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Approccio all’equilibrio termico da parte di un sistema macroscopico quantistico

Ho ritrovato Lebowitz cercando un suo articolo del 2009 realizzato con Goldstein, Mastrodonato, Tumulka e Zanghì (vedi #qui) e sono contento che il programma di ricerca di Boltzmann continui. L’abstract è il seguente:

We consider an isolated, macroscopic quantum system.

Let H be a micro-canonical “energy shell,” i.e., a subspace of the system’s Hilbert space spanned by the (finitely) many energy eigenstates with energies between E and E + delta E.

The thermal equilibrium macro-state at energy E corresponds to a subspace H_{eq} of H such that dimH_{eq}/dimH is close to 1.

We say that a system with state vector psi in H is in thermal equilibrium if psi is “close” to H_{eq}. We show that for “typical” Hamiltonians with given eigenvalues, all initial state vectors psi_0 evolve in such a way that psi_t is in thermal equilibrium for most times t.

This result is closely related to von Neumann’s quantum ergodic theorem of 1929.