Berry and Keating's work on periodic orbit theory shows quantum systems retain classically meaningful spectral structure well beyond the Ehrenfest timescale via the Heisenberg time.

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Berry and Keating(as researchers in quantum physics): Two physicists (Michael Berry and Jon Keating) who study how quantum systems behave; their work helps explain the connection between the quantum world (atoms and subatomic particles) and the classical world (everyday objects we can see and touch).
Ehrenfest timescale(as a time threshold in quantum mechanics): A measure of how long it takes for quantum behavior to look noticeably different from classical behavior; beyond this time, we'd normally expect quantum weirdness to make things unpredictable.
Heisenberg time(as a later time threshold in quantum mechanics): A much longer timescale (named after physicist Werner Heisenberg) where quantum systems start showing hidden patterns and structure again, even if they seemed chaotic in between.
Periodic orbit theory(as a mathematical framework in physics): A way of understanding systems by looking at paths that repeat themselves over and over—like planets orbiting the sun in predictable cycles.

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