Simons Collaboration on Localization of Waves Annual Meeting 2020

Date & Time


Location

Gerald D. Fischbach Auditorium
160 5th Ave
New York, NY 10010 United States

View Map

Thurs: 8:30 AM – 5 PM
Fri: 8:30 AM – 2 PM

Registration Closed

Invitation Only

Participation is by invitation only. All participants must register.

Organizers
Svitlana Mayboroda, University of Minnesota
Marcel Filoche, Ecole Polytechnique

The Simons Collaboration on Localization of Waves Annual Meeting will bring together world leading mathematicians and physicists whose work illuminates profound connections between disorder, geometric complexity, and the behavior of waves, or harnesses recent advances in mathematical analysis for important applications in physics involving wave localization. Building bridges from harmonic analysis to cold atoms or nitride-based LEDs, and from the geometric measure theory to transport in organic semiconductors, the meeting will enable discussions and cross-fertilization of ideas between scientists of a wide variety of backgrounds and will also offer an opportunity to present the collaboration’s most recent advances.

  • Agendaplus--large

    Thursday, February 20

    8:30 AMCHECK-IN & BREAKFAST
    9:30 AMShuji Nakamura | History of InGaN-based LED
    Marcel Filoche, Ecole Polytechnique| The Localization Landscape: Order Through Disorder
    10:30 AMBREAK
    11:00 AMTerence Tao | Delocalization of Eigenvectors of Random Matrices
    12:00 PMLUNCH
    1:00 PMRichard Friend | Organic Electronics
    2:00 PMBREAK
    2:30 PMSvitlana Mayboroda | The Hidden Landscape of Wave Localization
    3:30 PMBREAK
    4:00 PMCharles Fefferman | The One Electron Model of Graphene
    5:00 PMDAY ONE CONCLUDES

    Friday, February 21

    8:30 AMCHECK-IN & BREAKFAST
    9:30 AMMichael Berry | Coherent Destructive Inteference: Superoscillations and Wave Geometry
    10:30 AMBREAK
    11:00 AMPeter Sarnak | The Topologies of Nodal Sets of Random Monochromatic Waves
    12:00 PMLUNCH
    1:00 PMSteven Kivelson | How Interactions Change the Physics of Wave Localization
    2:00 PMMEETING CONCLUDES
  • Abstractsplus--large

    Shuji Nakamura
    Materials and ECE Departments
    Solid State Lighting and Energy Center
    University of California, Santa Barbara

    History of InGaN-based LED

    In the 1970s and ’80s, efficient blue and green light-emitting diodes (LED) were the last missing elements for solid-state display and lighting technologies due to the lack of suitable materials. By that time, III-nitride alloys were regarded as the least decent candidates due to various ‘impossible’ difficulties. However, a series of unexpected breakthroughs in the 1990s changed people’s view. Finally, in 1993, the first high-efficient InGaN blue LEDs were invented and commercialized. Nowadays, InGaN-based LEDs have become the most widely used light source in many applications.
     

    Marcel Filoche
    Directeur de recherche CNRS
    Physique de la Matière Condensée, Ecole Polytechnique

    The Localization Landscape: Order Through Disorder

    Standing waves in disordered or complex systems can be subject to an intriguing phenomenon which has puzzled physics and mathematical communities for more than 60 years, called wave localization. This phenomenon consists of a concentration of the wave energy in a very restricted subregion of the entire domain and has been observed in mechanics, acoustics and quantum physics. We will show the existence of an underlying structure for wave localization in all system types. This structure, called ‘localization landscape,’ is the solution to a Dirichlet problem associated to the wave equation. Going further, the landscape also defines an ‘effective localization potential,’ providing a new insight into the confinement of the waves in disordered media. This potential allows us to predict the localization region, the energies of the localized modes, the density of states and the long-range decay of the wave functions.

    As an example, we present here the implementation of this tool into a semiclassical drift-diffusion transport model of semiconductor devices. We will show how this novel model enables us to account for quantum effects at the nanoscale and to compute light absorption and light emission between localized quantum states, granting an acceleration of the computation time of full LED simulations (carrier transport and light emission) by several orders of magnitude compared to the Schrödinger-Poisson drift-diffusion (SP-DD) type approach.
     

    Terence Tao
    Department of Mathematics
    University of California, Los Angeles

    Delocalization of Eigenvectors of Random Matrices

    We survey a number of techniques that have been successfully used in recent years to establish delocalization results for eigenvalues of various random matrix ensembles, such as Wigner matrices.
     

    Richard Friend
    Cavendish Laboratory
    University of Cambridge

    Organic Electronics

    Pi-conjugated organic molecules and polymers now provide a set of well-performing semiconductors that support devices, including light-emitting diodes (LEDs) as used in smartphone displays and lighting, field-effect transistors (FETs) and photovoltaic diodes (PVs). These are attractive materials to manufacture, particularly for these large-area applications, but as Friend will explore in this talk, their electronic properties are very different from standard semiconductors such as silicon. Firstly, electronic overlap between adjacent molecules is relatively poor, and this often drives localization of electronic states. Secondly, dielectric screening is weak so that Coulomb interactions between charges and spin exchange energies are large. Management of transport and of excited state spin is fundamental for efficient LED and solar cells operation. I will discuss in particular recent progress in the control of emissive spin singlet excited states and non-emissive spin triplet excited states.
     

