E R G O D I C I T Y, E I G E N S TAT E T H E R M A L I Z AT I O N , - PowerPoint PPT Presentation

L O R E N Z O C A M P O S V E N U T I ( U S C ) E R G O D I C I T Y, E I G E N S TAT E T H E R M A L I Z AT I O N , A N D T H E F O U N D AT I O N O F C L A S S I C A L A N D Q U A N T U M S TAT- M E C H Lorenzo Campos Venuti Lawrence Liu arXiv:1904.02336 D O L O M I T E S J U LY 2 0 1 9

G E N E R A L Q U E S T I O N Question: How do we build equilibrium statistical mechanics starting from the microscopic laws? Classical laws Quantum laws (Newton) ? What is ergodicity here? One possibility is One possibility is ETH Boltzmann’s ergodic [Deutsch91, Srednicki94, hypothesis (to be proved in Berry77, Rigol-Dunjko- actual models) Olshanii08] (to be proved in actual models) Large math literature: Shnirelman74, Zeldtich87, Sunada97, Rudnik&Sarnak94, Hassell08…