2023 Simons Collaboration on the Localization of Waves Annual Meeting

The fourth annual meeting of the Simons Collaboration on the Localization of Waves hosted 110 world-class scientists (70 in person and 40 remote) in New York City to discuss their work in understanding and exploiting the localization of waves brought about by a disordered environment or complex geometry, and related wave behaviors.

Collaboration Director, Svitlana Mayboroda (University of Minnesota), kicked off the presentations with, “Localization of Waves: Director’s Overview,” which touched on all of the various projects and their developments over the past year, marked by the Fields Medal awarded to PI Hugo Duminil-Copin, and the Nobel Prize in Physics awarded to PI Alain Aspect. Professor Wolfgang Ketterle’s (Massachusetts Institute of Technology) talk, “Ultracold Atoms, Interacting Spins, and Quantum Simulations,” presented groundbreaking work on the manipulation of interacting cold atoms with light at a deep sub-wavelength scale. Professor Peter Sarnak (Princeton University) then connected remotely to discuss recent findings and conjectures on the asymptotic behavior of high energy eigenfunctions on manifolds in his talk, “Some Mathematical Problems of Quantum Chaos.” Founding PI Claude Weisbuch (École Polytechnique and University of California at Santa Barbara) presented theoretical and experimental work unveiling the mechanisms of charge carrier localization at the nanoscale in his talk, “Carrier Localization in III-Nitrides versus Conventional III-V Semiconductors: A Study on the Effects of Alloy Disorder in Semiconductors Using Landscape Theory and the Schrödinger Equation.” Concluding the speakers on the first day was Professor Eugenia Malinnikova (Stanford University), who demonstrated sharp control inequalities ruling the variations of Laplacian eigenfunctions in her talk entitled “Laplace Eigenfunctions and the Frequency Function Method.” Day One concluded with PI and speaker dinner at Scampi.

Day Two began with a talk by Jacqueline Bloch (Université Paris-Saclay) entitled “Polariton in Semiconductor Lattices: Exploring Out-of-Equilibrium Physics in an Open System,” that detailed remarkable experiments exploiting strong light-matter coupling in semiconductors to investigate key theoretical problems, in particular the scaling exponents of the KPZ equation. Collaboration PI and 2022 Fields Medal recipient, Hugo Duminil-Copin (Université de Genève) then presented “New Techniques in 2D Spin Systems and Random Height Functions,” showing the deep connections existing between spin models (Ising, XY, Heisenberg) and percolation problems on lattices. The conference concluded with a stimulating presentation by Professor Carlo Beenakker (Universiteit Leiden) entitled, “Road to Reality: Quantum Mechanics without Complex Numbers.” Professor Beenakker explained how Majorana fermions can be modeled through a real (not complex) dynamical equation, and how these specific particles might help to explore new questions on condensed matter physics.

A gratifying aspect of the meeting was that, despite the wide diversity of backgrounds of the participants, there were lively discussions across disciplinary boundaries throughout.

The Annual Meeting allowed for the Collaboration to again gather and discuss our goals and objectives as we continue our wide reaching and highly impactful studies.

• Svitlana Mayboroda will extend her work on developing a new calculus to account for the structures recently unveiled in phase space by the collaboration in the Wigner-Weyl approach. Together with Guy David, David Jerison and Hugo Duminil-Copin, she will explore the properties of the level sets of waves and of the localization landscape in disordered media.
• Marcel Filoche, Svitlana Mayboroda and Hugo Duminil-Copin will investigate the percolation properties of the level sets of the localization landscape, and especially their relation with the prediction of the mobility edge.
• In cold atom experiments, Alain Aspect’s team, in collaboration with Marcel Filoche and Svitlana Mayboroda, will determine the mobility edge in 3D speckle potentials using their recently developed cutting-edge experimental platform, as well as the critical exponents of the Anderson transition.
• In collaboration with James Speck, Doug Arnold will investigate the detailed structure of electronic eigenstates in disordered nitride-based alloys, especially at energies close to the delocalization transition where they are expected to adopt a multifractal nature.
• Claude Weisbuch and James Speck, in collaboration with Marcel Filoche, will experimentally assess electronic transport in nitride-based disordered alloys. Marcel Filoche’s team will develop a Wigner-Weyl approach to transport in the localization landscape theory, the last building block before achieving a quantum drift-diffusion model of semiconductors, which promises to be the future design tool for semiconductor devices at the nanoscale.
• Richard Friend’s team, in collaboration with Marcel Filoche, will implement dynamical aspects of localization in the localization landscape theory and, in particular, investigate the role played by temperature in the absorption tails of perovskites and organic

We are grateful to the Simons Foundation for the opportunity to continue our research into this exciting topic and look forward to sharing even more results of our efforts at the next Simons Foundation Annual Meeting, February 15 & 16, 2024.

Svitlana Mayboroda
University of Minnesota and ETH Zürich

Localization of Waves: Director’s Overview
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Svitlana Mayboroda will provide an overview of the progress and future plans of the Simons Collaboration on Localization of Waves.
 

