Dynamic quantum revivals in phase space

Vladimir S. Filinov

Gonzalo G. de Polavieja

The theory of quantal revivals is extended to Hamiltonians that are time dependent through the slow noncyclic change of some parameters. It is shown by generalizing the cyclic geometric phase (Berry's phase) to noncyclic Hamiltonians that there is a noncyclic geometric displacement for all quantum revivals. The treatment of the classical mechanical geometric angle is also extended to open paths in parameter space and its semiclassical relation with the noncyclic geometric phase derived. The displacement of the revivals is then shown to be given by the total angle shift on the final torus sum of the dynamical angle and the noncyclic geometric angle.

Ashish Kumar Patra, Saikumar Krithivasan

Wave packet revivals and fractional revivals are hallmark quantum interference phenomena that arise in systems with nonlinear energy spectra, and their signatures in expectation values of observables have been studied extensively in earlier work. In this article, we build on these studies and extend the analysis in two important directions. First, we investigate fractional revival dynamics in angular momentum observables, deriving explicit expressions for the time evolution of their moments and demonstrating that higher-order angular momentum moments provide clear and selective signatures of fractional revivals. Second, we examine classical analogs of quantum revival phenomena and elucidate structural similarities between quantum fractional revivals and recurrence behavior in representative classical systems. Using the Kerr-type nonlinear Hamiltonian as a paradigmatic model, we analyze the autocorrelation function, moment dynamics, and phase-space structures, supported by visualizations such as quantum carpets. Our results broaden the range of experimentally accessible diagnostics of fractional revivals and provide a unified perspective on revival phenomena across quantum and classical dynamical systems.

Kazuma Nagao

Jens Peder Dahl

A. A. Michailidis, C. J. Turner, Zlatko Papić +2 more

The relaxation of few-body quantum systems can strongly depend on the initial state when the system's semiclassical phase space is mixed; i.e., regions of chaotic motion coexist with regular islands.In recent years, there has been much effort to understand the process of thermalization in strongly interacting quantum systems that often lack an obvious semiclassical limit.The time-dependent variational principle (TDVP) allows one to systematically derive an effective classical (nonlinear) dynamical system by projecting unitary many-body dynamics onto a manifold of weakly entangled variational states.We demonstrate that such dynamical systems generally possess mixed phase space.When TDVP errors are small, the mixed phase space leaves a footprint on the exact dynamics of the quantum model.For example, when the system is initialized in a state belonging to a stable periodic orbit or the surrounding regular region, it exhibits persistent many-body quantum revivals.As a proof of principle, we identify new types of "quantum many-body scars," i.e., initial states that lead to long-time oscillations in a model of interacting Rydberg atoms in one and two dimensions.Intriguingly, the initial states that give rise to most robust revivals are typically entangled states.On the other hand, even when TDVP errors are large, as in the thermalizing tilted-field Ising model, initializing the system in a regular region of phase space leads to a surprising slowdown of thermalization.Our work establishes TDVP as a method for identifying interacting quantum systems with anomalous dynamics in arbitrary dimensions.Moreover, the mixed phase space classical variational equations allow one to find slowly thermalizing initial conditions in interacting models.Our results shed light on a link between classical and quantum chaos, pointing toward possible extensions of the classical Kolmogorov-Arnold-Moser theorem to quantum systems.