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This study analyzed the scar-like localization in the time-average of a time-evolving wavepacket on a desymmetrized stadium billiard. When a wavepacket is launched along the orbits, it emerges on classical unstable periodic orbits as a scar in stationary states. This localization along the periodic orbit is clarified through the semiclassical approximation. It essentially originates from the same mechanism of a scar in stationary states: piling up of the contribution from the classical actions of multiply repeated passes on a primitive periodic orbit. To achieve this, several states are required in the energy range determined by the initial wavepacket.
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Type V Collagen in Scar Tissue Regulates the Size of Scar after Heart Injury
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Central nervous system (CNS) trauma activates a persistent repair response that leads to fibrotic scar formation within the lesion. This scarring is similar to other organ fibrosis in many ways; however, the unique features of the CNS differentiate it from other organs. In this review, we discuss fibrotic scar formation in CNS trauma, including the cellular origins of fibroblasts, the mechanism of fibrotic scar formation following an injury, as well as the implication of the fibrotic scar in CNS tissue remodeling and regeneration. While discussing the shared features of CNS fibrotic scar and fibrosis outside the CNS, we highlight their differences and discuss therapeutic targets that may enhance regeneration in the CNS.more » « less
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Quantum many-body scar states are highly excited eigenstates of many-body systems that exhibit atypical entanglement and correlation properties relative to typical eigenstates at the same energy density. Scar states also give rise to infinitely long-lived coherent dynamics when the system is prepared in a special initial state having finite overlap with them. Many models with exact scar states have been constructed, but the fate of scarred eigenstates and dynamics when these models are perturbed is difficult to study with classical computational techniques. In this work, we propose state preparation protocols that enable the use of quantum computers to study this question. We present protocols both for individual scar states in a particular model, as well as superpositions of them that give rise to coherent dynamics. For superpositions of scar states, we present both a system-size-linear depth unitary and a finite-depth nonunitary state preparation protocol, the latter of which uses measurement and postselection to reduce the circuit depth. For individual scarred eigenstates, we formulate an exact state preparation approach based on matrix product states that yields quasipolynomial-depth circuits, as well as a variational approach with a polynomial-depth ansatz circuit. We also provide proof of principle state-preparation demonstrations on superconducting quantum hardware.more » « less
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1016/j.cell.2020.06.030
