Martinez, André Precise exponential estimates in adiabatic theory. (English) Zbl 0808.47053 J. Math. Phys. 35, No. 8, 3889-3915 (1994). Summary: General adiabatic evolutions associated to Hamiltonians, which admit a holomorphic extension with respect to the time variable in a complex strip, and whose spectrum satisfies a gap condition are studied. An explicit rate of exponential decay is given, which is related to simple geometric quantities associated to the spectrum of the Hamiltonian, for the transition probability between the two parts of the spectrum when the evolution is taken from \(-\infty\) to \(+\infty\). Cited in 20 Documents MSC: 47N50 Applications of operator theory in the physical sciences 82B10 Quantum equilibrium statistical mechanics (general) Keywords:adiabatic evolutions; holomorphic extension with respect to the time variable in a complex strip; gap condition; exponential decay; transition probability × Cite Format Result Cite Review PDF Full Text: DOI References: [1] DOI: 10.1007/BF01343193 · doi:10.1007/BF01343193 [2] DOI: 10.1143/JPSJ.5.435 · doi:10.1143/JPSJ.5.435 [3] DOI: 10.1016/0003-4916(59)90082-X · Zbl 0084.44403 · doi:10.1016/0003-4916(59)90082-X [4] DOI: 10.1063/1.1704127 · doi:10.1063/1.1704127 [5] DOI: 10.1088/0370-1328/89/1/302 · Zbl 0144.23501 · doi:10.1088/0370-1328/89/1/302 [6] DOI: 10.1007/BF01206948 · Zbl 0493.47009 · doi:10.1007/BF01206948 [7] DOI: 10.1007/BF02096867 · Zbl 0782.58056 · doi:10.1007/BF02096867 [8] DOI: 10.1007/BF02096867 · Zbl 0782.58056 · doi:10.1007/BF02096867 [9] Dykhne A. M., Sov. Phys. JETP 14 pp 941– (1962) [10] DOI: 10.1016/0003-4916(91)90297-L · Zbl 0875.60022 · doi:10.1016/0003-4916(91)90297-L [11] DOI: 10.1007/BF02096616 · Zbl 0768.34038 · doi:10.1007/BF02096616 [12] DOI: 10.1007/BF02099288 · Zbl 0755.35104 · doi:10.1007/BF02099288 [13] DOI: 10.1063/1.530255 · Zbl 0776.35056 · doi:10.1063/1.530255 [14] DOI: 10.1142/S0129055X92000224 · Zbl 0769.34006 · doi:10.1142/S0129055X92000224 [15] Lithner L., Arkiv f. Matematik 5 (18) pp 281– (1965) [16] DOI: 10.1080/03605308408820335 · Zbl 0546.35053 · doi:10.1080/03605308408820335 [17] Sjöstrand J., Astérisque 95 (1982) [18] DOI: 10.1007/BF02102061 · Zbl 0753.35057 · doi:10.1007/BF02102061 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.