Talks

Usually, quantum theory (QT) is introduced by giving a list of abstract mathematical postulates, including the Hilbert space formalism and the Born rule. Even though the result is mathematically sound and in perfect agreement with experiment, there remains the question of why this formalism is a natural choice, and how QT could possibly be modified in a consistent way. My talk is on recent work with Lluis Masanes, where we show that five simple operational axioms actually determine the formalism of QT uniquely. This is based to a large extent on Lucien Hardy's seminal work. We start with the framework of "general probabilistic theories", a simple, minimal mathematical description for outcome probabilities of measurements. Then, we use group theory and convex geometry to show that the state space of a bit must be a 3D (Bloch) ball, finally recovering the Hilbert space formalism. There will also be some speculation on how to find natural post-quantum theories by dropping one of the axioms.

It is commonly believed that the current problems in the capital markets are a result of the financial models developed by academic mathematicians and industry practitioners. In fact, many of us have been pointingout for years that banks were involved in very risky activities, which produced illusory short term profits. In this talk, I will give a short introduction to the theory behind pricing and hedging derivative contracts (options). A derivative contract is based on an underlying asset. The standard model for the underlying asset price movement assumes that prices evolve according to a random walk with a drift. It is possible for an option seller to set up a hedging portfolio, which is then dynamically rebalanced in response to changes in the underlying asset price. Then, regardless of the random movement of the asset price, the seller of the option is able to pay out the value of the this contract at expiry. There is strong evidence that the normal market behavior assumed by standard models is punctuated by occasional large jumps or drops in prices (e.g. subprime mortgages). These processes are called "jump diffusion" models. A simulation of a trading strategy which exploits these market characteristics shows that bankers can produce apparent profits for many years, followed by enormous losses. The compensation system widely used in the financial sector encourages these sorts of activities. In essence, this bonus system allows executives and traders to be rewarded for apparent short term profits, and to walk away unscathed after producing staggering losses.

I propose late-time moduli decay as the common origin of baryons and dark matter. The baryon asymmetry is produced from the decay of new TeV scale particles, while dark matter is created from the chain decay of R-parity odd particles. The baryon and dark matter abundances are mainly controlled by the dilution factor from moduli decay, which is typically in the range 10^{-9}-10^{-7}. The exact number densities are determined by simple branching fractions from modulus decay, which are expected to be of similar order in the absence of symmetries. This scenario can naturally lead to the observed baryon asymmetry and, for moderate suppression of the two-body decays of the modulus to R-parity odd particles, can also yield the correct dark matter abundance in the 5-500 GeV mass range. I will present an explicit model for late-time baryogenesis along this line and discuss some of its cosmological and phenomenological consequences.

We review situations under which a standard quantum adiabatic condition fails. We reformulate the problem of adiabatic evolution as the problem of Hamiltonian eigenpath traversal, and give convergence conditions in terms of the length of the eigenpath and the minimum energy gap of the Hamiltonians. We introduce a randomized evolution method that can be used to traverse the eigenpath and prove its convergence and cost. We then describe more efficient methods for the same task and show that their implementation complexity is close to optimal.

The DEAP-3600 single-phase liquid-argon dark matter detector is under construction at SNOLAB. The fundamental goal of the design is to increase the volume of the detector while having the liquid argon contact the smallest possible surface comprising only clean acrylic and wavelength shifter. Specifically DEAP-3600 is a spherical detector with a 1000 kg fiducial mass and a design background rate less than 0.1 events in the WIMP region of interest in three years of data taking. Design sensitivity to WIMP dark matter at 100 GeV is 10-46 cm2. In order to achieve this ambitious goal an extensive program of background reduction and control is underway for all detector components including the acrylic vessel, process system, photomultiplier tubes and TPB wavelength shifter. Efforts to obtain acrylic with bulk Uranium and Thorium contamination below 0.3 and 1.3 ppt respectively and Pb-210 contamination below 1.1x10-8 ppt will be described. A resurfacer is under development to ensure that the surface contamination of acrylic is removed. Even with these stringent controls fiducialization will be required to reduce surface backgrounds by a factor of 1000. Preliminary studies are promising. We have operated the DEAP-1 prototype detector underground at SNOLAB; results from the DEAP-1 runs will be discussed and the impact of those runs on DEAP-3600 will be discussed. SNOLAB has recently made the “phase 2” expansion (including the cryopit and two drifts) part of the clean space. A photo essay showing recent progress in the facility and the experimental program will be presented.

The standard method to study nonperturbative properties of quantum field theories is to Wick rotate the theory to Euclidean space and regulate it on a Euclidean Lattice. An alternative is "fuzzy field theory". This involves replacing the lattice field theory by a matrix model that approximates the field theory of interest, with the approximation becoming better as the matrix size is increased. The regulated field theory is one on a background noncommutative space. I will describe how this method works and present recent progress and surprises.