Quantum ‘birthmark’ Reveals Systems Never Fully Forget Their Origins

Scientists have discovered a persistent and universal ‘quantum birthmark’ within the dynamics of quantum systems, revealing a surprising memory of their initial conditions. Ivy Xiaoya, Anton M. Graf, and Eric J. Heller from Harvard University, alongside Joonas Keski-Rahkonen from Tampere University, demonstrate that this effect, an enhancement of long-time return probability, transcends chaotic behaviour and depends solely on fundamental symmetries and the system’s dimensionality. This research establishes a complete theoretical framework for understanding this universal contribution, challenging classical notions of ergodicity and thermalisation by showing evolution inevitably preserves an imprint of its origin.

Symmetry-controlled persistence of initial conditions in quantum chaotic systems leads to observable consequences in the long-time dynamics

Scientists have uncovered a universal memory effect within quantum dynamics, revealing that a system’s initial conditions permanently influence its behaviour, even when exhibiting fully chaotic characteristics. This phenomenon, termed the quantum birthmark, manifests as an increased probability of returning to a non-stationary state compared to predictions based on typical ergodic behaviour.
The research details a complete theoretical framework for this universal contribution, demonstrating its dependence solely on the global symmetry class and accessible Hilbert-space dimension, independent of the underlying microscopic dynamics. These findings suggest that quantum evolution inherently preserves an unavoidable, symmetry-controlled imprint of its origin, challenging conventional expectations of ergodicity and established thermalization scenarios.

This work establishes that quantum systems, unlike their classical counterparts, do not readily “forget” their beginnings. The quantum birthmark arises from the long-time return probability of any initial state, exhibiting an enhancement relative to the overlap with a generic ergodic state. Researchers have derived a mathematical expression for this effect, demonstrating that the ratio of self-overlap to overlap with an ergodic state is consistently greater than two, due to a universal factor dependent on system symmetries.

This universal factor, denoted as P UQB, is rigorously proven to be greater than or equal to two even in fully chaotic systems described by random matrix theory, and can be further modified by additional symmetries present in the system. The study extends beyond spectral analysis, focusing on the time-domain behaviour of quantum systems.

By examining the evolution of localized wavepackets, the research highlights a deviation from classical ergodic flow, where long-time averages should show no preference for the initial conditions. Instead, quantum dynamics demonstrably retains a persistent memory of its origins. Numerical simulations using a billiard system further illustrate the universal birthmark effect, confirming the theoretical predictions and providing a visual representation of this quantum phenomenon.

This discovery has implications for understanding thermalization in quantum systems, suggesting that the standard eigenstate thermalization hypothesis may require refinement. The research indicates that even in systems exhibiting characteristics of thermalization, a subtle yet pervasive memory of the initial state remains, potentially influencing long-term behaviour. Furthermore, the framework developed in this study provides a unified perspective on various types of quantum scarring, offering a deeper understanding of how initial conditions can shape the quantum landscape.

Calculation of return probabilities within accessible Hilbert space using random matrix theory provides insights into quantum chaos

Researchers investigated the enduring memory of initial conditions within dynamical systems, even those exhibiting chaotic behaviour. The study centred on identifying a ‘birthmark’, an enhancement of long-time return probability for non-stationary states compared to ergodic states, and developing a comprehensive theoretical framework to describe this universal contribution.

This framework depends solely on the global symmetry class and accessible Hilbert-space dimension, remaining independent of the specific microscopic dynamics governing the system. Central to the work was a detailed calculation performed within the accessible Hilbert space, utilising Dirichlet/Schur, Weyl techniques to determine the probabilities Paa and Pab.

Specifically, for d-dimensional accessible sectors, Paa was calculated to be 2d+1 for the Gaussian Unitary Ensemble (GUE) and 3d+2 for the Gaussian Orthogonal Ensemble (GOE), while Pab was found to be 1/N. Consequently, the product Paa Pab equals 2N d + 1 for GUE and 3N d + 2 for GOE, values which reduce to universal formulas when d equals N.

