Past Quantum Field Theory Seminar

The problem of Anderson localization in graphene

has generated a lot of renewed attention since graphene flakes

have been accessible to transport and spectroscopic probes.

The popularity of graphene derives from it realizing planar Dirac

fermions. I will show under what conditions disorder for

planar Dirac fermions does not result in localization but rather in a

metallic state that might be called a topological metal.

We demonstrate a scheme for controlling a large quantum system by acting

on a small subsystem only. The local control is mediated to the larger

system by some fixed coupling Hamiltonian. The scheme allows to transfer

arbitrary and unknown quantum states from a memory to the large system

("upload access") as well as the inverse ("download access").

We give sufficient conditions of the coupling Hamiltonian for the

controllability

of the system which can be checked efficiently by a colour-infection game on

the graph

that describes the couplings.

Modern molecular biology research produces data on a massive scale. This

data

is predominantly high-dimensional, consisting of genome-wide measurements of

the transcriptome, proteome and metabalome. Analysis of these data sets

often

face the additional problem of having small sample sizes, as experimental

data

points may be difficult and expensive to come by. Many analysis algorithms

are

based upon estimating the covariance structure from this high-dimensional

small sample size data, with the consequence that the eigenvalues and eigenvectors

of

the estimated covariance matrix are markedly different from the true values.

Techniques from statistical physics and Random Matrix Theory allow us to

understand how these discrepancies in the eigenstructure arise, and in

particular locate the phase transition points where the eigenvalues and

eigenvectors of the estimated covariance matrix begin to genuinely reflect

the

underlying biological signals present in the data. In this talk I will give

a

brief non-specialist introduction to the biological background motivating

the

work and highlight some recent results obtained within the statistical

physics

approach.

We provide both a diagrammatic and logical system to reason about

quantum phenomena. Essential features are entanglement, the flow of

information from the quantum systems into the classical measurement

contexts, and back---these flows are crucial for several quantum informatic

scheme's such as quantum teleportation---, and mutually unbiassed

observables---e.g. position and momentum. The formal structures we use are

kin to those of topological quantum field theories---e.g. monoidal

categories, compact closure, Frobenius objects, coalgebras. We show that

our diagrammatic/logical language is universal. Informal

appetisers can be found in:

* Introducing Categories to the Practicing Physicist

http://web.comlab.ox.ac.uk/oucl/work/bob.coecke/Cats.pdf

* Kindergarten Quantum Mechanics

http://arxiv.org/abs/quant-ph/0510032

Apologies - this seminar is CANCELLED