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Syllabus Random Schrodinger Operators - 80831
עברית
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Last update 18-02-2020
HU Credits: 2

Degree/Cycle: 2nd degree (Master)

Responsible Department: Mathematics

Semester: 2nd Semester

Teaching Languages: English and Hebrew

Campus: E. Safra

Course/Module Coordinator: Prof Jonathan Breuer

Coordinator Email: jbreuer@math.huji.ac.il

Coordinator Office Hours: By appointment

Teaching Staff:
Prof Jonathan Breuer

Course/Module description:
The course will deal with the spectral theory of random Schroedinger operators. We will focus on proofs of localization, properties of the density of states, eigenvalue statistics, and the extended states conjecture for the Anderson model for high dimensions.

Course/Module aims:
The students will know the basic concepts and techniques in the study of random Schroedinger operators.

Learning outcomes - On successful completion of this module, students should be able to:
On successful completion of this module, students should be able to read a current paper in the area and even start a research project.

Attendance requirements(%):
none

Teaching arrangement and method of instruction: lectures

Course/Module Content:
-Introduction to ergodic and random Schroedinger operators
- The spectral measure and the density of states
- What is localization
- Eigenvalue statistics
- Absolutely continuous spectrum

Required Reading:
none

Additional Reading Material:
-Stollmann: "Caught by disorder"
- Kirsch: "An invitation to random Schroedinger operators" (paper)
- Carmona, Lacroix: "Spectral Theory of Random Schroedinger Operators"
- Aizenman, Warzel: "Random Operators: Disorder Effects on Quantum Spectra and Dynamics"

Course/Module evaluation:
End of year written/oral examination 0 %
Presentation 0 %
Participation in Tutorials 0 %
Project work 100 %
Assignments 0 %
Reports 0 %
Research project 0 %
Quizzes 0 %
Other 0 %

Additional information:
 
Students needing academic accommodations based on a disability should contact the Center for Diagnosis and Support of Students with Learning Disabilities, or the Office for Students with Disabilities, as early as possible, to discuss and coordinate accommodations, based on relevant documentation.
For further information, please visit the site of the Dean of Students Office.
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