Scars and Other Weak Localization Effects in Classically Chaotic Systems

Giulio Casati, Robert Graham, Italo Guarneri +1 more

Bertrand Evrard, Andrea Pizzi, S. I. Mistakidis +1 more

Quantum many-body scars consist of a few low-entropy eigenstates in an otherwise chaotic many-body spectrum, and can weakly break ergodicity resulting in robust oscillatory dynamics. The notion of quantum many-body scars follows the original single-particle scars introduced within the context of quantum billiards, where scarring manifests in the form of a quantum eigenstate concentrating around an underlying classical unstable periodic orbit. A direct connection between these notions remains an outstanding problem. Here, we study a many-body spinor condensate that, owing to its collective interactions, is amenable to the diagnostics of scars. We characterize the system's rich dynamics, spectrum, and phase space, consisting of both regular and chaotic states. The former are low in entropy, violate the eigenstate thermalization hypothesis, and can be traced back to integrable effective Hamiltonians, whereas most of the latter are scarred by the underlying semiclassical unstable periodic orbits, while satisfying the eigenstate thermalization hypothesis. We outline an experimental proposal to probe our theory in trapped spin-1 Bose-Einstein condensates.

Martin C. Gutzwiller

Shane Dooley, Luke Johnston, Patrick Gormley +1 more

Quantum many-body scars (QMBSs) offer a mechanism for weak ergodicity breaking, enabling nonthermal dynamics to persist in a chaotic many-body system. While most studies of QMBS focus on anomalous eigenstate properties or long-lived revivals of local observables, their potential for quantum information processing remains largely unexplored. In this work, we demonstrate that perfect quantum state transfer can be achieved in a strongly interacting, quantum chaotic spin chain by exploiting a sparse set of QMBS eigenstates embedded within an otherwise thermal spectrum. These results show that QMBSs in chaotic many-body systems may be harnessed for information transport tasks typically associated with integrable models.

Dominique Delande

Lisandro A. Raviola, Gabriel G. Carlo, Alejandro M. F. Rivas

We study the stability of classical structures in chaotic systems when a dissipative quantum evolution takes place. We consider a paradigmatic model, the quantum baker map in contact with a heat bath at finite temperature. We analyze the behavior of the purity, fidelity and Husimi distributions corresponding to initial states localized on short periodic orbits (scar functions) and map eigenstates. Scar functions, that have a fundamental role in the semiclassical description of chaotic systems, emerge as robust relative to other states (which are localized on classical structures) against environmental perturbations. Also, purity and fidelity show a complementary behavior as decoherence measures.