Ergodic behavior—in which a system explores all its possible physical states over time—is the foundation of statistical mechanics. A hallmark of classical ergodicity is the complete loss of memory of initial conditions. For instance, a ball bouncing around on a chaotic billiard table eventually visits every part of the table with equal probability. Hence, after a long time, it is no longer possible to deduce its starting point—the memory of its origin has been erased. But what happens to memory in the quantum version of this system? If one launches an initially localized wave packet on a quantum billiard “table,” it quickly scrambles and evolves into a randomly looking time-dependent state. However, Anton Graf from Harvard University and colleagues now show that the time-averaged probability of finding the quantum system back in its initial state is increased by at least a factor of 2 compared to any other unrelated state—and this enhancement persists even in the infinite-time limit [1]. This imprint, which the researchers call a quantum birthmark, could lead to better understanding of the elusive quantum nature of ergodicity and of the bridge between classical and quantum chaos.
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