Quantum 'birthmarks' hold lasting traces of a system's past

October 11, 2026 feature Quantum 'birthmarks' hold lasting traces of a system's past Ingrid Fadelli Author Lisa Lock Scientific Editor Robert Egan Senior Editor Some classical physical systems can explore many configurations over time until their long-term behavior no longer reveals their starting conditions. The sampling of available configurations according to the appropriate statistical distribution is a property called ergodicity. Quantum systems, which are governed by the laws of quantum mechanics, could instead retain some traces of their beginnings. In a paper published in Physical Review X, researchers at Harvard University and other institutions introduced the idea of quantum birthmarks, statistical traces of initial states and early development that persist in quantum systems that do not exchange information with their surroundings. "The paper grew out of a simple tension in quantum chaos: classically, an ergodic system is expected to forget its initial conditions, but quantum evolution can retain traces of its past through coherence effects," Joonas Keski-Rahkonen, senior author of the paper, told Phys.org. "We wanted to know whether this memory is a special feature of phenomena like quantum scars, where individual eigenstates break the expectation of classical-like ergodicity, or something far more general, as it turned out to be." Describing and testing the idea of quantum birthmarks Keski-Rahkonen and his colleagues wanted to develop a theoretical framework describing how an initial quantum state and its early evolution in time could leave permanent traces on a quantum system's long-term behavior. In addition, they wanted to connect this idea to how classical chaos and ergodicity are typically studied. "For a long time, we had been thinking about how to generalize the key ideas behind quantum scarring," said Keski-Rahkonen. "Remarkably, in our recent work, all our different threads converged in a single concept: the quantum birthmark. Sometimes different roads really do lead to the same destination." The term quantum scarring is used to describe patterns in which a quantum particle has an unusually high probability of being found near specific repeating paths, even if its classical counterpart would explore the available space. Building on this idea, Keski-Rahkonen and his colleagues started exploring the possibility that a quantum system could exhibit a lasting statistical trace of its starting state and early evolution. "In the everyday world, chaos essentially resets the system to a blank state," said Keski-Rahkonen. "What we found is that quantum systems can't fully hide their history, even amid chaos. This fact manifests as a quantum birthmark: a persistent memory of where a quantum state started and how it evolved early on. Even after the initial state appears to have become fully scrambled and featureless, it remains more likely to revisit its own history than an otherwise comparable random state would—even though, from the standpoint of classical chaotic dynamics, all such states should be equally likely." In their work, the researchers first showed mathematically that evolving states in isolated quantum systems retain statistical traces of their past, limiting their ability to achieve the complete loss of memory expected in classically ergodic systems. They described these persistent traces of history as quantum birthmarks. "Our framework splits the birthmark effect into two parts: a universal memory factor, omnipresent for any nonstationary (evolving) quantum state and governed by the symmetries of the system, and a revival factor, which arises from early-time recurrences that are related to phenomena like quantum scars or other slowdowns in phase-space exploration," said Keski-Rahkonen. "This second piece leads to what we call the maximum exploration principle. In other words, there is a kind of Cinderella effect: If the initial state hasn't explored the full available phase space by the stroke of midnight (formally, the Thouless time), it never will." The researchers' framework suggests that all early recurrences will slow the exploration of new regions of phase space (the space of possible positions and momenta) and strengthen the so-called birthmark effect. In contrast, classically ergodic systems can continue exploring the available phase space without this quantum limitation. "A quantum system doesn't have that luxury," said Keski-Rahkonen. "In sharp contrast to the common narrative, a quantum system not only remembers its origin forever (the universal factor)—surprising enough on its own—but also retains traces of its early history (the revival factor). Our framework merges these two surprising facts into a single, unified phenomenon we coined the quantum birthmark." To illustrate their framework, the team performed computer calculations for a particle confined within a stadium-shaped enclosure. The resulting long-term probability patterns retained traces of the particle's starting state and early motion, with quantum scars strengthening the birthmark effect. Possible implications of the new construct This study provides a mathematical framework showing how traces of initial states and their early development can persist in isolated quantum systems. In addition, it offers tools that could be used to characterize and systematically study these quantum birthmarks. "This study establishes a generic constraint on quantum ergodicity," said Keski-Rahkonen. "This matters because the assumption of ergodicity underlies, for instance, thermodynamics itself. Our work revises the common narrative around the quantum nature of ergodicity, prompting a rethinking of how quantum systems thermalize and pushing us to reconsider quantum-classical correspondence more broadly." Keski-Rahkonen and his colleagues hope that their recent work will contribute to the reestablishment of the lost connection between quantum mechanics and the classical, dynamics-based view of chaos and ergodicity. Instead of focusing only on the individual fixed-energy states of quantum systems, their framework examines how they change over time and retain traces of their past. "Our notion of the quantum birthmark moves beyond the analysis of individual eigenstates or eigenenergies that are the dominant lens in quantum chaos research," said Keski-Rahkonen. "In particular, our framework generalizes the idea of scarring from special states tied to periodic orbits to any generic nonstationary quantum state, associated with any classical trajectory. Conversely, quantum scars can now be understood as a special case of the broader quantum birthmark phenomenon." The researchers' framework could serve as a general theoretical construct under which the many known types of quantum scarring studied in the past can be unified. In addition, the team's findings could help researchers interpret other quantum memory and localization effects, in which quantum states remain concentrated instead of spreading freely. For instance, the authors discuss connections to many-body localization, involving interacting particles, and identify a birthmark contribution to paired peaks in forward and backward scattering in disordered systems. The team's plans for further research Keski-Rahkonen and his colleagues are now planning further research aimed at deepening and refining their quantum-birthmark framework. "One intriguing direction is to work out the explicit implications of the phenomenon for quantum thermalization and ergodicity," said Keski-Rahkonen. "We are also interested in extensions where not just a single state, but an entire region of Hilbert space remains statistically favored, an effect we call a quantum birthplace. Generally speaking, it remains largely unexplored how chaos enters the quantum picture, whether in phase space or in the time domain, where quantum birthmarks operate." The researchers hope to eventually fill what they consider a significant gap in the fundamental understanding of the quantum nature of chaos. Their framework could potentially help to achieve this goal. "Another active line of research is to explore more thoroughly how broadly the birthmark picture extends beyond the model systems studied here," added Keski-Rahkonen. "Particularly interesting directions include many-body and open quantum systems, quantum simulators, the role of decoherence, and identifying which experimentally accessible observables reveal the effect most clearly. Looking further ahead, we envision that quantum birthmarks, together with quantum scars, could eventually be harnessed to power next-generation quantum technologies." Written for you by our author Ingrid Fadelli, edited by Lisa Lock, and fact-checked and reviewed by Robert Egan—this article is the result of careful human work. We rely on readers like you to keep independent science journalism alive. If this reporting matters to you, please consider a donation (especially monthly). You'll get an ad-free account as a thank-you. Publication details Anton M. Graf et al, Quantum Birthmarks: Ergodicity Breaking Beyond Scarring, Physical Review X (2026). DOI: 10.1103/dhzb-28rb Journal information: Physical Review X © 2026 Science X Network