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A new ensemble interpretation of quantum mechanics is proposed according to which the ensemble associated to a quantum state really exists: it is the ensemble of all the systems in the same quantum state in the universe. Individual systems within the ensemble have microscopic states, described by beables. The probabilities of quantum theory turn out to be just ordinary relative frequencies probabilities in these ensembles. Laws for the evolution of the beables of individual systems are given such that their ensemble relative frequencies evolve in a way that reproduces the predictions of quantum mechanics. These laws are highly non-local and involve a new kind of interaction between the members of an ensemble that define a quantum state. These include a stochastic process by which individual systems copy the beables of other systems in the ensembles of which they are a member. The probabilities for these copy processes do not depend on where the systems are in space, but do depend on the distribution of beables in the ensemble. Macroscopic systems then are distinguished by being large and complex enough that they have no copies in the universe. They then cannot evolve by the copy law, and hence do not evolve stochastically according to quantum dynamics. This implies novel departures from quantum mechanics for systems in quantum states that can be expected to have few copies in the universe. At the same time, we are able to argue that the centre of masses of large macroscopic systems do satisfy Newton's laws.

After quickly reviewing what we have learned about neutrinos during the past decade, I present an overview of different mechanisms responsible for non-zero neutrino masses, also discussing the possibility of experimentally deciding which one, if any, is correct.

One of the key features of the quantum Hall effect (QHE) is the fractional charge and statistics of quasiparticles. Fractionally charged anyons accumulate non-trivial phases when they encircle each other. In some QHE systems an unusual type of particles, called non-Abelian anyons, is expected to exist. When one non-Abelian particle makes a circle around another anyon this changes not only the phase but even the direction of the quantum-state vector in the Hilbert space. This property makes non-Abelian anyons promising for fault-tolerant quantum computation. Several experiments allowed an observation of fractional charges. Probing exchange statistics is more difficult and has not been accomplished for identical anyons so far. We will discuss how the statistics can be probed with Mach-Zehnder interferometry, tunneling experiments and far-from-equilibrium fluctuation-dissipation theorem.

I will discuss the growth of entanglement under a quantum quench at point contacts of simple fractional quantum Hall fluids and its relation with the measurement of local observables. Recently Klich and Levitov recently proposed that, for a free fermion system, the noise generated from a local quantum quench provides a measure of the entanglement entropy. In this work, I will examine the validity of this proposal in the context of a strongly interacting system, the Laughlin FQH states. We find that local quenching in fractional quantum Hall junctions gives time dependent correlation functions that have universal behavior on sufficiently long time and length scales. The growth of entanglement entropy and the noise generated by the quench are generally unrelated quantities.

The spin 1/2 Heisenberg model on a triangular lattice with interchain exchange, J', weaker than the intrachain exchange J, is a particularly well-studied frustrated magnet because of its relevance to Cs2CuCl4, which is thought to be in close proximity to a spin liquid phase. Although an incomensurate spiral state is stable for J'~J, a variet of theoretical studies find evidence for spin liquid behavior well before the decoupled chain limit, J'=0, is reached. However, a renormalization group approach found the surprising result that a collinear antiferromagnetic phase was stable for small J'/J. This talk will briefly review earlier studies and present new results on the relative stability of spiral, collinear and spin liquid phases.

Very recently, it has been recognized that excitations out of the ground state of materials known as spin ice can be viewed as magnetic monopoles, the magnetic analog to electric charges. Like electrons and positrons, these particles possess a charge of +Q or -Q and therefore attract or repel each other. Magnetic monopoles, however, can be accelerated using a magnetic field instead of an electric field. In this talk, I will report on experiments deep into the frozen state of the spin ice material holmium titanate where monopoles are few and far between and the material responds very slowly to a changing magnetic field. Taking advantage of the extremely sensitive magnetic field detector known as a superconducting quantum interference device (SQUID), we measure the rate at which the monopoles are created, move about and are eventually annihilated. A surprisingly simple law emerges at low temperatures, known as an Arrhenius law, suggesting that the generation of these magnetic charges requires an energy that does not change in temperature and for a yet unknown reason, is precisely 3 times the energy required to make a single, bare monopole.

We begin with a fundamental approach to quantum mechanics based on the unitary representations of the group of diffeomorphisms of physical space (and correspondingly, self-adjoint representations of a local current algebra). From these, various classes of quantum configuration spaces arise naturally. One obtains in addition the usual exchange statistics for spatial dimension d >2, induced by representations of the symmetric group, while for d = 2, the approach led to an early prediction of intermediate or “anyonic” statistics induced by unitary representations of the braid group. After reviewing these ideas, which are based on joint work with R. Menikoff and D. H. Sharp at Los Alamos National Laboratory, we shall discuss briefly some analogous possibilities for infinite-dimensional configuration spaces, including anyonic statistics for extended objects in 3-dimensional space.

Geometrical frustration in magnetic systems provides a rich playground to study the emergence of novel ground states. In systems where not all magnetic couplings can be simultaneously satisfied, conventional long range magnetic order is often precluded, or pushed to much lower emperature scales than would be expected from the strength of the magnetic interactions. Dy2Ti2O7 has a pyrochlore lattice, where the magnetic Dy ions lie on the vertices of corner sharing tetrahedra. The Dy magnetic moments are constrained by crystal fields to lie along local <111> axes, pointing towards or away from the tetrahedral centres. With a ferromagnetic interaction between nearest neighbours, the ground state for each tetrahedron has two spins pointing in and two out. Due to the number of possible ways of satisfying this constraint, the overall ground state is highly degenerate; in fact this system can be mapped onto the problem of water ice where each oxygen atom has two strongly bound and two weakly bound protons, leading the magnetic problem to be referred to as spin ice. Recent theoretical work in understanding the magnetic excitation in spin ice, where the spin flip excitations can be described in terms of magnetic monopoles. Bramwell et al., reported muon spin rotation measurements of spin ice which they interpreted in terms of this monopole picture. In contrast to the work of Bramwell et al., our muon spin relaxation measurements do not exhibit highly temperature dependent Arrhenius processes expected for monopoles. Instead we report temperature independent spin fluctuations well into the spin ice state and that the previous interpretations are incorrect.

Utilizing the Baym-Kadanoff formalism with the polarization function calculated in the random phase approximation, the dynamics of the ν=0, ±1, ±2, ±3, ±4 quantum Hall states in bilayer graphene is analyzed. In particular, in the undoped graphene, corresponding to the ν =0 state, two phases with nonzero energy gap, the ferromagnetic and layer asymmetric ones, are found. The phase diagram in the plane (Δ0,B), where Δ0 is a top-bottom gates voltage imbalance, is described. It is shown that the energy gaps in these phases scale linearly, ΔE~10 B [T] K, with magnetic field. The ground states of the doped states, with ν=±1, ±2, ±3, ±4, are also described. The comparison of these results with recent experiments in bilayer graphene is presented.