Talks

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.