Quantum Birthmarks: Ergodicity Breaking Beyond Scarring

TL;DR

This paper introduces the concept of quantum birthmarks, which are persistent signatures of initial conditions in quantum systems that cause non-ergodic behavior, challenging classical ergodicity and extending scar theories.

Contribution

It presents a general framework for quantum birthmarks, demonstrating their universal and revival-enhanced effects, and identifies their presence in systems like the stadium billiard with quantum scars.

Findings

Quantum birthmarks cause persistent non-ergodic behavior.

Quantum scars can significantly enhance birthmarks.

The framework applies to arbitrary non-stationary quantum states.

Abstract

A hallmark of classical ergodicity is the complete loss of memory of the initial conditions due to eventual uniform covering of {\it a priori} available phase space. In quantum counterparts of such systems, however, this classical ergodic ideal is fundamentally limited: Here, we introduce the concept of a \emph{quantum birthmark}, a permanent signature left by the initial state and its early-time evolution in a general quantum system, which gives rise to non-ergodic behavior persisting even in the infinite-time limit. We present a birthmark framework outlining a ubiquitous memory effect for an arbitrary, non-stationary state composed of two factors conspiring together: the universal and the revival-enhancement. The former sets the minimal amplification carried by the time evolution of a quantum state based on global symmetries, whereas the latter incorporates the further enhancement stemming from the early dynamics, particularly prominent in the presence of recurrences that occur before the Heisenberg time. As a concrete example, we identify quantum birthmarks in the venerable stadium billiard, where they can be significantly enhanced by quantum scars. Finally, we discuss the broader implications of quantum birthmarks, including their role as a natural extension of all types of scarring theories to generic non-stationary quantum systems and prospects for experimental observation. Generally, our work opens an unexplored avenue for understanding the elusive quantum nature of ergodicity.