# Wave Functions in Thermal Equilibrium—GAP Measures and Canonical Typicality

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Roderick Tumulka, Rutgers University
I will talk about the claim that a quantum system in thermal equilibrium at temperature $1/\beta$ has a random wave function whose distribution is a particular probability measure on Hilbert space called $GAP(\beta )$. This is roughly analogous to the familiar claim that a classical system in thermal equilibrium at temperature $1/\beta$ has a random phase point $(q,p)$ whose distribution has density proportional to $\exp{-\beta H(q,p)}$ with $H(q,p)$ the Hamiltonian function. I will explain how the GAP measures are defined in terms of the system's Hamiltonian operator $H$, what precisely the claim about quantum systems means, and how it is connected to Schrödinger's cat and to the typicality of the canonical density matrix $\exp{-\beta H}$.