Roderich Tumulka

Dirac wave functions of positive energy with arbitrarily small position uncertainty

Abstract We consider wave functions in the Hilbert space H=L2(R3,C4) of a single Dirac particle, specifically from the positive-energy subspace H+ of the free Dirac Hamiltonian. Over the decades, various authors hypothesized that for wave functions from H+, there is a positive lo...

Grand-Canonical Typicality

Abstract We study how the grand-canonical density matrix arises in macroscopic quantum systems. “Canonical typicality” is the known statement that for a typical wave function $$\Psi $$ Ψ from a micro-canonical energy shell of a quantum system S weakly coupled to a large but finit...