Pulsars have enormous magnetic fields whose energy density
dwarfs the rest mass density of their plasma magnetosphere. In this
regime of a plasma, the particles drop out of the description, leaving a set of
equations for the electromagnetic field alone. This non-linear,
deterministic system is known as force-free electrodynamics, and turns out to
have some beautiful and bizarre features. I will give a pedagogical
introduction to these equations and their role in astrophysics and then discuss
our recent contributions. We have taken a geometric viewpoint, using the
null structure of spacetime to unify previous exact solutions and discover new
ones. We have found non-stationary, non-axisymmetric solutions that
describe the outer magnetosphere of pulsars, including those that are
accelerated or torqued. We have derived the standard cartoon of the
aligned pulsar magnetosphere from an explicit, minimal set of assumptions.
Time permitting, I will also discuss some properties of black hole
magnetospheres: Blandford-Znajek energy extraction, non-scattering force-free
waves, and the no-ingrown-hair theorem.
In 2004, Kim and Chan reported torsional
oscillator experiments on 4He crystals which showed evidence of
“non-classical rotational inertia”, the mass decoupling expected for a
long-sought “supersolid” state. It soon
became clear that this behavior is not a property of perfect crystals – defects
are involved. In 2007, we made elastic
measurements which showed, to our surprise, that the shear modulus of solid 4He
increases dramatically below 0.2 K, with the same dependence on temperature,
amplitude and 3He impurity concentration as the torsional oscillator
anomaly. These shear modulus changes are
due to dislocations and their interactions with impurities and vacancies. Our experiments raised an obvious question – could
the torsional oscillator behavior be an artifact of the elastic changes, rather
than evidence of supersolidity? During
the past two years it has become clear that the answer is “yes” and interest
has focused on the properties of dislocations in a quantum solid like 4He. By growing high quality single crystals in
optical cells, we have now been able to explore the behavior of dislocations in
4He in unprecedented detail. In some crystals the dislocations reduce the shear modulus by more than 80%, an extraordinary
effect we describe as “giant plasticity”. Solid helium has proved to be an ideal system in which to do materials
science, as well as to address fundamental questions about quantum solids.
Local-type primordial non-Gaussianity couples
statistics of the curvature perturbation \zeta on vastly different physical
scales. Because of this coupling, statistics (i.e. the polyspectra) of \zeta in
our Hubble volume may not be representative of those in the larger universe -- that
is, they may be biased. The bias depends on the local background value of
\zeta, which includes contributions from all modes with wavelength k ~< H_0
and is therefore enhanced if the entire post-inflationary patch is large
compared with our Hubble volume. I will discuss the bias to
locally-measured statistics for general local-type non-Gaussianity. I will
discuss three examples in detail: (i) the usual fNL, gNL model, (ii) a strongly
non-Gaussian model with \zeta ~ \zeta_G^p, and (iii) two-field non-Gaussian
initial conditions. In each scenario one may generate statistics in a
Hubble-size patch that are weakly Gaussian and consistent with observations
despite the fact that the statistics in the larger, post-inflationary patch
look very different. Finally, I will present a worked example of how the
variation in local statistics arises in the curvaton scenario.
The FQHE is exhibited by electrons moving on a 2D surface
through which a magnetic flux passes, giving rise to
flat bands with extensive degeneracy (Landau
levels). The degeneracy
of a partially-filled Landau level is lifted by Coulomb
repulsion between the electrons, which at certain rational fillings, leads
to gapped incompressible
topologically-ordered fluid states exhibiting the FQHE. Successful model wavefunctions for FQHE states, such as the Laughlin and
Moore-Read states, are surprisingly related to Euclidean conformal field
theory, even though they are gapped incompressiible quantum fluids with a
fundamental unit of area set by the area per magnetic flux quantum h/e.
The model wavefunctions are parametrized by a
continuously-variable Euclidean metric,
just like the Euclidean conformal group of the cft to which they are related.
This metric is fixed locally both by the form of the
projected Coulomb interaction within the partially-filled Landau level, and by
local gradients of the tangential electric field on the 2D surface, promoting
it from a static flat metric fixed globally by the cft, to a dynamic local
physical degree of freedom of the FQHE fluid with area-preserving zero-point fluctuations
that leave an imprint in the ground-state structure function.
