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DTSTAMP:20210308T200000Z
UID:1614953543349@events.msu.edu
CATEGORIES:Conferences / Seminars / Lectures
DTSTART:20210308T200000Z
DTEND:20210308T210000Z
SUMMARY:Math Seminar Series
DESCRIPTION:
 Shiwen Zhang, U Minnesota, will be speaking.\n
 \n
 The presentation title is "The landscape law 
 for tight binding Hamiltonians."\n
 \n
 Contact 
 Jeffrey Hudson Schenker (schenke6@msu.edu) for 
 more information.\n
 \n
 The localization landscape 
 theory, introduced in 2012 by Filoche and 
 Mayboroda, considers the so-called the landscape 
 function u solving Hu=1 for an operator 
 H. The landscape theory has remarkable power 
 in studying the eigenvalue problems of H and 
 has led to numerous landscape baked'' results 
 in mathematics, as well as in theoretical 
 and experimental physics. In this talk, we will 
 discuss some recent results of the landscape 
 theory for tight-binding Hamiltonians H=-Delta+V 
 on Z^d. We introduce a box counting function, 
 defined through the discrete landscape 
 function of H. For any deterministic bounded 
 potential, we give estimates for the integrated 
 density of states from above and below by 
 the landscape box counting function, which 
 we call the landscape law. For the Anderson model, 
 we get a refined lower bound for the IDS, 
 throughout the spectrum. We will also discuss 
 some numerical experiments in progress on 
 the so-called practical landscape law for the 
 continuous Anderson model. This talk is based 
 on joint work with D. N. Arnold, M. Filoche, 
 S. Mayboroda, and Wei Wang.\n\n
 Price: free\n
 Sponsor: Department of Mathematics\n
 Sponsor's Homepage: https://www.math.msu.edu/\n
 Contact name: Department of Mathematics\n
 Contact phone: (517) 353-0844\n
 for more info visit the web at:\n 
 https://www.math.msu.edu/Seminars/CalendarView.aspx?month-of=September2016\n
LOCATION:Online via Zoom
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