Talks

When small, hard particles are suspended in a fluid, they make it more resistant to flow. The higher the particle concentration, the higher the viscosity. Add enough particles and fluid stops flowing entirely, becoming a jammed solid - this makes intuitive sense.

Less intuitive and more intriguing are suspensions that flow smoothly if pushed gently, but that suddenly solidify if you push too hard. This behaviour is called Discontinuous Shear Thickening (DST). You can try it yourself by mixing cornstarch with water - in the right proportions, the mixture will flow smoothly when stirred gently, but will refuse to flow at all if stirred too hard.

More than an interesting kitchen trick, DST has important real-world consequences. It can cause catastrophic failure of industrial pumping equipment, but can also have life-saving applications to bulletproof vests.

For many years, the mechanism behind DST was unclear, but we have very recently found a new and stunningly simple explanation based on the idea that the contacts between particles become less lubricated and more frictional as the force between them increases. Although this dependence is typically gradual, when a fluid gets close to the “jamming” point, global instabilities can result in the sudden switching from liquid to solid.

Michael Cates (Lucasian Professor of Mathematics, University of Cambridge) will explain this peculiar form of “bulletproof custard” with a few equations, plenty of diagrams, and even some hands-on demonstrations.

Non-abelian anyons have drawn much interest due to their suspected existence in two-dimensional condensed matter systems and for their potential applications in quantum computation. In particular, a quantum computation can in principle be realized by braiding and fusing certain non-abelian anyons. These operations are expected to be intrinsically robust due to their topological nature. Provided the system is kept at a
temperature T lower than the spectral gap, the density of thermal excitations is suppressed by an exponential Boltzman factor. In contrast to the topological protection however, this thermal protection is not scalable: thermal excitations do appear at constant density for any non-zero temperature and so their presence is unavoidable as the size of the computation increases. Thermally activated anyons can corrupt the encoded
data by braiding or fusing with the computational anyons.

In the present work, we generalize a fault-tolerant scheme introduced by Harrington for the toric-code to the setting of non-cyclic modular anyons. We prove that the quantum information encoded in the fusion space of a non-abelian anyon system can be preserved for arbitrarily long times with poly-log overhead. In particular, our model accounts for noise processes which lead to the creation of anyon pairs from the vacuum, anyon diffusion, anyon fusion as well as errors in topological charge measurements.
Related Arxiv #: arXiv:1607.02159

Scale invariant transfer matrices and Hamiltonians Abstract We investigate the possibility of strictly scale invariant transfer matrices in quantum spin chains based on a certain planar algebra, both as operators and as quadratic forms.

Experimentalists have recently been able to engineer non-trivial topological band structures using ultracold atoms in optical lattices.

Motivated by ongoing experimental efforts to tune interactions, we explore the interplay between strong correlations and topology in these systems. Focusing on the Haldane-Hubbard honeycomb model as an example, we show that its strongly interacting Mott limit exhibits various chiral magnetic orders, including a wide regime of triple-Q tetrahedral order. Incorporating an additional third-neighbour hopping frustrates and ultimately "quantum-melts" the tetrahedral magnetic order. From analysing low energy spectra, many-body Chern numbers, entanglement spectra, and modular matrices, we identify the molten state as a chiral spin liquid with gapped semion excitations. Our numerical results suggest that this frustration induced melting may be realised as an exotic continuous quantum phase transition. Finally, we discuss recent results which point toward a common mechanism of realising chiral spin liquids through the continuous melting of non-coplanar magnetic "parent" states.

The space of causal diamonds recently brought to attention by de Boer et al. and Czech et al. provides an organizing principle for the dependence of entanglement entropy in conformal field theories on the spatial subregion considered. I will show that the inclusion relation of causal diamonds does not give rise to a consistent notion of a causal structure and thus does not provide an alternate metric on this space. I will also show that the entanglement entropy of ball shaped regions is not enough to reconstruct the areas of higher dimensional bulk surfaces in a static geometry. Instead, I will provide a new direction for the reconstruction of the areas of bulk surfaces from boundary data in holography, using the shape derivatives of the entanglement entropy of nearly ball shaped regions.

I will discuss the properties, and constraints on, new light

particles, which appear in many extensions of the Standard Model. An

especially well motivated example is the QCD axion, and I will show how

its mass and couplings can be extracted at high precision. I will also

discuss its properties at finite temperature, and possible distinguishing

features if it makes up dark matter. More generally, strong constraints on

the couplings of new light particles to the Standard Model come from their

production in the hot cores of stars, and the effect on stellar cooling.

The large electron density in stellar cores gives large thermal effects,

and I will show how these can parametrically change the production rates

compared to a 'tree level' calculation.

We argue that moduli stabilization severely constrains the evolution following transitions between weakly coupled de Sitter vacua and can induce a strong selection bias towards inflationary cosmologies. We carefully discuss gravitational vacuum decays and resolve a naive sign ambiguity in the exponential of the decay rate. Equipped with this clear understanding of vacuum decay we then turn towards constraints on the cosmological evolution after transitions in weakly coupled flux compactifications. The energy density of domain walls between vacua typically destabilizes Kahler moduli and triggers a runaway towards large volume. This decompactification phase can collapse the new de Sitter region unless inflation lasts for more than roughly 60 efolds. High scale inflation is vastly favored. Our results illustrate the necessity to understand inflationary initial conditions at least at a basic level, before making predictions in the landscape.

In order to solve the problem of quantum gravity, we first need to pose the problem. In this talk I will argue that the problem of quantum gravity arises already in the domain of quantum mechanics and the relativity principle. Specifically, the relativity principle implies that the concept of inertial motion should extend also to those systems that are in quantum superpositions of inertial motions. By contrast, relativistic quantum field theory only considers the point of view of classical observers in states of definite relative motion (i.e. the observers of a quantum field do not include inertial observers in quantum superpositions). The problem is that, if we extend the class of inertial observers to include quantum observers, the manifold of local events becomes ill-defined, as `locality' itself becomes an observer-relative property of an event. Thus, the Relativity Principle and the Superposition Principle are jointly opposed to the concept of a space-time manifold of local events, and our understanding of relativistic quantum theory needs to be revised before gravity even enters the picture.

In this talk, I will address a major conceptual and technical concern of non-perturbative quantum gravity: the quantum superposition of causal structures of space-times. I will discuss a class of theories that can address the problem, their flaws, and their relation to general relativity.

The Wigner-Eckart theorem is a well known result for tensor operators of SU(2) and, more generally, any compact Lie group. I will show how it can be generalised to arbitrary Lie groups, possibly non-compact. The result relies on the knowledge of recoupling theory between finite-dimensional and arbitrary admissible representations, which may be infinite-dimensional; the particular case of the Lorentz group will be studied in detail. As an application, the Wigner-Eckart theorem will be used to construct an analogue of the Jordan-Schwinger representation, previously known only for finite-dimensional representations of the Lorentz group, valid for infinite-dimensional ones.