Search Talks

We study the possibility of a self-correcting quantum memory based on stabilizer codes with geometrically-local stabilizer generators. We prove that the distance of such stabilizer codes in D dimensions is bounded by O(L^{D-1}) where L is the linear size of the D-dimensional lattice. In addition, we prove that in D=1 and D=2, the energy barrier separating different logical states is upper-bounded by a constant independent of L. This shows that in such systems there is no natural energy dissipation mechanism which prevents errors from accumulating. Our results are in contrast with the existence of a classical 2D self-correcting memory, the 2D Ising ferromagnet.

The “clock ambiguity” is a general feature of standard formulations of quantum gravity, as well as a much wider class of theoretical frameworks. The clock ambiguity completely undermines any attempt at uniquely specifying laws of physics at the fundamental level. In this talk I explain in simple terms how the clock ambiguity arises. I then present a number of concrete results which suggest that a statistical approach to physical laws could allow sharp predictions to emerge despite the clock ambiguity. Along the way, I get to ask some interesting questions about what we expect of fundamental laws of physics, and give some surprising answers.

We start by studying the non-computational geometry of fractionally-dimensioned measure-zero dynamically-invariant subsets of phase space, associated with certain deterministic nonlinear dissipative dynamical systems. Then, by studying the asymptotic states of the Hawking Box, the existence of such invariant subsets is conjectured for gravitationally-bound systems. The argument hinges around the phase-space properties of black holes. Like Penrose, it is assumed that phase-space volumes shrink when the contents of the Hawking Box contain black holes. However, unlike Penrose, we do not argue for any corresponding phase-space divergence when the Box does not contain black holes. We now make the hypothesis that these invariant phase-space subsets play a primitive role in fundamental physics; specifically that the state of the universe (“reality”) lies on such an invariant subset (now and hence forever). Attention is focussed on the implications of this hypothesis for the foundations of quantum theory. For example, what are referred to as “measurements” of the quantum state, are defined in terms of symbolic dynamics on the invariant set, relative to some partition of the invariant set. This immediately leads to the notion that any theory which treats these invariant sets as primitive, must be contextual (since counterfactual perturbations almost certainly take states off the measure-zero invariant set and hence to “unreal” regions of phase space where the symbolic partition is undefined). This in turn leads to a new perspective, both on the foundations of quantum theory and on the role of gravity in formulating these foundations. In particular, a measurement-free Neo-Copenhagen Interpretation of quantum theory, based on the Invariant Set Hypothesis will be presented.

In this talk I will discuss gravitational wave production by early universe sources. I will focus on the gravitational waves produced by a network of cosmic strings and the bounds that can be placed on cosmic string model parameters using current and future experiments. I will also talk about recent work on gravitational waves produced by sources in the early universe when the expansion of the universe cannot be neglected. As an example of such a process I will consider the preheating epoch that may follow inflation.

The discovery of integrability in the large N limit of the prototypical realization of the AdS/CFT correspondence has raised the hope that the spectrum of scale dimensions in N=4 SYM (and strings in AdS_5 x S^5) might be known exactly, i.e. to all orders in the coupling constant. So far, most of the efforts focused on closed strings and periodic boundary conditions. In this talk I will discuss how these ideas are extended to open string and open boundary conditions. In particular how to obtain exact expressions for the boundary scattering matrices, discuss the integrability of the boundary conditions and how finite size effects may be taken into account.

In the closed system setting I will show how to obtain extremely accurate adiabatic QC by proper choice of the interpolation between the initial and final Hamiltonians. Namely, given an analytic interpolation whose first N initial and final time derivatives vanish, the error can be made to be smaller than 1/N^N, with an evolution time which scales as N and the square of the norm of the time-derivative of the Hamiltonian, divided by the cube of the gap (joint work with Ali Rezakhani and Alioscia Hamma). In the open system setting I will describe a method for protecting adiabatic QC by use of a hybrid encoding-dynamical decoupling scheme. This strategy can be used to protect spin-based universal adiabatic QC against arbitrary 1-local noise using only global magnetic fields. By combining error bounds for the closed and open system settings, I will show that in principle the method is scalable to arbitrarily large computations. References: Closed system case: arXiv:0808.2697 Open system case: Phys. Rev. Lett. 100, 160506 (2008)

I\'ll discuss three promising upcoming experimental measurements that will probe the expansion history of the universe: (1) growth bases tests of Dark Energy with the Sunyaev-Zeldovich Effect, including new results from the South Pole Telescope and APEX-SZ, (2) inflationary constraints that will be provided by the next generation of CMB-polarization experiments, with prospects from EBEX, and (3) standard ruler measurements from Baryon Acoustic oscillations, including an introduction to an ambitious new Canadian Hydrogen Intensity Mapping initiative called CHIME. The talk will build on the PI-presentation last week from SPT-collaborator Jeff McMahon. I\'ll focus on the experimental aspects of each measurement, it\'s interface to theory, and spend most of the time on (3) CHIME.

A modified version of the double potential formalism for the electrodynamics of dyons is constructed. Besides the two vector potentials, this manifestly duality invariant formulation involves four additional potentials, scalar potentials which appear as Lagrange multipliers for the electric and magnetic Gauss constraints and potentials for the longitudinal electric and magnetic fields. In this framework, a static dyon appears as a Coulomb-like solution without string singularities. Dirac strings are needed only for the Lorentz force law, not for Maxwell\'s equations. The magnetic charge no longer appears as a topological conservation law but as a surface integral on a par with electric charge. The theory is generalized to curved space. As in flat space, the string singularities of dyonic black holes are resolved. As a consequence all singularities are protected by the horizon and the thermodynamics is shown to follow from standard arguments in the grand canonical ensemble.

This course is aimed at advanced undergraduate and beginning graduate students, and is inspired by a book by the same title, written by Padmanabhan. Each session consists of solving one or two pre-determined problems, which is done by a randomly picked student. While the problems introduce various subjects in Astrophysics and Cosmology, they do not serve as replacement for standard courses in these subjects, and are rather aimed at educating students with hands-on analytic/numerical skills to attack new problems.