    Svitlana Mayboroda
    Northrop Professor
    Department of Mathematics
    University of Minnesota

    The Hidden Landscape of Wave Localization

    Complexity of the geometry, randomness of the potential and many other irregularities of the system can cause powerful, albeit quite different, manifestations of localization, a phenomenon of confinement of waves, or eigenfunctions, to a small portion of the original domain. In the present talk, we show that behind a possibly disordered system, there exists a structure, referred to as a ‘landscape function,’ which predicts the location and shape of the localized eigenfunctions, a pattern of their exponential decay, and delivers accurate bounds for the corresponding eigenvalues. In particular, we establish non-asymptotic estimates from above and below on the integrated density of states of the Schroedinger operator using a counting function for the minima of the localization landscape. The results are deterministic and rely on a new uncertainty principle. Narrowing down to the context of disordered potentials, Mayboroda derives the best currently available bounds on the integrated density of states for the Anderson model.
     

    Charles Fefferman
    Herbert E. Jones University Professor of Mathematics
    Princeton University

    The One Electron Model of Graphene

    Many remarkable properties of graphene arise already in the spectral theory of certain Schroedinger operators in the plane. The relevant potentials have the ‘honeycomb’ symmetries of the tiling of the plane by regular hexagons. Fefferman’s talk presents results and unsolved problems regarding such Schroedinger operators (joint work with Michael Weinstein and James Lee Thorp).
     

    Michael Berry
    Emeritus Professor of Physics
    University of Bristol, UK

    Coherent Destructive Interference: Superoscillations and Wave Geometry

    In physics, the mathematical phenomenon of superoscillations, in which functions vary faster than their fastest Fourer components (‘faster than they should’), is associated with almost-destructive interference. It occurs near phase singularities of waves of all kinds (optical, acoustic, quantum, ocean tides, etc.). Superoscillations are associated with quantum weak measurements. They are a compact way to represent fractals (e.g., the Weierstrass nondifferentiable function) to specified resolution. In light represented by scalar waves and in many contexts in quantum physics, superoscillations are rather common, but in vector light, represented by electric fields — and more so when magnetic fields are included — they are unexpectedly rare. One scheme for sub-wavelength imaging is based on superoscillations. Superoscillations in red light can escape as gamma radiation.

    Peter Sarnak
    Institute for Advanced Study
    Princeton University

    The Topologies of Nodal Sets of Random Monochromatic Waves

    The topology of a hyper-surface in P^n(R) of high degree can be very complicated. However, if we choose such an algebraic hyper-surface — or nodal set of a monchromatic wave — at random, there is a corresponding universal law for its distribution over connected components. Little is known about these laws, and aspects appear to be dramatically different for n=2 and n>2. The zero sets of monochromatic waves are a model for nodal sets of eigenfunctions of quantizations of chaotic Hamiltonians.
     

    Steven Kivelson
    Institute for Theoretical Physics
    Stanford University

    How Interactions Change the Physics of Wave Localization

    ‘Anderson localization’ typically refers to a property of noninteracting quantum particles in a random potential, or more generally to the solution of a wave equation in a random medium. In physical systems, particles interact with each other and this — even if the interactions are in some sense arbitrarily weak — can qualitatively change the nature of the resulting phases of matter. Kivelson will discuss — both from a theoretical perspective and by invoking the results of experiment — some examples in which interactions fundamentally change the physically interesting properties of a macroscopic collection of quantum particles (i.e., electrons) in a random medium.

  • Public Lectureplus--large

    Simons Foundation Lecture
    Wednesday, February 19, 2020

    Alain Aspect, Institut d’Optique Graduate School & Ecole Polytechnique
    From Einstein’s Doubts to Quantum Technologies: A New Quantum Revolution

    Tea 4:15-5:00 PM
    Lecture 5:00-6:15 PM

    Participation is optional; separate registration is required. For more information see the lecture’s page.

  • Travelplus--large

    Air and Train

    Groups A & B
    The foundation will arrange and pay for all air and train travel to the conference for those in Groups A & B. Please provide your travel specifications by clicking the registration link above. If you are unsure of your group, please refer to your invitation sent via email.
    Group C
    Individuals in Group C will not receive travel or hotel support. Please register at the link above so that we can capture your dietary requirements. If you are unsure of your group, please refer to your invitation sent via email.

    Personal Car

    For participants driving to Manhattan, The James Hotel New York, NoMad offers valet parking. Please note there are no in-and-out privileges when using the hotel’s garage, therefore it is encouraged that participants walk or take public transportation to the Simons Foundation.
  • Hotelplus--large

    Participants in Groups A & B who require accommodations are hosted by the foundation for a maximum of three nights at The James Hotel New York, NoMad. Any additional nights are at the attendee’s own expense.

    The James Hotel New York, NoMad
    22 East 29th Street
    New York, NY 10016
    (between 28th and 29th Streets)

    To arrange accommodations, please register at the link above.

    For driving directions to The James, please click here.

  • Contactsplus--large

    Travel & Hotel Assistance
    Elise Volpe, CrowdControl Events
    simons@crowdcontrol.io
    631-923-6757

    Registration and General Meeting Assistance
    Meghan Fazzi
    Manager, Events and Administration, MPS, Simons Foundation
    mfazzi@simonsfoundation.org
    (212) 524-6080

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