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Studies in History and Philosophy of Science Part B Studies in History and Philosophy of Modern Physics

Chaos out of order: Quantum mechanics, the correspondence principle and chaos

Gordon Belot, John Earman

Published Jun 1, 1997• 77 citations
Publisher
DOI
10.1016/s1355-2198(96)00025-1

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The correspondence principle is a cornerstone in the entire construction of quantum mechanics. This principle has been recently challenged by the observation of an early-time exponential increase of the out-of-time-ordered correlator (OTOC) in classically nonchaotic systems [E. B. Rozenbaum et al., Phys. Rev. Lett. 125, 014101 (2020)PRLTAO0031-900710.1103/PhysRevLett.125.014101]. Here, we show that the correspondence principle is restored after a proper treatment of the singular points. Furthermore, our results show that the OTOC maintains its role as a diagnostic of chaotic dynamics.
Conventional wisdom currently has it that chaotic behavior is either strongly suppressed or absent in quantum models. Indeed, some researchers have concluded that these considerations serve to undermine the correspondence principle, thereby raising serious doubts about the adequacy of quantum mechanics as a fundamental physical theory. Thus, the quantum chaos question is a prime subject for philosophical analysis. The most significant reasons given for the absence or suppression of chaotic behavior in quantum models are the linearity of Schrödinger's equation and the unitarity of the time-evolution described by that equation. Both are shown in this essay to be irrelevant by demonstrating that the crucial feature for chaos is the nonseparability of the Hamiltonian. That demonstration indicates that quantum chaos is likely to be exhibited in models of open quantum systems. A measure for probing such models for chaotic behavior is developed, and then used to show that quantum mechanics has chaotic models for systems having a continuous energy spectrum. The prospects of this result for vindicating the essence of the correspondence principle are then briefly examined.