Scientific Series

If a pure quantum state is drawn at random, this state will almost surely be almost maximally entangled. This is a well-known example for the "concentration of measure" phenomenon, which has proved to be tremendously helpful in recent years in quantum information theory. It was also used as a new method to justify some foundational aspects of statistical mechanics. In this talk, I discuss recent work with David Gross and Jens Eisert on concentration in the set of pure quantum states with fixed mean energy: We show typicality in this manifold of quantum states, and give a method to evaluate expectation values explicitly. This involves some interesting mathematics beyond Levy's Lemma, and suggests potential applications such as finding stronger counterexamples to the additivity conjecture.

Most often, the dark matter puzzle is analyzed along a single perspective, thus trying to answer a single question. Either "what is the dark matter?", focusing on its microscopic nature, or "how is dark matter distributed in the universe?" focusing on the large scale structure of the universe, or still "how does it affect what we observe in the sky?". Both my scientific interests and some random fluctuations at the beginning of my career have conspired so that I would take on projects in all these fields. Leaving aside the ambition -- and the impossible task -- to be comprehensive, I will review some interesting aspects of these fields and some of my contributions, ranging from using astrophysical cross-correlations to put constraints on the neutrino masses, to the interplay between Higgs searches at colliders and dark matter experiments, to using gamma ray observations to detect and measure properties of extra dimensions.

CMB measurements reveal a very smooth early universe. We propose a mech- anism to make this smoothness natural by weakening the strength of gravity at early times, and therefore altering which initial conditions have low entropy.

The basic structure of quantum mechanics was delineated in the early days of the theory and has not been modified since. Still it is interesting to ask whether that basic structure can be altered or generalized. In the last decade Bender et al have shown that one of the fundamental assumptions of quantum mechanics, that operators are represented by Hermitian matrices, can to an extent be relaxed. In this theory, the parity (P) and time-reversal (T) operators play a role analogous to the Hermitian conjugate. Recently we have extended the realm of `PT quantum mechanics' to include systems that are odd under time-reversal (T^2 = - 1), in the interest of constructing the PT-analogue of the Dirac equation. We find that the fundamental representation of the Dirac equation, which describes relativistic fermions, remains unchanged in the generalization to the non-Hermitian theory. Higher dimensional representations, which ordinarily decouple into pairs of Dirac fermions in Hermitian quantum mechanics, here describe new types of particles with extremely compelling properties. Most notably we have constructed a toy model representing two generations of massless neutrinos that nonetheless undergo flavor oscillations; furthermore this model is Lorentz invariant and unitary in time. The Standard Model requires that the neutrino be massive in order to accomodate the observed flavor oscillations, thus this toy model represents a significant departure from Standard Model physics.

One of the main science objectives for the Laser Interferometer Space Antenna (LISA) is to quantitatively map the strong field regions around compact objects using Extreme-Mass-Ratio Inspirals (EMRIs). This idea has been shown to be possible in principle, however in practice only inspirals in a Kerr spacetime have been studied in detail. A spacetime mapping algorithm for an EMRI inspiral into a generic compact object is formulated using ideas from integrable systems. I discuss several aspects of the theoretical development required to make the problem tractable. Some recent results about particle orbits around "Bumpy Black" holes are highlighted.

It is a prime interest to understand gravitational physics and to develop cosmological applications exploiting the next generation of surveys, scheduled to be launched in the near future, such as SDSS3, DES, XCS, JDEM or EUCLID. The future precision surveys are promising to resolve outstanding problems in modern physics. With the level of precision available in future surveys, we can use the high resolution maps expected to be gained from next-generation surveys to test the foundations of gravity and particle physics. The gravity known to us at solar system scales (GR: general relativity) is possibly challenged at cosmological scales. The measured cosmic acceleration that we have ascribed to the presence of dark energy (DE) could be a signal that GR is broken in some way.

I will describe a new connection between supersymmetry, geometry and computer science. An exploration of the equations of supersymmetry has revealed a geometrical sub-structure whose classification depends on self-dual error correcting codes.

The BCFW recursion relations define Yang-Mills and gravity amplitudes in terms of lower-point amplitudes. I will discuss several connections between the internal consistency of this recursive definition and the allowed interactions of massless, higher-spin particles.

Although the observational evidence for cosmological inflation is growing, the physical mechanism behind it is still unknown. In part this is because inflation probably occurred at energy scales many orders of magnitude higher than that at man-made or astrophysical particle accelerators. So how can we learn about inflation? How does it constrain microphysical theory? One approach to answering these questions is primarily theoretical: attempting to embed inflation in fundamental theories of quantum gravity, such as string theory. Another approach is primarily observational: looking for signatures left by light fields that existed during inflation, such as isocurvature fluctuations from the QCD-axion. In this talk I discuss work on these two approaches.

For a quantum system with a d-dimensional Hilbert space, a symmetric informationally complete measurement (SIC) can be thought of as a set of d^2 pure states all having the same overlap. Constructions of SICs for composite systems usually do not make use of the composite structure but treat the system as a whole. Indeed for some cases, one can prove that a SIC cannot have the symmetry that one naturally associates with the composite structure. In this talk I give one example showing how a SIC for three qubits can be constructed from SICs for the individual qubits. I ask whether the strategy used in this example might apply to other composite cases.

The problem of the quantum backreaction in expanding spaces is an old, as yet unresolved, question. In this talk I will consider the one-loop backreaction of a massless scalar which couples to the Ricci scalar in an expanding space with constant deceleration. I will show that the infrared divergences, which generically plague the one loop stress energy, can be removed by matching onto an earlier radiation era. An insignificant backreaction occurs, unless the coupling to the Ricci scalar is negative. Similar results hold for the graviton backreaction.