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Entropy of Bogoliubov automorphisms of CAR and CCR algebras with respect to quasi-free states. (English) Zbl 1081.46514

Summary: We compute the dynamical entropy of Bogoliubov automorphisms of CAR and CCR algebras with respect to arbitrary gauge-invariant quasi-free states. This completes the research started by E. Størmer and D. Voiculescu [Commun. Math. Phys. 133, No. 3, 521–542 (1990; Zbl 0743.46051)] and continued by H. Narnhofer and W. Thirring [In: G. G.Emch et al. (eds.), “On Klauder’s path: a field trip. Essays in honor of John R. Klauder” (World Scientific, Singapore), 127–145 (1994; Zbl 0942.46505) and Y. M.Park and H. H.Shin [Commun. Math. Phys. 152, No. 3, 497–537 (1993; Zbl 0786.46049)].

MSC:

46L55 Noncommutative dynamical systems
46L35 Classifications of \(C^*\)-algebras
81S05 Commutation relations and statistics as related to quantum mechanics (general)
82C10 Quantum dynamics and nonequilibrium statistical mechanics (general)
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[1] DOI: 10.1017/S0143385797085027 · Zbl 0886.58055 · doi:10.1017/S0143385797085027
[2] DOI: 10.1016/0022-1236(77)90052-0 · Zbl 0341.46049 · doi:10.1016/0022-1236(77)90052-0
[3] DOI: 10.1007/BF01225381 · Zbl 0637.46073 · doi:10.1007/BF01225381
[4] DOI: 10.1007/s002200050386 · Zbl 0932.46058 · doi:10.1007/s002200050386
[5] DOI: 10.1007/BF01228341 · Zbl 0826.46060 · doi:10.1007/BF01228341
[6] DOI: 10.1007/BF02096617 · Zbl 0786.46049 · doi:10.1007/BF02096617
[7] DOI: 10.1007/BF02097008 · Zbl 0743.46051 · doi:10.1007/BF02097008
[8] DOI: 10.1007/BF02108329 · Zbl 0824.46079 · doi:10.1007/BF02108329
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