Universal Quantum Birthmark: Ghost of the quantum past

Quantum dynamics retains a permanent and universal memory of its initial conditions, even in systems whose spectra display fully chaotic, random-matrix behavior. This effect, known as the quantum birthmark, appears as an enhancement of the long-time return probability of any non-stationary state compared to the overlap with a typical ergodic state. In this work, we develop the full theoretical foundation for this universal contribution that depends only on the global symmetry class and accessible Hilbert-space dimension, not on the microscopic dynamics. Our findings reveal that quantum evolution preserves an unavoidable, symmetry-controlled imprint of its origin, a quantum effect calling into question classical expectations of ergodicity and the resulting thermalization scenarios.

💡 Research Summary

The authors investigate a strikingly universal memory effect in quantum dynamics that they term the “quantum birthmark” (QB). Unlike classical chaotic systems, where ergodicity guarantees that trajectories eventually forget their initial conditions, a quantum system retains a permanent imprint of its starting state even when its energy spectrum exhibits fully chaotic random‑matrix statistics. The QB manifests as an enhancement of the long‑time return probability of any non‑stationary state relative to the overlap with a typical ergodic state.

Mathematically, the long‑time averaged self‑overlap is
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