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.
Thursday, February 20
8:30 AM CHECK-IN & BREAKFAST 9:30 AM Shuji Nakamura | History of InGaN-based LED
Marcel Filoche, Ecole Polytechnique| The Localization Landscape: Order Through Disorder
10:30 AM BREAK 11:00 AM Terence Tao | Delocalization of Eigenvectors of Random Matrices 12:00 PM LUNCH 1:00 PM Richard Friend | Organic Electronics 2:00 PM BREAK 2:30 PM Svitlana Mayboroda | The Hidden Landscape of Wave Localization 3:30 PM BREAK 4:00 PM Charles Fefferman | The One Electron Model of Graphene 5:00 PM DAY ONE CONCLUDES
Friday, February 21
8:30 AM CHECK-IN & BREAKFAST 9:30 AM Michael Berry | Coherent Destructive Inteference: Superoscillations and Wave Geometry 10:30 AM BREAK 11:00 AM Peter Sarnak | The Topologies of Nodal Sets of Random Monochromatic Waves 12:00 PM LUNCH 1:00 PM Steven Kivelson | How Interactions Change the Physics of Wave Localization 2:00 PM MEETING CONCLUDES
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.
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.
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.
University of Cambridge
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.
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.
Herbert E. Jones University Professor of Mathematics
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).
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.
Institute for Advanced Study
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.
Institute for Theoretical Physics
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.
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
Air and Train
Groups A & BThe 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.
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Personal CarFor 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.
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.
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