This series covers all areas of research at Perimeter Institute, as well as those outside of PI's scope.
I will describe recent work by Cutler&Holz and Hirata, Holz, & Cutler showing that a highly sensitive, deci-Hz gravitational-wave mission like BBO or Decigo could measure cosmological parameters, such as the Hubble constant H_0 and the dark energy parameters w_0 and w_a, far more accurately than other proposed dark-energy missions.
This talk will discuss some surprising links which have emerged in the last few years between two at first sight distinct areas of mathematical physics: the spectral properties of certain simple schroedinger-like equations, and the Bethe ansatz techniques which are used to compute the energies of states in integrable quantum field theories. No knowledge of either area will be assumed.
The quantum states postulated to occur in situations of the "Schroedinger's Cat" type are essentially N-particle GHZ states with N very large compared to 1,and their observation would thus be particularly compelling evidence for the ubiquity of the phenomenon of entanglement. However, in the traditional quantum measurement literature considerable scepticism has been expressed about the observability of this kind of "macroscopically entangled" state, primarily because of the putatively disastrous effect on it of decoherence.
An entirely new kind of band insulator was discovered recently. These new electronic states - called "topological insulators" - are fundamentally different from standard band insulators. They are distinguished by the fact that their edges (in the 2D case) or surfaces (in the 3D case) support gapless transport which is extremely robust. In the two dimensional case, topological insulators can be thought of as time reversal invariant analogues of integer quantum Hall states.
Theoretical insights originated from the study of black holes combined with developments in string theory indicate that space time and gravity are emergent. A central role in these developments is played by the holographic principle. I will present a heuristic argument that indicates that at a microscopic level gravity is an entropic force caused by changes in the available phase space due to the displacement of material bodies. Refinement of the argument makes clear that this entropic view on gravity is consistent with quantum mechanics and supported by various results in string theory.
Frustrated magnets are materials in which localized magnetic moments, or spins, interact through competing exchange interactions that cannot be simultaneously satisfied, giving rise to a large degeneracy of the system ground state. Under certain conditions, this can lead to the formation of fluid-like states of matter, so-called spin liquids, in which the constituent spins are highly correlated but still fluctuate strongly down to a temperature of absolute zero.
The primordial density fluctuations that seeded large-scale structure are known to be nearly Gaussian, as predicted by most early universe models like slow-roll inflation. Many of these models predict a small (but nonzero!) amount of primordial non-gaussianity, which can subtly affect the statistics of CMB anisotropies. Surprisingly, even a small primordial non-gaussianity can produce enormous changes in the large-scale clustering of galaxies and quasars at late times.
We study a novel state of matter: algebraic Bose liquid (ABL). An ABL is a quantum bosonic system on a 2d or 3d lattice that does not break any symmetry in its ground state, but still able to stabilize a gapless spectrum. At high energy these boson systems only have the simplest U(1) global symmetry associated with the conservation of boson number, but at low energy the system is described by self-dual gauge fields. In this talk we will present two new ABL phases emerged from a quantum Boson model on the cubic lattice.
Recently, a new class of topological states has been theoretically predicted and experimentally realized. The topological insulators have an insulating gap in the bulk, but have topologically protected edge or surface states due to the time reversal symmetry. In two dimensions the edge states give rise to the quantum spin Hall (QSH) effect, in the absence of any external magnetic field. I shall review the theoretical prediction of the QSH state in HgTe/CdTe semiconductor quantum wells, and its recent experimental observation.