QM3 Quantum Matter meets Maths   RSS

Planned sessions

Gil Refael 21/09/2020, 17:00 — 18:00 Europe/Lisbon — Instituto Superior Técnico
, Institute for Quantum Information and Matter

Floquet higher-order topological insulators: principles and path towards realizations

The co-existence of spatial and non-spatial symmetries together with appropriate commutation/anticommutation relations between them can give rise to static higher-order topological phases, which host gapless boundary modes of co-dimension higher than one. Alternatively, space-time symmetries in a Floquet system can also lead to anomalous Floquet boundary modes of higher co-dimensions, with different commutation/anticommutation relations with respect to non-spatial symmetries. In my talk I will review how these dynamical analogs of the static HOTI's emerge, and also show how a coherently excited phonon mode can be used to support non-trivial Floquet higher-order topological phases. If time allows, I will also review recent work on Floquet engineering and band flattening of twisted-bilayer graphene.

Tom Claeys 28/09/2020, 17:00 — 18:00 Europe/Lisbon — Instituto Superior Técnico
, Université Catholique de Louvain

Deformed Airy kernel determinants: from KPZ tails to initial data for KdV

Fredholm determinants associated to deformations of the Airy kernel are closely connected to the solution to the Kardar-Parisi-Zhang (KPZ) equation with narrow wedge initial data, and they also appear as largest particle distribution in models of positive-temperature free fermions. I will explain how logarithmic derivatives of the Fredholm determinants can be expressed in terms of a $2\times 2$ Riemann-Hilbert problem.

This Riemann-Hilbert representation can be used to derive precise lower tail asymptotics for the solution of the KPZ equation with narrow wedge initial data, refining recent results by Corwin and Ghosal, and it reveals a remarkable connection with a family of unbounded solutions to the Korteweg-de Vries (KdV) equation and with an integro-differential version of the Painlevé II equation.

Masud Haque 12/10/2020, 17:00 — 18:00 Europe/Lisbon — Instituto Superior Técnico
, Maynooth University

Eigenstate Thermalization, random matrices and (non)local operators in many-body systems

The eigenstate thermalization hypothesis (ETH) is a cornerstone in our understanding of quantum statistical mechanics. The extent to which ETH holds for nonlocal operators (observables) is an open question. I will address this question using an analogy with random matrix theory. The starting point will be the construction of extremely non-local operators, which we call Behemoth operators. The Behemoths turn out to be building blocks for all physical operators. This construction allow us to derive scalings for both local operators and different kinds of nonlocal operators.

Barry Simon 19/10/2020, 13:00 — 14:00 Europe/Lisbon — Instituto Superior Técnico
, Caltech

Berry's Phase, $\operatorname{TKN}^2$ Integers and All That: My work on Topology in Condensed Matter Physics 1983-1993

I will give an overview of my work on topological methods in condensed matter physics almost 40 years ago. Include will be Homotopy and $\operatorname{TKN}^2$ integers, holonomy and Berry's phase and quarternions and Berry's phase for Fermions. If time allows, I'll discuss supersymmetry and pairs of projections.

Joseph Maciejko 26/10/2020, 17:00 — 18:00 Europe/Lisbon — Instituto Superior Técnico
, University of Alberta

Hyperbolic band theory

The notions of Bloch wave, crystal momentum, and energy bands are commonly regarded as unique features of crystalline materials with commutative translation symmetries. Motivated by the recent realization of hyperbolic lattices in circuit QED, I will present a hyperbolic generalization of Bloch theory, based on ideas from Riemann surface theory and algebraic geometry. The theory is formulated despite the non-Euclidean nature of the problem and concomitant absence of commutative translation symmetries. The general theory will be illustrated by examples of explicit computations of hyperbolic Bloch wavefunctions and bandstructures.

Benoît Douçot 09/11/2020, 17:00 — 18:00 Europe/Lisbon — Instituto Superior Técnico
, LPTHE, Sorbonne Université

Jiannis K. Pachos 16/11/2020, 17:00 — 18:00 Europe/Lisbon — Instituto Superior Técnico
, University of Leeds

Gourab Ray 30/11/2020, 17:00 — 18:00 Europe/Lisbon — Instituto Superior Técnico
, University of Victoria

Universality of dimers via imaginary geometry

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The goal of QM3 is to discuss recent topics in quantum matter from a mathematical perspective while building bridges between the physics and mathematics communities.

Organizers: Bruno Mera, João Pimentel Nunes, José Mourão, Pedro Ribeiro, Roger Picken, Vitor Rocha Vieira
Zoom password: send an email to one of the organizers to ask for the password.