Eugene Kanzieper (Holon Institute of Technology) | Random Matrix Theory of the Power Spectrum in Quantum Chaotic Systems |
Abstract:
The power spectrum analysis of stochastic spectra has emerged as a powerful tool for studying both system-specific and universal properties of complex systems. In the context of complex quantum systems, it reveals whether the corresponding classical dynamics is regular or chaotic, or a mixture of both, and encodes a ‘degree of chaoticity’. In combination with other long- and short-range spectral fluctuation measures, it provides an effective way to identify system symmetries, determine a degree of incompleteness of experimentally measured spectra, and get the clues about systems’ internal structure. In this talk, I shall formulate a random-matrix-theory approach to the power spectrum of energy level fluctuations in fully chaotic quantum structures. In the particular case of broken time-reversal symmetry, our theory produces a parameter-free prediction for the power spectrum expressed– in the domain of its universality – in terms of a fifth Painlevé transcendent. Finally, I shall present fair evidence that a universal Painlevé V curve can be observed in the power spectrum of nontrivial zeros of the Riemann zeta function. Deviations from universality will also be briefly discussed.
When: November 16, 2022 2:00 PM (Israel Standard Time).
Where: Room 108, Multipurpose Bldg. & over Zoom
Note the unusual room for this talk!