The curious connection to cft appears to be that the Virasoro algebra plays a fundament role in
both cft and FQHE, for apparently-unrelated reasons. In the FQHE it
derives from a chiral
"gravitional"
(geometric) topologically-protected anomaly at the edge of the fluid that is also
revealed in the entanglement spectrum of a cut through the bulk fluid.
Alan Turing was one of our great 20th century
mathematicians, and a pioneer of computer science. However, he may best be
remembered as one of the leading code breakers of Bletchley Park during World
War II. It was Turing's brilliant insights and mathematical mind that helped to
break Enigma, the apparently unbreakable code used by the German military. We
present a history of both Alan Turing and the Enigma, leading up to this
fascinating battle of man against machine - including a full demonstration of
an original WWII Enigma Machine!
Transversal
implementations of encoded unitary gates are highly desirable for
fault-tolerant quantum computation. It is known, however, that
transversal gates alone cannot be computationally universal. I will show
that the limitation on universality can be circumvented using only
fault-tolerant error correction, which is already required anyway. This
result applies to ``triorthogonal'' stabilizer codes, which were recently
introduced by Bravyi and Haah for state distillation. I will show that
triothogonal codes admit transversal implementation of the
controlled-controlled-Z gate, and then demonstrate a transversal Hadamard construction
which uses error correction to preserve the codespace. I will also discuss how
to adapt the distillation procedure of Bravyi and Haah to Toffoli gates,
improving on existing Toffoli distillation schemes.
Superfluidity and superconductivity are two remarkable
phenomena in which, at low temperatures, materials abruptly gain the ability to
flow without friction. Microscopic quantum theories of these phases of matter
were constructed in blockbuster papers of Lev Landau (1940) and John Bardeen,
Leon Cooper, and J. Robert Schrieffer
(1957). The actual explanation of
the flow, however, is rooted in a
Einstein paper of 1924 that introduces a condensate, a quantum configuration describing a finite
fraction of the particles in the system.
Superfluidity can then be understood in terms of the wave
function for this configuration, which necessarily extends over a finite
fraction of the system. Neither
blockbuster paper mentions Einstein or the crucial idea of a condensate wave
function. The reasons for this omission are mooted.
We propose a simple renormalizable
model of baryogenesis and asymmetric dark matter generation at the electroweak
phase transition. Our setup utilizes the two Higgs doublet model plus two
complex gauge singlets, the lighter of which is stable dark matter. The dark
matter is charged under a global symmetry that is broken in the early universe
but restored during the electroweak phase transition. Because the ratio of
baryon and dark matter asymmetries is controlled by model parameters, the dark
matter need not be light. Thus, new force carriers are unnecessary and the
symmetric dark matter abundance can be eliminated via Higgs portal interactions
alone. The dark matter mass is also constrained within a window around the weak
scale. One of the main predictions of this model is CP violating Higgs signals
at the LHC and future colliders.
I'll discuss a
number of insights into the process of nonlinear structure formation which come
from the study of random walks crossing a suitably chosen barrier. These
derive from a number of new results about walks with correlated steps, and
include a unified framework for the peaks and excursion set frameworks for
estimating halo abundances, evolution and clustering, as well as nonlinear,
nonlocal and stochastic halo bias, all of which matter for the next generation
of large scale structure datasets.
We argue that the
scale-free spectrum that is observed in the cosmic microwave background is the
result of a phase transition in the early universe. The observed tilt of
the spectrum, which has been measured to be 0.04, is shown to be equal to the
anomalous scaling dimension of the correlation function. The phase
transition replaces inflation as the mechanism that produces this spectrum. The tilt further indicates that there is a fundamental small length scale in
nature that we have not yet observed in any other way.
Gamma-ray bursts are
the most luminous and energetic explosions known in the universe. They
appear in two varieties: long- and short-duration. The long GRB
result from the core-collapse of massive stars, but until recently the origin
of the short GRBs was shrouded in mystery. In this talk I will present
several lines of evidence that point to the merger of compact objects binaries
(NS-NS and/or NS-BH) as the progenitor systems of short GRBs. Within this
framework, the observational data also allow us to independently determine the
merger rate of these systems as input to the Advanced LIGO event rate, to infer
the merger distribution timescale, and to determine the energy scale of the
mergers. In addition, using radio to X-ray observations of short GRBs we
can determine the expected electromagnetic properties of Advanced LIGO sources.