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The study of large, complicated systems employing statistics and probability theory to extract average properties and to provide a connection between mechanics and thermodynamics.

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Existence of gap when the first energy level has an infinite degeneracy

Consider a Hamiltonian $H_N$ on a finite system with the following properties: It has a unique ground state The first excited energy level has a degeneracy $N$ (there are $N$ eigenstates for the firs …
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