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1	PARTICLE REPRESENTATIONS FOR FINITE GAP OPERATORS (BAKER-AKHIEZER). SCHILLING, RANDOLPH JAMES. January 1982 (has links) It is known that finite gap potentials of Hill's equation y" + q(τ)y = Ey can be obtained as solutions of an integrable dynamical system: uncoupled harmonic oscillators constrained to move on the unit sphere in configuration space--The Neumann System. This Dissertation systematizes and generalizes this result. First, the theory of Baker-Akhiezer functions is placed on a solid mathematical foundation. Guided by the theory of Baker-Akhiezer functions and Riemann surfaces, trace formulas, particle systems, constraints, integrals and Lax pairs are systematically constructed for the particle system of the ℓ x ℓ matrix differential operator of order n. Matrices. Hill determinant. Neumann problem.
2	The derivation and quasinormal mode spectrum of acoustic anti-de sitter black hole analogues Babb, James Patrick 08 March 2013 (has links) Dumb holes (also known as acoustic black holes) are fluid flows which include an "acoustic horizon:" a surface, analogous to a gravitational horizon, beyond which sound may pass but never classically return. Soundwaves in these flows will therefore experience "effective geometries" which are identical to black hole spacetimes up to a conformal factor. By adjusting the parameters of the fluid flow, it is possible to create an effective geometry which is conformal to the Anti-de Sitter black hole spacetime- a geometry which has recieved a great deal of attention in recent years due to its conjectured holographic duality to Conformal Field Theories. While we would not expect an acoustic analogue of the AdS-CFT correspondence to exist, this dumb hole provides a means, at least in principle, of experimentally testing the theoretical properties of the AdS spacetime. In particular, I have calculated the quasinormal mode spectrum of this acoustic geometry. / Graduate / 0986 / 0753 / jpbabb@yahoo.ca Quasinormal Modes Wave Equations Acoustic Black Holes Acoustics AdS-CFT analogue gravity Anti-de Sitter Sound String Theory Fluid Mechanics Frobenius Method General Relativity Hawking Radiation Hill Determinant Einstein field equations curvature Conformal Spacetimes Black Hole Perturbation Theory

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PARTICLE REPRESENTATIONS FOR FINITE GAP OPERATORS (BAKER-AKHIEZER).

The derivation and quasinormal mode spectrum of acoustic anti-de sitter black hole analogues