Quantum Birthmarks: Breaking Ergodicity Beyond Scarring

Chaotic classical systems are widely associated with ergodicity, typically manifesting as a loss of memory of the initial state in favor of the uniform exploration of phase space. In quantum systems, ergodicity can break down, leading to deviations from classical behavior that have been studied in various forms, such as quantum scars and Hilbert space fragmentation

Building on this, we introduce the maximum rate theorem, which demonstrates that ergodicity breaks down if a phase space cell thought to be available cannot be accessed during each unit time step within the critical time cutoff, typically on the order of the Heisenberg time. This framework unifies previously studied interference effects, including enhancement factors and recurrences (e.g., scars), which lead to ubiquitous amplifications of the probability of revisitation in time-evolving quantum states.

As a non-classical effect, birthmarks emerge, which in a closed quantum system describe a set of states dynamically close to the initial state that maintain enhanced probability, even in the infinite time limit. In a broader context, this phenomenon can be viewed as a generalized form of quantum scarring.

We explore how these birthmarks can be investigated in physical systems and how they impact quantum measurements.