433 research outputs found
Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics
It is shown how to resolve the apparent contradiction between the macroscopic
approach of phase space and the validity of the uncertainty relations. The main
notions of statistical mechanics are re-interpreted in a quantum-mechanical
way, the ergodic theorem and the H-theorem are formulated and proven (without
"assumptions of disorder"), followed by a discussion of the physical meaning of
the mathematical conditions characterizing their domain of validity.Comment: English translation by Roderich Tumulka of J. von Neumann: Beweis des
Ergodensatzes und des H-Theorems. 41 pages LaTeX, no figures; v2: typos
corrected. See also the accompanying commentary by S. Goldstein, J. L.
Lebowitz, R. Tumulka, N. Zanghi, arXiv:1003.212
Cyclotomic matrices over real quadratic integer rings
We classify all cyclotomic matrices over real quadratic integer rings and we
show that this classification is the same as classifying cyclotomic matrices
over the compositum all real quadratic integer rings. Moreover, we enumerate a
related class of symmetric matrices; those matrices whose eigenvalues are
contained inside the interval [-2,2] but whose characteristic polynomials are
not in Z[x].Comment: 13 page
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