相关论文: Quantum revivals, geometric phases and circle map …
We investigate the dependence of Poincar\'e recurrence-times statistics on the choice of recurrence-set, by sampling the dynamics of two- and four-dimensional Hamiltonian maps. We derive a method that allows us to visualize the direct…
The quantum form of the Poincar\'e recurrence theorem stipulates that a system with a time-independent Hamiltonian and discrete energy levels returns arbitrarily close to its initial state in a finite time. Qubit systems, being highly…
Within the framework of simple perturbation theory, recurrence time of quantum fidelity is related to the period of the classical motion. This indicates the possibility of recurrence in near integrable systems. We have studied such…
The Poincar\'e recurrence theorem shows that conservative systems in a bounded region of phase space eventually return arbitrarily close to their initial state after a finite amount of time. An analogous behavior occurs in certain quantum…
Wave packets in a system governed by a Hamiltonian with a generic nonlinear spectrum typically exhibit both full and fractional revivals. It is shown that the latter can be eliminated by inducing suitable geometric phases in the states, by…
Quantum algorithms are built enabling to find Poincar\'e recurrence times and periodic orbits of classical dynamical systems. It is shown that exponential gain compared to classical algorithms can be reached for a restricted class of…
Beyond the rotating-wave approximation, the dynamics of a quantum oscillator interacting strongly and off-resonantly with a two-level system exhibit beatings, whose period equals the revival time of the two-level system. On a longer time…
The concept of quantum revivals is extended to many-body systems and the implications of traversing a quantum phase transition are explored. By analyzing two different models, the vibron model for the bending of polyatomic molecules and the…
We study the phase space of periodically modulated gravitational cavity by means of quantum recurrence phenomena. We report that the quantum recurrences serve as a tool to connect phase space of the driven system with spectrum in quantum…
Quantum revivals are investigated for the dynamics of an atom in a driven gravitational cavity. It is demonstrated that the external driving field influences the revival time significantly. Analytical expressions are presented which are…
We calculate the quantum revival time for a wave-packet initially well localized in a one-dimensional potential in the presence of an external periodic modulating field. The dependence of the revival time on various parameters of the driven…
Statistics of Poincar\' e recurrence for a class of circle maps, including sub-critical, critical, and super-critical cases, are studied. It is shown how the topological differences in the various types of the dynamics are manifested in the…
For chaotic classical systems, the distribution of return times to a small region of phase space is universal. We propose a simple tool to investigate multiple returns in quantum systems. Numerical evidence for the baker map and kicked top…
Recurrence in the classical random walk is well known and described by the P\'olya number. For quantum walks, recurrence is similarly understood in terms of the probability of a localized quantum walker to return to its origin. Under…
We report fractional revival phenomena in an ultracold matter wave inside a ring waveguide. The specific fractional revival times are precisely identified and corresponding spatial density patterns are depicted. Thorough analyses of the…
By different methods we show that for dynamical chaos in the standard map with critical golden curve the Poincar\'e recurrences P(\tau) and correlations C(\tau) asymptotically decay in time as P ~ C/\tau ~ 1/\tau^3. It is also explained why…
The revival structure of wave packets is examined for quantum systems having energies that depend on two nondegenerate quantum numbers. For such systems, the evolution of the wave packet is controlled by two classical periods and three…
The numerical prediction, theoretical analysis, and experimental verification of the phenomenon of wave packet revivals in quantum systems has flourished over the last decade and a half. Quantum revivals are characterized by initially…
The statistics of Poincar\'e recurrence times in Hamiltonian systems typically shows a power-law decay with chaotic trajectories sticking to some phase-space regions for long times. For higher-dimensional systems the mechanism of this…
The effect of quantum collapse and revival is a fascinating interference phenomenon. In this paper the phenomenon is demonstrated analytically and numerically for a simple system, a slightly anharmonic Hamiltonian. The initial wave-function…