2025/11/03 by T. C. Dorlas, Dorlas, T. C.
Computer Science · Mathematics · Physics and Astronomy · #46G10 #60G10 #82B10 #82B20 #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Information and Cryptography #Quantum Mechanics and Applications #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.2511.01686
openalex publication_date 2025/11/03 · openalex created_date 2025/11/06 · openalex updated_date 2026/07/28
We reconsider the quantum analogue of Varadhans Theorem proved by Petz, Raggio and Verbeure. They proved this theorem using standard techniques in quantum statistical mechanics of lattice systems to arrive at a variational formula over states on an operator algebra, which can subsequently be reduced to a variational formula in terms of a single real variable. In this paper a new proof is given using a quantum version of the large deviation analysis together with the Trotter product formula. The proof is subsequently extended to the general case of q non-commuting variables resulting in a variational formula for general mean-field quantum spin systems as first derived by Raggio and Werner.