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Mathematical Physics Seminar

Hal Tasaki - Nature abhors a vacuum: The role of effective dimension in thermalization of an isolated macroscopic quantum system

Location:  Zoom
Date & time: Wednesday, 27 December 2023 at 10:45AM - 11:45PM

Hal Tasaki – Gakushuin University

Wednesday, December 27th, 10:45AM EST (Zoom meeting starts at 10:30 EDT) 

Nature abhors a vacuum: The role of effective dimension in thermalization of an isolated macroscopic quantum system

 

I will discuss the problem of thermalization, i.e., the approach to thermal equilibrium, of an isolated macroscopic quantum system evolving under quantum mechanical unitary time evolution.  I will first see that an initial state with a sufficiently large effective dimension (the effective number of energy eigenstates that constitute the state) generally thermalizes, and discuss when the effective dimension should be large.  I will then summarize my recent work with Naoto Shiraishi (arXiv:2310.18880) about a simple model (a free fermion chain) in which the presence of thermalization (in a restricted sense) can be rigorously established without relying on any unproven assumptions.  The basic ingredients are the new strategy for constructing a nonequilibrium state with a large effective dimension and the proof of the absence of degeneracy in energy eigenvalues based on some number-theoretic facts.

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