Universal Quantum Birthmark: Ghost of the quantum past

TL;DR

This paper uncovers a universal quantum memory effect called the quantum birthmark, which persists regardless of the system’s chaotic nature, challenging classical ideas of ergodicity and thermalization.

Contribution

It provides a comprehensive theoretical framework for the quantum birthmark, showing it depends only on symmetry class and Hilbert-space dimension, not microscopic details.

Findings

Quantum evolution retains a universal memory of initial conditions.

The quantum birthmark depends solely on symmetry class and Hilbert-space dimension.

This effect questions classical assumptions of ergodicity and thermalization.

Abstract

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.