Scientific Series

Problematic growths of curvature and anisotropy are found in nonsingular bouncing cosmologies that include both an ekpyrotic phase and a bouncing phase. Classically, initial curvature and anisotropy that are suppressed during the ekpyrotic phase will grow back exponentially during the nonsingular bouncing phase. Besides, curvature and shear perturbations are generated by quantum fluctuations during the ekpyrotic phase. In the bouncing phase, an adiabatic curvature perturbation grows to dominate and gives rise to a blue spectrum that spoils the scale-invariance. Meanwhile, a scalar shear perturbation grows nonlinear and creates an overwhelming anisotropy that disrupts the nonsingular bounce altogether. We examine the common origin of these problems and discuss possible ways to avoid them.

Besides their experimental relevance in condensed matter and quantum information science, quantum spin systems are an interesting playground to study decoherence and quantum entanglement. Random matrices are used since the 50' to model quantum chaotic dynamics and complex quantum systems. I introduce new random matrix models which lead to explicit solutions for some simple open or closed quantum spin systems. They allow to probe the various dynamical regimes of decoherence and the emergence of the classical phase space for the spin, in particular in the non-Markovian regimes where no master equations are available.

In this talk I will provide evidence supporting the Dolan/Nirschl/Osborn conjecture for the precise form of the amplitude of four-point functions of 1/2-BPS operators in N=4 SYM theory at strong coupling and in the large N limit. I will also discuss the methods that allowed the evaluation of amplitudes involving operators of arbitrary conformal dimension.

Quantum theory can be thought of as a noncommutative generalization of Bayesian probability theory, but for the analogy to be convincing, it should be possible to describe inferences among quantum systems in a manner that is independent of the causal relationship between those systems. In particular, it should be possible to unify the treatment of two kinds of inferences: (i) from beliefs about one system to beliefs about another, for instance, in the Einstein-Podolsky-Rosen or "quantum steering" phenomenon, and (ii) from beliefs about a system at one time to beliefs about that same system at another time, for instance, in predictions or retrodictions about a system undergoing dynamical evolution or undergoing a measurement. I will present a formalism that achieves such a unification by making use of "conditional quantum states", a noncommutative generalization of conditional probabilities. I argue for causal neutrality by drawing a comparison with a classical statistical theory with an epistemic restriction. (Joint work with Matthew Leifer).

The talk consists of two parts: (1) Quasi-single inflation, where the isocurvature direction has mass of order Hubble parameter. This part is based on 0911.3380 and new results about higher mass, and a sharp turn in trajectory. (2) Multi-stream inflation, where the inflationary trajectory bifurcates. This part is based on 0903.2123, 1006.5021 and a on-going project on calculating the bifurcation probability in a complicated landscape.

We report on our recent progress to investigate materials classes exhibiting d+id superconductivity, where topologically nontrivial pairing phases can emerge. Specifically, motivated by recent experimental progress, we show that graphene doped to the van Hove regime can give rise to a plethora of interesting ordering instabilities such as spin density wave and superconductivity. As a function of system parameters such as doping and range of Coulomb interaction, we explain which instability is favored by the system, and analyze the effect of long-range interactions on superconductivity giving rise to a competition between singlet d+id and triplet f wave. We also outline our work in progress for other materials classes which we believe are promising to stabilize such interesting topological superconducting states of matter.

It has been well-known that topological phenomena with fractional excitations, i.e., the fractional quantum Hall effect (FQHE) will emerge when electrons move in Landau levels. In this talk, I will show FQHE can emergy even in the absence of Landau levels in interacting fermion models and boson models. The non-interacting part of our Hamiltonian contains topologically nontrivial flat band.

The parity invariance of spinfoam gravity is an open question. Naively, parity breaking should reside in the sign of the Immirzi parameter. I show that the new Lorentzian vertex formula is in fact independent of this sign, suggesting that the dynamics is parity-invariant. The situation with boundary states and operators is more complicated. I discuss parity-related pieces of the transition amplitude and graviton propagator in the large-spin 4-simplex limit. Numerical results indicate patterns similar to those in the Euclidean case. In particular, parity-related components of the graviton propagator differ by a phase. I discuss possible resolutions of this issue.

Ideas about information are pervasive, yet the fundamental nature and structure of information - if indeed it has one! - remains elusive. Work done from many different perspectives, including those of physics, biology, logic, computer science, statistics, and game and decision theory, has yielded insights into various aspects of information. Could there be a comprehensive, unified theory? We shall chart a particular path, focusing on the idea of *information flow*, and show how common mathematical structures arise in the description of information flow in computer science, logic and quantum information.

Correlations in quantum states are sometimes inaccessible if only restricted types of quantum measurements can be performed, an effect known as quantum data hiding. For example highly entangled states shared by two parties might appear uncorrelated if the parties can only measure locally their shares of the state and communicate classically with each other. In this talk I will first discuss how a better understanding of the peculiar type of correlations found in quantum data hiding states is useful in addressing two challenges of quantum information theory: the design of efficient algorithms for determining if a quantum state is entangled, and the establishment of area laws in gapped local Hamiltonians. Second, I will present new efficient ways of generating data hiding, e.g. employing random local quantum circuits, and will briefly discuss the relevance of this approach to the problem of proving quick equilibration of quantum systems unitarily interacting with a large environment.

We use the mathematical language of sheaf theory to give a unified treatment of non-locality and contextuality, which generalizes the familiar probability tables used in non-locality theory to cover Kochen-Specker configurations and more. We show that contextuality, and non-locality as a special case, correspond exactly to *obstructions to the existence of global sections*. We describe a linear algebraic approach to computing these obstructions, which allows a systematic treatment of arguments for non-locality and contextuality. A general correspondence is shown between the existence of local hidden-variable realizations using negative probabilities, and no-signalling. Maximal non-locality is generalized to maximal contextuality, and characterized in purely qualitative terms, as the non-existence of global sections in the support. Some ongoing work with Shane Mansfield and Rui Soares Barbosa is described, which identifies *cohomological obstructions* to the existence of global sections, opening the possibility of applying the powerful methods of cohomology to non-locality and contextuality.