecke algebra. We propose similar construction based on the $G/G$ gauged WZW model leading to the representation theory of the double affine Hecke algebra. The relation with the Nahm transform and the geometric Langlands correspondence is briefly discussed.Comment: 48 pages, typos corrected, one reference adde

Gigahertz optoacoustic imaging for cellular imaging

Photoacoustic imaging exploits contrast mechanisms that depend on optical and thermomechanical properties of optical absorbers. The photoacoustic signal bandwidth is dictated by the absorber size and the laser pulse width. In this work we demonstrate that photoacoustic signals can be detected from micron and sub-micron particles. We anticipate applications to include cellular imaging with nanometer sized contrast agents such as gold nanoshells, nanorods, and nanocages. An existing acoustic microscopy system was used (the SASAM 1000, kibero GmbH). This platform is developed on an Olympus IX81 optical microscope with a rotating column that has an optical condenser for transmission optical microscopy and an acoustic module for the acoustic microscopy. The adapted optoacoustic module consists of a Qswitched Nd:YAG solid-state-laser (Teem Photonics, France) generating sub-nanosecond pulses. Scans were acquired of microparticles (1 µm black Toner particles) and cells. The confocal arrangement allowed high signal to noise ratio photoacoustic signals (>30 dB) to be detected at approximately 400 MHz. The particles of various sizes produced signals of different frequency content. In imaging mode, the full width half maximum (FWHM) was measured to be 3.6 µm for the 400 MHz transducer which is in general agreement theory for a 0.3 NA objective (4.3µm). Moreover, images are generated from single melanoma cells, generated by the endogenous contrast from the intracellular melanin