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Quantum resurgence. (Résurgence quantique.) (French) Zbl 0807.35105
Ann. Inst. Fourier 43, No. 5, 1509-1534 (1993); Corrigendum ibid. 44, No. 3, 987 (1994).
Summary: Quantum-mechanical spectral functions admit semiclassical asymptotic expansions in the form of divergent series in powers of Planck’s constant. Quantum resurgence expresses their divergence and Borel resummation in detail in terms of the complex classical trajectories. Two examples are shown: the Selberg zeta function and the quartic oscillator spectrum.

MSC:
35P20 Asymptotic distributions of eigenvalues in context of PDEs
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
40G10 Abel, Borel and power series methods
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