Wolfgang Ketterle
Massachusetts Institute of Technology

Ultracold Atoms, Interacting Spins and Quantum Simulations
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Ultracold atoms offer a unique platform to study the fundamental physics of interacting spins and magnetism. In optical lattices, we have realized paradigmatic Heisenberg models, including the special XX-model which can be exactly solved by mapping it to non-interacting fermions. In these studies, the spin-spin interactions come from superexchange or second-order tunneling. In contrast, dysprosium atoms have a magnetic moment of 10 Bohr magnetons and can directly interact via magnetic fields. We have observed such magnetic interactions in a bilayer system where we could adjust the bilayer separation in the 50 nm range using a new superresolution technique.
 

Peter Sarnak
Princeton University

Some Mathematical Problems of Quantum Chaos

Peter Sarnak will review the expectations and challenges in understanding the topography of high frequency eigenstates of quantizations of chaotic Hamiltonians with few degrees of freedom.
 

Claude Weisbuch
École Polytechnique

Carrier Localization in III-Nitrides versus Conventional III-V Semiconductors: A Study on the Effects of Alloy Disorder in Semiconductors Using Landscape Theory and the Schrödinger Equation
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Why does compositional disorder impact so drastically electronic transport and light emission in some semiconductor alloys, while it has almost no effect in others? Beyond its academic interest, this question has a profound impact on the energy savings performance of LEDs, a major component of energy efficiency. In this talk, Claude Weisbuch will show how the localization landscape theory helps us answer this puzzling question: the landscape-based effective potentials of III-nitride alloys exhibit much larger fluctuations compared to other III-V semiconductors, particularly for holes, revealing their localization properties, a fact confirmed by direct solutions to Schrödinger’s equation. However, computations also show that electron wavefunctions should be all delocalized, while photoemission experiments have observed electron localization, for instance in InxGa1-xN (indium gallium nitride) samples at low temperature. Weisbuch will show that, to understand this apparent paradox, one has also to account for the Coulomb interaction between electrons and holes in a random disordered alloy. This results in a class of semiconductor quasiparticles with hybrid properties in between hydrogenoïd excitons and disorder-localized free particles. These simulations correlate well with experimental results displaying localization-free behavior for low alloy indium concentrations and at temperatures above 150K.
 

Eugenia Malinnikova
Stanford University

Laplace Eigenfunctions and the Frequency Function Method
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A classical idea in the study of eigenfunctions of the Laplace–Beltrami operator is that they behave like polynomials of degree corresponding to the eigenvalue. Eugenia Malinnikova will discuss several properties of eigenfunctions which confirm this idea, including the Bernstein and Remez inequalities. As a corollary, Malinnikova will formulate a local version of the celebrated Courant theorem on the number of nodal domains of eigenfunctions.
 

Jacqueline Bloch
CNRS / University of Paris-Saclay

Polariton in Semiconductor Lattices: Exploring Out-of-Equilibrium Physics in an Open System
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Photonic resonators, coupled within a lattice, have appeared in the recent years as a powerful synthetic platform to imprint on light some of the fascinating physical properties that can emerge in condensed matter, or even to go beyond what exists in nature. For instance, light can become superfluid, present spin-orbit coupling, spin Hall effect or propagate along topologically protected edge states.
In the present talk, Jacqueline Bloch will discuss the influence of the openness of the system on the physics. Indeed, photons constantly leak out from the cavities, so that the system needs being continuously pumped for a steady state to be reached. The steady state can be strongly out of equilibrium. Moreover, the engineering of the drive, that is, injecting photons in a very controlled way, provides a new tool to tailor the band structure and manipulate the topology of lattices.
After a general introduction to polariton lattices, Bloch will illustrate this driven dissipative physics by presenting two recent experiments. First, Bloch will show how to evidence experimentally that polariton condensates belong to a different universality class than their equilibrium counterpart, namely the Kardar–Parisi–Zhang (KPZ) universality class. Second, Bloch will present how we could generate a non-trivial topological interface in a lattice, using the interplay of drive engineering and non-linearity.
 

Hugo Duminil-Copin
Université de Genève and IHÉS

New Techniques in 2D Spin Systems and Random Height Functions

In this talk, Hugo Duminil-Copin will describe recent progress in our understanding of 2D lattice spin systems. Duminil-Copin will explain developments in graphical representations of the spin O(n) model, Potts, and Ashkin–Teller models, as well as connections between the behavior of these systems and localized/delocalized behavior in random height functions. This progress may shed new light on conformal invariance, the BKT phase transition of the XY model and Polyakov’s conjecture for spin O(n) models with n>2.
 

Carlo Beenakker
Leiden University

Road to Reality: Quantum Mechanics without Complex Numbers
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Since Schrödinger, we know that the fundamental equation of quantum mechanics contains the imaginary number i, the square root of minus one. This seems unavoidable, but in recent years we have discovered a class of materials that are described by a real wave equation. The materials are called topological superconductors, and the particles that they host are called Majorana fermions. This topic is of fundamental interest, but it may also find applications in the context of quantum computers.