Talks

A closed quantum system is ergodic and satisfies equilibrium statistical physics when it completely loses local information of its initial condition under time evolution, by 'hiding' the information in non-local properties like entanglement. In the last decade, a flurry of theoretical work has shown that ergodicity can be broken in an isolated, quantum many-body system even at high energies in the presence of disorder, a phenomena known as many-body localization (MBL). In this novel phase of matter, highly excited states of an interacting system can serve as quantum memory and even protect exotic forms of quantum order. Recent claims of experimental observation of MBL in two dimensions using ultra-cold atoms has further raised a plethora of intriguing questions.

In one dimension, the strongly localized regime is described in terms of quasi-local integrals of motion, also known as l-bits. Based on this picture I will describe an efficient tensor network method to efficiently represent the entire spectrum of fully many-body localized systems. This ansatz is also successful at capturing features of the MBL to thermal transition. For higher dimensions, I will develop a refined phenomenology of MBL in terms of l*-bits which are only 'approximately' conserved, based on the stability of the localized phase to perturbations on the boundary. I will conclude with a bird's-eye view of some of the open problems in this rapidly growing field.

The Feynman diagram expansion for a Wilson loop observable in Chern-Simons gauge theory generates an infinite series of topological invariants for framed knots.  In this talk, I will describe a new perturbative formalism which conjecturally generates the same invariants for Legendrian knots in the standard contact R^3.  The formalism includes a `perturbative' localization principle which drastically simplifies the structure of calculations.  As time permits, I will provide some examples and applications.  This talk is based upon joint work with Brendan McLellan and Ruoran Zhang.

Quantum Field Theories are interacting quantum systems described by an infinite number of degrees of freedom, necessarily living on an infinite-dimensional Hilbert space. Hence, many concepts from Quantum Information Theory have to be adapted before they can be applied to this setting. However, the task is worthwhile as we obtain new tools to understand the entanglement structure of theories describing the fundamental forces of nature. I will outline two approaches along this route, one bottom-down and one bottom-up strategy. First, general Lorentz invariant quantum fields are studied from a quantum information perspective. Second, I discuss the use of tensor networks to model the entanglement structure of quantum fields. The combination of both approaches yields new insights into Quantum Field Theory from an information theoretic point of view. I will end my talk by giving an outlook into future research directions.

Despite varying speed of light theories (VSL) should be considered as another type of alternative gravity theories with an extra scalar degree of freedom, their formulation causes the problems in view of breaking the light principle and relativity principle. Besides, there are a couple of physical contexts in which c plays the crucial role and it is uncertain that it has the same meaning everywhere. During my talk I will discuss some basic theoretical formulations of varying c theories and discuss their benefits as well as problems. Then, I will review some cosmological tests of VSL theories making also a comparative statistical analysis of the basic theoretical frameworks. Among them, the recent Moffat's varying c approach.