Scientific Series

 It is well known - to those who know it - that noise and randomness can enhance signal resolution. I'll present an easy-to-follow example from digital audio that illustrates the way in which adding noise ("dither") prior to measurement enhances the accuracy with which we are able to distinguish the features of the sound or image. I will then explore the way in which the environmental interactions prior to measurement ordinarily characterized as environment-induced decoherence may play a similar role.  The paradoxical conclusion is that the quasiclassical behavior associated with such systems may be a more accurate representation of the quantum world than what we think of as fully "quantum" behavior, which may in turn be artifactual, the result of errors similar to those introduced by the discretization (also known as "quantization") of data in digital audio and imaging.

The standard theory of topological insulators and superfluids (or superconductors) assumes that the fermionic elementary excitations in these systems – electrons in the insulator and Bogoliubov quasiparticles in the superfluid – do not interact with one another. In this talk I will discuss extensions of this theory to include the effects of interparticle interactions on the topological surface states of 3D topological insulators and superfluids. First, I will argue that bulk quantum fluctuations of the superfluid order parameter in the only 3D topological superfluid known to date, 3He-B, can generate an effective two-body interaction between the surface Majorana fermions.

Possible consequences of this interaction will be discussed. Second, I will propose an extension of the phenomenological Landau theory of Fermi liquids to the surface states of 3D topological insulators, leading to the concept of helical Fermi liquid.

Main properties of generalized contraction methods of Lie algebras, known also as expansion methods, are briefly introduced. Between some of their physical applications, one might study the nature of solutions in theories constructed with those expanded algebras. In particular, as we are interested in solutions that could be relevant in the context of AdS/CFT and Holographic Superconductors, we would like to study the holographic QFT dual to Chern-Simons gravity for an expansion of AdS algebra. As a first step, we studied charged static spherically symmetric BH solutions of a CS theory for the most simple extension of AdS symmetry: AdS×U(1). It is shown that in this kind of higher dimensional gravity, degeneracy in some sectors of the space of solutions can appear. In fact, arbitrary functions remain undetermined after the field equations are imposed. This is related to an increase in local symmetries and it is shown that the knowledge of these "accidental symmetries" can help to formulate a simple criterion that avoids unwanted degenerate ansatze. Finally, main properties of Pure Lovelock gravity are presented and some issues about black hole solutions this theory are also discussed.

Astrophysical observations of the structure of galaxies and clusters are no longer simply proving the existence of DM, but have sharpened into a discovery tool probing the particle physics of dark matter.  I discuss small scale structure anomalies for cold dark matter and their possible implications for dark matter physics, such as the existence of forces in the dark sector.   New results on cluster scales provide a new important handle for constraining dark matter's particle interactions.

High resolution CMB experiments, such as ACT, SPT, and the Planck satellite are making precision measurements of the secondary anisotropies caused by the thermal Sunyaev Zel'dovich (tSZ) effect from galaxy clusters. However, our ability to obtain cosmological information from this tSZ signal is limited by our theoretical understanding of the baryons in clusters and groups. I will discuss how cross correlation methods are providing new windows into the messy “Gastrophysics” of the intracluster medium and the potential for these methods to constrain various cosmological parameters.

Recent progress on the construction of holographic lattices and its applications to AdS/CMT correspondence will be briefly reviewed. Our special interests will focus on the building of bulk geometry of gravity whose holographic duals exhibit metal-insulator transitions (MIT).  In particular, the Peierls phase transition induced by charge density waves is implemented in a holographic manner. The holographic entanglement entropy close to quantum critical points will be discussed as well.

In an approach to quantum gravity where space-time arises from coarse graining of fundamentally discrete structures, black hole formation and subsequent evaporation could be described by a unitary evolution without the problems encountered by standard remnant scenarios or the schemes where information is assumed to come out with the radiation while semiclassical evaporation (firewalls and complementarity). I point out the possibility that the final state is purified by correlations with the fundamental pre-geometric structures (in the sense of Wheeler) which are available in such approaches, and, like defects in the underlying space-time weave, can carry zero energy.

In the last few years there has been significant interest in the possible applications of gauge-gravity duality to condensed matter systems. In this talk I will discuss recent applications of these holographic techniques to strongly correlated systems out of equilibrium. I will argue that insights from general relativity, hydrodynamics and quantum field theory may be combined to yield quantitative predictions for quantum transport.

We present a formal logic modeling some aspects of the behavior of the quantum measurement process, and study some properties of the models of this logic, from which we deduce some characteristics that any such model should verify. In the case of a Hilbert space of dimension at least 3, we then show that no model can lead to the prediction with certainty of more than one atomic outcome. Moreover, if the Hilbert space is finite dimensional, we can precisely describe the structure of the predictions of any model of our logic. As a consequence, we also prove that all the models of our logic make exactly the same predictions regarding whether a given sequence of outcomes is possible.

Symmetry-protected topological (SPT) phases can be thought of as generalizations of topological insulators. Just as topological insulators have robust boundary modes protected by time reversal and charge conservation symmetry, SPT phases have boundary modes protected by more general symmetries. In this talk, I will describe a method for analyzing 2D and 3D SPT phases using braiding statistics. More specifically, I will show that 2D and 3D SPT phases can be characterized by gauging their symmetries and studying the braiding statistics of their gauge flux excitations. The 3D case is of particular interest as it involves a generalization of quasiparticle braiding statistics to three dimensions.

In this talk I will discuss the non-equilibrium response of Chern insulators [1]. Focusing on the Haldane model, we study the dynamics induced by quantum quenches between topological and non-topological phases. A notable feature is that the Chern number, calculated for an infinite system, is unchanged under the dynamics following such a quench. However, in finite geometries, the initial and final Hamiltonians are distinguished by the presence or absence of edge modes. We study the edge excitations and describe their impact on the experimentally-observable edge currents and magnetization. We show that, following a quantum quench, the edge currents relax towards new equilibrium values, and that there is light-cone spreading of the currents into the interior of the sample. I will briefly comment on a complementary project to understand non-equilibrium charge transport using gauge-gravity duality and hydrodynamics.

[1] M. D. Caio, N. R. Cooper, M. J. Bhaseen, Quantum Quenches in Chern Insulators, arXiv:1504.01910