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Week of Month - Month
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25, September
Colloquium
Topic: TBA
Bard Ermentrout - University of Pittsburgh Host: (Lisa Fauci)
Abstract: TBA
Location: TBA
Time: 3:30 pm
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September 12-8
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08, September
Math Research Seminars Name
Topic: Integrability and Beyond
Speaker: Roman Riser - Tulane University
Abstract: The power spectrum has emerged as an effective tool for studying both system-specific and universal properties of quantum systems. In these 3 lectures we will study the power spectrum for the circular unitary ensemble (CUE). In the introduction, I will give an overview of results for the power spectrum. This will include a plot of the asymptotic limit for the CUE. We will compare it with numerical results for the zeros of the Riemann zeta function.
In the first lecture, I will derive a general representation for the power spectrum. Then we will review the definition and basic properties of the CUE and its joint probability distribution function of the eigenvalues. Next we deduce an exact representation of the power spectrum for the CUE with $N$ eigenvalues. In the second lecture, we will discuss the limit $N\rightarrow\infty$ and find a parameter free representation given in terms of the Painlev\'e V transcendent. In the last lecture, we will analyze the asymptotic formula and discuss its numerical evaluation.
Location: TBA
Time: 3:00
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