Quantum Chaos · Phase Transport Non-Closure

Claim: Quantum chaos arises when phase transport fails to close under classically chaotic frame evolution.

The Apparent Paradox

Yet quantum systems exhibit spectral statistics indistinguishable from chaos.

These describe outcomes, not mechanism.

Quantum mechanics is phase transport.

Classical chaos moves the transport frame beneath the phase.

When frames fail to close, phase coherence fragments.

Primitive: Phase accumulated along transported paths

Semiclassically, quantum amplitudes sum over paths:

$$ \psi \sim \sum_{\gamma} A_\gamma e^{i S_\gamma/\hbar} $$

In chaotic systems:

Phase cancellation becomes unavoidable.

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Primitive: Phase distribution under unitary transport

The Wigner function evolves under transport:

$$ \partial_t W = \{H, W\} + O(\hbar^2) $$

Classical chaos stretches and folds phase space.

Quantum resolution limits prevent closure.

Fine-scale phase information is lost.

↓

$$ \text{Geometric non-closure of paths} \iff \text{Phase-space decoherence} $$

Once phase correlations are destroyed, only symmetry constraints remain.

Spectral statistics follow transport-invariant ensembles.

The Ehrenfest time marks when transport non-closure exceeds phase resolution:

$$ t_E \sim \frac{1}{\lambda} \log \frac{1}{\hbar} $$

Not a breakdown of quantum mechanics, but of closure.