I will describe recent work in collaboration with Adam
Henderson, Alok Laddha, and Madhavan Varadarajan on the loop quantization of a
certain $G_{\mathrm{N}}\rightarrow 0$ limit of Euclidean gravity, introduced by
Smolin. The model allows one to test various quantization choices one is faced
with in loop quantum gravity, but in a simplified setting. The main results are the construction of
finite-triangulation Hamiltonian and diffeomorphism constraint operators whose
continuum limits can be evaluated in a precise sense, such that the quantum
Dirac algebra of constraints closes nontrivially and free of anomalies. The construction relies heavily on techniques
of Thiemann's QSD treatment, and lessons learned applying such techniques to
the loop quantization of parameterized scalar field theory and the
diffeomorphism constraint in loop quantum gravity. I will also briefly discuss the status of the
quantum constraint algebra in full LQG, and how some of the lessons learned from
the present model may guide us in that setting.
The last few years have seen new opportunities for
constraining the physics of neutron star interiors. I will first discuss the
current state of neutron star radius measurements and then go on to discuss
thermal tomography as a probe of the nuclear, magnetic, and transport
properties of neutron star crusts. In each case, I will emphasize the
astrophysics that must be understood to make reliable inferences about the
properties of dense matter from observations of neutron stars.
In one extreme, where the interactions
are sufficiently weak compared to the interactions, electrons form a “Fermi
liquid” – the state that accounts for the properties of simple metals. In the other extreme, where the interactions
are dominant, the electrons form various “Mott” insulating or “Wigner
crystalline” phases, often characterized by broken spatial and/or magnetic symmetries. Corresponding charge and/or magnetically
ordered insulating phases are common in nature.
Between these two extremes lie highly correlated electronic fluids, and
correspondingly a host of interesting and perplexing materials, including such
diverse systems as the cuprate and iron-based high temperature superconductors,
the failed metamagnet Sr3Ru2O7, and a variety
of quantum Hall fluids. Some insight
into electron fluids in this rich intermediate coupling regime can be obtained
from viewing them as partially melted electron solids, rather than as strongly
interacting gases. Here, analogies with
the liquid crystalline phases of complex classical fluids provide useful
guidance for a new approach to this key problem in condensed matter physics.
I will present recent work,
done in collaboration with Daniel Roberts, on the global memory of initial
conditions that is sometimes, but not always, retained by fluctuating fields on
de Sitter space, Euclidean anti de Sitter space, and regular infinite trees. I
will discuss applications to the structure of configuration space in de Sitter
space and eternal inflation.
Recent advances in analytical theory and numerical methods
enable some long-standing questions about transport in one dimension to be
answered; these questions are closely related to transport experiments in
quasi-1D compounds. The spinless fermion chain with nearest-neighbor
interactions at half-filling, or equivalently the XXZ model in zero magnetic
field, is an example of an integrable system in which no conventional conserved
quantity forces dissipationless transport (Drude weight); we show that there is
nevertheless a Drude weight and that at some points its contribution is from a
new type of conserved quantity recently constructed by Prosen. Adding an
integrability-breaking perturbation leads to a scaling theory of conductivity
at low temperature. Adding disorder, we study the question of how
Anderson localization is modified by interactions when the system remains fully
quantum coherent ("many-body localization"). We find that even
weak interactions are a singular perturbation on some quantities: entanglement
grows slowly but without limit, suggesting that dynamics in the possible
many-body localized phase are glass-like. If time permits, some results
on the fractional Luttinger's theorem and the 1D limit of quantum Hall states
will be presented.
I will discuss a
path-integral representation of continuum tensor networks that extends the
continuous MPS class for 1-D quantum fields to arbitrary spatial dimensions
while encoding desirable symmetries. The physical states can be interpreted as
arising through a continuous measurement process by a lower dimensional virtual
field with Lorentz symmetry. The resultant physical states naturally obey
entropy area laws, with the expectation values of observables determined by the
dissipative dynamics of the boundary field. The class offers the prospect of
powerful new analytical and computational tools to describe the physics of
strongly interacting field systems.
I present a candidate for a new derivation of black hole
entropy. The key observation is that the action of General Relativity in
bounded regions has an imaginary part, arising from the boundary term. The
formula for this imaginary part is closely related to the Bekenstein-Hawking
entropy formula, and coincides with it for certain classes of regions. This
remains true in the presence of matter, and generalizes appropriately to
Lovelock gravity. The imaginary part of the action is a versatile notion,
requiring neither stationarity nor any knowledge about asymptotic infinity.
Thus, it may provide a handle on quantum gravity in finite and dynamical
regions. I derive the above results, make connections with standard approaches
to black hole entropy, and speculate on the meaning of it all. Implications for
loop quantum gravity are also discussed.
The global warming
crisis is part of a bigger transformation in which humanity realizes that the
Earth is a finite system and that our population, energy usage, and the like
cannot continue to grow exponentially. While politics and economics pose the
biggest challenges, physicists are in a good position to help make this
transition a bit easier. After a quick review of the problems, we discuss a few
ways physicists can help.
We
develop a theory for describing composite objects in physics. These can be
static objects, such as tables, or things that happen in spacetime (such as a
region of spacetime with fields on it regarded as being composed of smaller
such regions joined together). We propose certain fundamental axioms which, it
seems, should be satisfied in any theory of composition. A key axiom is the
order independence axiom which says we can describe the composition of a
composite object in any order. Then we provide a notation for describing
composite objects that naturally leads to these axioms being satisfied. In any
given physical context we are interested in the value of certain properties for
the objects (such as whether the object is possible, what probability it has,
how wide it is, and so on). We associate a generalized state with an object.
This can be used to calculate the value of those properties we are interested
in for for this object. We then propose a certain principle, the composition
principle, which says that we can determine the generalized state of a
composite object from the generalized states for the components by means of a
calculation having the same structure as the description of the generalized
state. The composition principle provides a link between description and
prediction.
Cosmological results
from Planck, a third-generation satellite mission to measure the cosmic
microwave background, have just been announced. These results improve
constraints on essentially all cosmological parameters, and have implications
for several preexisting sources of tension with the standard cosmological
model, while also raising new puzzles. I will discuss these results and
their significance, as well as the next steps forward.
Entanglement distillation
transforms weakly entangled noisy states into highly entangled states, a
primitive to be used in quantum repeater schemes and other protocols designed
for quantum communication and key distribution. In this work, we present a comprehensive
framework for continuous-variable entanglement distillation schemes that
convert noisy non-Gaussian states into Gaussian ones in many iterations of the
protocol. Instances of these protocols include the recursive Gaussifier
protocol and the pumping Gaussifier protocol. The flexibility of these
protocols give rise to several beneficial trade-offs related to success
probabilities or memory requirements that can be adjusted to reflect
experimental specifics. Despite these protocols involving measurements, we
relate the convergence in this protocols to new instances of non-commutative
central limit theorems. Implications of the findings for quantum repeater
schemes are discussed.
I
will describe a discrete model of spacetime which is quantum-mechanical,
causal, and background free. The kinematics is described by networks whose
vertices are labelled with arrows. These networks can be evolved forwards (or
backwards) in time by using unitary replacement rules. The arrow structure
permits one to define dynamics without using an absolute time parameter.
Based on arXiv:1201.2489.