# My thesis

My thesis was on: "The Diffusion-Advection Model: The Role of Non-Hermiticity" by Ian Baynham.

Abstract:

The main part of this thesis is on how the non-Hermiticty of the diffusion-advection model effects its long-time diffusive transport behaviour in the critical dimension d=2. Original calaulations did not properly take into account the non-Hermiticity. We build an approach that takes into account non-hermiticity and allows for a consistent sum of logarithmic corrections. We use an extended space, like in [Chalker-Wang], which (after the rotation exp (i π σ2/4)) is formally equivalent to Nambu-Gorkov space. We found that the transport behaviour was not corrected and that the boundary to the density of complex eigenvalues collapsed to the real line as \omega tends to zero. We also investigated mesoscopic fluctuations in density distribution and found it to have log-normal tails.

# Some pieces of mathematics

• Irreducible representations of SU(2) from the space of homogeneous polynomials of two complex variables
(pdf file , ps file).
• Active diffeomorphisms and the Lie derivative
(pdf file , ps file).
• Fock-Bargmann representation - an exercise in complex analysis
(pdf file , ps file).
• Spin networks
(pdf file , ps file).

# Some undergraduate Physics and Mathematics notes

Fluid Mechanics (pdf file, ps file) (not quite finished).