PIRSA:21100008 Scientific Series Condensed Matter

DOI10.48660/21100008

Series: Quantum Matter

Chan, A. (2021). Many-Body Quantum Chaos and Spectral Form Factor . Perimeter Institute. https://pirsa.org/21100008

Chan, Amos. Many-Body Quantum Chaos and Spectral Form Factor . Perimeter Institute, Oct. 26, 2021, https://pirsa.org/21100008 

@misc{ pirsa_PIRSA:21100008,
  doi = {10.48660/21100008},
  url = {https://pirsa.org/21100008},
  author = {Chan, Amos},
  keywords = {Condensed Matter},
  language = {en},
  title = {Many-Body Quantum Chaos and Spectral Form Factor },
  publisher = {Perimeter Institute},
  year = {2021},
  month = {oct},
  note = {PIRSA:21100008 see, \url{https://pirsa.org}}
}

Abstract

The study of spectral statistics is of importance due to its universality and utility as a robust diagnostic of quantum chaos. For closed many-body quantum chaotic systems, I will present two results: (i) a quantum-classical mapping that connects the Thouless time, which characterizes the onset of RMT of the spectral form factor (SFF); and the spectral gap of a dual classical stochastic system; (ii) a set of Lyapunov exponents which characterize the spectral statistics in the thermodynamic limit. For open quantum systems with complex spectra, I will propose and analyze a generalized SFF, and show that dissipative quantum chaotic systems display a “dip-ramp-plateau” behaviour with a quadratic ramp.

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