Quantum chaotic systems usually obey the eigenstate thermalization hypothesis meaning individual energy eigenstates reproduce thermal expectation values. Quantum scars are special nonthermal eigenstates that concentrate probability along certain classical or many-body trajectories and so produce measurable departures from that thermal behavior. This distinction matters for interpretation of experiments and for potential control of quantum information in noisy platforms.
Wavefunction localization and phase-space patterns
A direct experimental signature is spatial or phase-space wavefunction localization. In single-particle systems, eigenstates that are scars show pronounced intensity along unstable classical periodic orbits rather than being evenly spread. This was first described by Eric J. Heller Harvard, who linked concentrated wavefunction weight to classical structures. Imaging of wavefunctions or Husimi phase-space distributions reveals these localized patterns, whereas thermal eigenstates display uniform random-wave structure consistent with ergodicity.
Entanglement and dynamical revivals
Scarred eigenstates and the dynamics they support have anomalously low entanglement entropy compared with nearby thermal states at the same energy. That reduced entanglement leads to experimentally observable long-lived coherent oscillations or revivals following specific quenches from product initial states. Many-body scars were observed by Hannes Bernien Harvard and Mikhail Lukin Harvard using a Rydberg-atom quantum simulator where particular initial product states produced persistent revivals while generic states rapidly thermalized. Such dynamical fingerprints are robust probes because they are directly accessible in time-resolved measurements.
Spectral and statistical fingerprints
Spectrally, scars show up as atypical eigenstates embedded within an otherwise thermal spectrum. Level statistics in the bulk remain consistent with chaotic Wigner-Dyson distributions, but matrix elements of local observables for scarred states deviate strongly from microcanonical predictions. Experimentally this appears as narrow bands of high overlap between certain eigenstates and experimentally preparable basis states, and as systematic outliers in expectation-value versus energy plots that would be smooth for thermal eigenstates.
These experimental signatures together—localized phase-space structure, low entanglement and long-lived revivals, and anomalous spectral observables—distinguish quantum scars from thermal eigenstates. The phenomenon is consequential for quantum simulators and computing because rare nonthermal states can preserve coherence and memory in otherwise thermalizing systems, a nuance that depends on platform details and experimental control in laboratory environments.