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Friday, April 10th 2009

2:30 pm:

The common wisdom suggests that simple small field models of inflation share similar properties such as red spectral index, undetectable gravitational waves (GW), undetectable running of the spectral index and undetectable non-gaussianity. In this talk I will explain the reasons for these properties and show that all of them are due to oversimplification of the models. I will demonstrate how one can design small single field models which cover all the parameter space allowed by WMAP5, for example, a small field model with detectable GW of r=0.2. Moreover, these models exhibit detectable non-gaussianity of f_{NL}>5 without exiting the slow-roll regime, making them easy targets for detection.

Friday, October 2nd 2009

11:00 am:

Abstract:

We propose a Gaussian scalar field theory in a curved 2-D metric with an event horizon as the low-energy effective theory for a weakly confined, invariant Random Matrix ensemble. The presence of an event horizon naturally generates Hawking radiation, which introduces a finite temperature in the model in a non-trivial way. A similar mapping with a gravitational analogue model has been constructed for a Bose-Einstein condensate pushed to flow at a velocity higher than its speed of sound, with Hawking radiation as sound waves propagating over the cold atoms. All these systems share the same non-trivial 2-point correlation function, which breaks translational invariance. Our work suggests a three-fold connection between a moving BEC system, black-hole physics and unconventional RMEs.

Monday, December 7th 2009

2:00 pm:

It is shown that the Smorodinsky-Winternitz potential, BC_2 rational model, 3-body Calogero model, Wolves potential are all the members of a continuous family of planar solvable and integrable Schroedinger equations marked by some continuous parameter. Their spectra is always linear in quantum numbers. Hidden algebra of the family for integer values of the parameter is uncovered. It is non-semi-simple Lie algebra gl(2)x R^{k+1} realized as vector fields on line bundles over k-Hirzebruch surface. Obtained potential admits quasi-exactly solvable (QES) generalization with the same hidden algebra gl(2) x R^{k+1}. The question about super-integrability of the QES potential remain open yet.Classical-mechanical analogue of the family is presented. It has a property of integrability while the solvability is replaced by a feature that all finite trajectories are closed.

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