The Quantum Carpets in a Leaky-Box: Poincare's Recurrences in the Continuous Spectrum

Explore an in-depth lecture on quantum mechanics and complex analysis, focusing on the concept of quantum carpets in a leaky-box system. Delve into the generalization of Poincare's recurrence theorem for continuous spectra, achieved through an innovative approach to defining branch cuts of complex functions. Discover how this method leads to a novel integral representation of quantum carpets and enables the renormalization of resonant states as both space and time-convergent. Examine the relationship between quantum carpet coherence and Wigner function properties in the canonical time-frequency phase space. Investigate how distortions in the Wigner function shape directly impact the dynamics' ability to produce revivals as sharp as the initial wave packet. Gain valuable insights into advanced quantum mechanics concepts and their mathematical representations throughout this hour-long presentation.