Chaotic Quantum Systems Possess Surprisingly Fewer Dimensions Than Expected

Koji Hashimoto of Kyoto University and colleagues from Saitama University have identified a link between quantum chaos and the geometry of probability distributions. They reveal that the effective dimension of the Wasserstein space decreases as a quantum system exhibits increasing chaotic behaviour. Applying optimal transport methods to a quantum coupled harmonic oscillator, the team found that exponential growth in out-of-time ordered correlations, or quantum scrambling, creates a folding structure within this space, potentially explaining the observed dimensional reduction. The Wasserstein distance accurately identifies the Lyapunov exponent at a critical point, and branching structures signal the presence of quantum scar states. This new approach offers a key diagnostic set…