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Around the transfer operator and the Trotter-Kato formula. (English) Zbl 0835.47050
Demuth, M. (ed.) et al., Partial differential operators and mathematical physics. International conference in Holzhau, Germany, July 3-9, 1994. Basel: Birkhäuser Verlag. Oper. Theory, Adv. Appl. 78, 161-174 (1995).
Summary: In preceding papers we have shown how the analysis of the transfer matrix method in statistical mechanics permits us to get a very natural result for the splitting for the transfer matrix. The purpose of this note is to analyze the link between this result and previous results obtained by J. Sjöstrand concerning the splitting between the two first eigenvalues of the Schrödinger operator.
We present here improved results and analyze as a byproduct the convergence in the Trotter-Kato formula in a particular (non abstract but relatively general) case. As is known this is strongly related with the Feynman-Kac formula.
For the entire collection see [Zbl 0815.00009].

47N50 Applications of operator theory in the physical sciences
81S40 Path integrals in quantum mechanics
82B10 Quantum equilibrium statistical mechanics (general)