Scientific Series

One of the key features of the quantum Hall effect (QHE) is the fractional charge and statistics of quasiparticles. Fractionally charged anyons accumulate non-trivial phases when they encircle each other. In some QHE systems an unusual type of particles, called non-Abelian anyons, is expected to exist. When one non-Abelian particle makes a circle around another anyon this changes not only the phase but even the direction of the quantum-state vector in the Hilbert space. This property makes non-Abelian anyons promising for fault-tolerant quantum computation. Several experiments allowed an observation of fractional charges. Probing exchange statistics is more difficult and has not been accomplished for identical anyons so far. We will discuss how the statistics can be probed with Mach-Zehnder interferometry, tunneling experiments and far-from-equilibrium fluctuation-dissipation theorem.

I will discuss the growth of entanglement under a quantum quench at point contacts of simple fractional quantum Hall fluids and its relation with the measurement of local observables. Recently Klich and Levitov recently proposed that, for a free fermion system, the noise generated from a local quantum quench provides a measure of the entanglement entropy. In this work, I will examine the validity of this proposal in the context of a strongly interacting system, the Laughlin FQH states. We find that local quenching in fractional quantum Hall junctions gives time dependent correlation functions that have universal behavior on sufficiently long time and length scales. The growth of entanglement entropy and the noise generated by the quench are generally unrelated quantities.

We begin with a fundamental approach to quantum mechanics based on the unitary representations of the group of diffeomorphisms of physical space (and correspondingly, self-adjoint representations of a local current algebra). From these, various classes of quantum configuration spaces arise naturally. One obtains in addition the usual exchange statistics for spatial dimension d >2, induced by representations of the symmetric group, while for d = 2, the approach led to an early prediction of intermediate or “anyonic” statistics induced by unitary representations of the braid group. After reviewing these ideas, which are based on joint work with R. Menikoff and D. H. Sharp at Los Alamos National Laboratory, we shall discuss briefly some analogous possibilities for infinite-dimensional configuration spaces, including anyonic statistics for extended objects in 3-dimensional space.

Mass, a concept familiar to all of us, is also one of the deepest mysteries in nature. Almost all of the mass in the visible universe, you, me and any other stuff that we see around us, emerges from QCD, a theory with a negligible microscopic mass content. How does QCD and the family of gauge theories it belongs to generate a mass? This class of non-perturbative problems remained largely elusive despite much effort over the years. Recently, new ideas based on compactification have been shown useful to address some of these. Two such inter-related ideas are circle compactifications, which avoid phase transitions and large-N volume independence. Through the first one, we realized the existence of a large-class of "topological molecules", e.g. magnetic bions, which generate mass gap in a class of compactified gauge theories. The inception of the second, the idea of large-N volume independence is old. The new progress is the realization of its first working examples. This property allows us to map a four dimensional gauge theory (including pure Yang-Mills) to a quantum mechanics at large-N.

Using the framework of deconstruction, we construct simple, weakly-coupled supersymmetric models that explain the Standard Model flavor hierarchy and produce a flavorful soft spectrum compatible with precision limits. Electroweak symmetry breaking is fully natural/ the mu-term is dynamically generated with no B mu-problem and the Higgs mass is easily raised above LEP limits without reliance on large radiative corrections. These models possess the distinctive spectrum of superpartners characteristic of 'effective supersymmetry': the third generation superpartners tend to be light, while the rest of the scalars are heavy.

I will describe the current state of our attempts to characterize the nature of the Dark Energy, the name given to the unknown phenomenology that is driving the observed accelerating cosmic expansion. There is a historical analogy between our current situation and the days of confusion before the advent of quantum mechanics. But while quantum physics emerged in a single academic generation, I fear that our attaining a deeper understanding of Dark Energy may not be as rapid. I will outline some steps we can take to try to avoid an extended period of sophisticated confusion and intellectual stagnation.

We use a field theoretic generalization of the Wigner-Weisskopf method to study the stability of the Bunch-Davies vacuum state for a massless, conformally coupled interacting test field in de Sitter space. A simple example of the impact of vacuum decay upon a non-gaussian correlation is discussed. Single particle excitations also decay into two particle states, leading to particle production that hastens the exiting of modes from the de Sitter horizon resulting in the production of \emph{entangled superhorizon pairs} with a population consistent with unitary evolution. We find a non-perturbative, self-consistent "screening" mechanism that shuts off vacuum decay asymptotically, leading to a stationary vacuum state in a manner not unlike the approach to a fixed point in the space of states.