The research further employed analysis of eigenstate stacking to reveal antiscarring phenomena, building upon prior work demonstrating scarring from periodic orbits in chaotic systems. A recent extension of this work, documented in a 2025 publication, examined antiscarring within a chaotic spinor condensate, utilising a combination of theoretical modelling and experimental observation.

This involved characterising the distribution of eigenstates and identifying deviations from expected random matrix behaviour, providing evidence for the breakdown of ergodicity beyond the realm of quantum scars. The team’s methodology connected these observations to the birthmark effect, demonstrating that evolution inevitably leaves a symmetry-controlled imprint of its origin.

Long-time return probability reveals persistent quantum memory of initial conditions in many-body systems

Researchers demonstrated that quantum dynamics retains a permanent memory of initial conditions, even within systems exhibiting fully chaotic, random-matrix spectra. This effect, termed the quantum birthmark, manifests as an enhancement of the long-time return probability of any non-stationary state when compared to the overlap with a typical ergodic state.

The work establishes a theoretical foundation for this universal contribution, revealing its dependence solely on the global symmetry class and accessible Hilbert-space dimension, independent of microscopic dynamics. Specifically, the long-time average probability of a state evolving from an initial condition exhibits a ratio of Paa/Pab exceeding the ergodic standard of unity by a universal factor, denoted as P UQB, which is greater than or equal to 2.

This enhancement arises regardless of spectral qualities expected from random matrix theory, indicating a symmetry-controlled imprint of the system’s origin. The research further details that this universal factor, P UQB, is determined by global symmetries and the dimensionality of the accessible Hilbert space.

Furthermore, a revival enhancement factor, P RQB, greater than or equal to 1, accounts for short-time dynamics and corrects for recurrences potentially attributable to periodic orbits. The combined effect of P UQB and P RQB results in a ratio Paa/Pab demonstrably greater than 2, signifying a substantial and unavoidable non-ergodic memory within quantum evolution.

This finding challenges classical expectations of ergodicity and conventional thermalization scenarios, suggesting a persistent influence of initial conditions on the system’s long-term behaviour. The study highlights that every initial quantum state and its subsequent evolution experiences this universal enhancement, implying a fundamental limitation to the complete “forgetting” of initial conditions even in chaotic systems. This pervasive memory effect, the quantum birthmark, fundamentally alters the understanding of quantum dynamics and its relationship to classical analogues of thermalization.

Symmetry and dimensionality define universal quantum memory retention capabilities

Scientists have established a comprehensive theory describing a universal memory effect inherent in quantum dynamics, termed the quantum birthmark. This effect manifests as an enhanced long-term return probability for non-stationary states compared to ergodic expectations, indicating that a system’s initial conditions leave a lasting imprint on its evolution.

The strength of this birthmark is determined solely by the system’s symmetry class and the dimensionality of its accessible Hilbert space, remaining independent of the specific underlying dynamics. The findings demonstrate a more complex picture of non-ergodic behaviour in classically chaotic systems than previously understood, extending beyond the ergodicity of individual energy eigenstates and linking back to classical dynamical perspectives.

Quantum birthmarks represent a novel viewpoint on the quantum foundations of ergodicity, revealing that evolution unavoidably preserves a symmetry-controlled record of a system’s origin. The authors acknowledge that artificially amplified effects can occur when analysing the quantum birthmark, particularly if relevant symmetries and energy constraints are not properly considered.

The research clarifies that once all relevant a priori constraints are accounted for, the symmetry-reduced description consistently yields expected bounds, effectively normalizing the observed enhancement. Future research may focus on exploring the implications of these findings for understanding thermalization scenarios and the broader relationship between quantum and classical ergodicity. The work was supported by the National Science Foundation and several individual foundations providing financial assistance to the researchers.