After reviewing the basics of Coleman deLuccia tunneling, especially in the thin-wall limit, I discuss an (almost) exact tunneling solution in a piecewise linear and quadratic potential. A comparison with the exact solution for a piecewise linear potential demonstrates the dependence of the tunneling rate on the exact shape of the potential. Finally, I will mention applications when determining initial conditions for inflation in the landscape. Based on arXiv:1102.4742 [hep-th].

Neutrino oscillations has been observed and confirmed at two mass splittings (\Delta m^2), which is consistent with three generations of neutrinos and an unitary mixing matrix. Despite the rapid progress in understanding neutrino oscillations in the last decade, two large questions remain about neutrino oscillation parameters at \Delta m^2 ~ 0.001 eV^2. Is \theta_{23} exactly 45 degrees, indicating an additional symmetry in neutrino mixing? Is \theta_{13} non-zero, which would mean there could be CP violation in the neutrino sector. If \theta_{13} is large enough, then such CP violation could be studied with future high intensity experiments such as the proposed Long Baseline Neutrino experiment in the US (LBNE). The Tokai-To-Kamioka (T2K) long baseline neutrino experiment is designed to precisely measure \nu_{\mu} disappearance (\Delta m^2_{23}, \theta_{23}) and search for \nu_e appearance (\theta_{13}). A beam of muon neutrinos is generated at the J-PARC facility in Tokai-mura, Japan, and is sampled by two near detectors, ND280 and INGRID, before reaching the Super-Kamiokande detector, 295km away. In this talk, a first look at \nu_{\mu} disappearance and \nu_e appearance will be shown from T2K, from the inaugural 6 month run ending in June 2010 (3.23x10^19 protons on target, at 15.5 kW x 10^7s).

Correlation functions in the gauge-gravity correspondence (AdS/CFT) are dual to scattering amplitudes in anti-de Sitter space (AdS). In this talk, I will describe how techniques that were recently developed to study scattering amplitudes in flat space can be generalized to AdS leading to a new and efficient method of computing correlation functions in AdS/CFT. References: 1) S. Raju, "Generalized Recursion Relations for Correlators in the Gauge Gravity Correspondence", Phys.Rev.Lett. 106 (2011) 091601. http://arxiv.org/abs/arXiv:1011.0780 2) S. Raju, "Recursion Relations for AdS/CFT Correlators", http://arxiv.org/abs/arXiv:1102.4724

Cross-correlation of gravitational-wave (GW) data streams has been used to search for stochastic backgrounds, and the same technique was applied to look for periodic GWs from the low-mass X-ray binary (LMXB) Sco X-1. Recently a technique was developed which refines the cross-correlation scheme to take full advantage of the signal model for periodic gravitational waves from rotating neutron stars. By varying the time window over which data streams are correlated, the search can "trade off" between parameter sensitivity and computational cost. I describe this cross-correlation method and potential applications to search LIGO and Virgo data for periodic GWs from systems with partially-known parameters, such as supernova remnants without an associated known pulsar, the center of the Milky Way Galaxy, and LMXBs

In many physical scenarios, close relations between the bulk properties of quantum systems and theories associated to their boundaries have been observed. In this work, we provide an exact duality mapping between the bulk of a quantum spin system and its boundary using Projected Entangled Pair States (PEPS). This duality associates to every region a Hamiltonian on its boundary, in such a way that the entanglement spectrum of the bulk corresponds to the excitation spectrum of the boundary Hamiltonian. We study various specific models, like a deformed AKLT , an Ising-type , and Kitaev's toric code, both in finite ladders and infinite square lattices. In the latter case, some of those models display quantum phase transitions. We find that a gapped bulk phase with local order corresponds to a boundary Hamiltonian with local interactions, whereas critical behavior in the bulk is reflected on a diverging interaction length of the boundary Hamiltonian. Furthermore, topologically ordered states yield non-local Hamiltonians. As our duality also associates a boundary operator to any operator in the bulk, it in fact provides a full holographic framework for the study of quantum many-body systems via their boundary. Work done in collaboration with Didier Poilblanc, Norbert Schuch, and Frank Verstraete.