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Quantum-mechanical cumulant dynamics near stable periodic orbits in phase space: Application to the classical-like dynamics of quantum accelerator modes

Radka Bach, Keith R. Burnett, M. B. d’Arcy +1 more

We formulate a general method for the study of semiclassical-like dynamics in stable regions of a mixed phase space, in order to theoretically study the dynamics of quantum accelerator modes. In the simplest case, this involves determining solutions, which are stable when constrained to remain pure-state Gaussian wave packets, and then propagating them using a cumulant-based formalism. Using this methodology, we study the relative longevity, under different parameter regimes, of quantum accelerator modes. Within this attractively simple formalism, we are able to obtain good qualitative agreement with exact wave-function dynamics.We formulate a general method for the study of semiclassical-like dynamics in stable regions of a mixed phase space, in order to theoretically study the dynamics of quantum accelerator modes. In the simplest case, this involves determining solutions, which are stable when constrained to remain pure-state Gaussian wave packets, and then propagating them using a cumulant-based formalism. Using this methodology, we study the relative longevity, under different parameter regimes, of quantum accelerator modes. Within this attractively simple formalism, we are able to obtain good qualitative agreement with exact wave-function dynamics.

arXiv:physics/0310143Physical Review AMar 29, 200517 citations

Quantum localization on classical periodic orbits

Orsay Cedex

Annals of PhysicsMay 1, 19910 citations

Quantum Mechanical Cumulant Dynamics near Stable Periodic Orbits in Phase Space

Radka Bach, D'Arcy, M B, S. A. Gardiner +1 more

We formulate a general method for the study of semiclassical-like dynamics in stable regions of a mixed phase-space. This involves determining stable Gaussian wavepacket solutions, and then propagating them using a cumulant-based formalism. We apply our method to the problem of quantum accelerator modes, determining their relative longevity under different parameter regimes, and obtaining good qualitative agreement with exact wavefunction dynamics.

Oct 29, 20030 citations

Quantum trajectories emerging from classical phase space

Felipe Olivares, Angel Ricardo Plastino, Bernard H. Soffer

Physica A Statistical Mechanics and its ApplicationsFeb 16, 20111 citation

Dynamics of Classical and Quantum Particles in Constant-Linear-Acceleration Frames

WORLD SCIENTIFIC eBooksSep 1, 20060 citations

Publisher's Note: Quantum state exchange between indirectly coupled modes [Phys. Rev. A71, 032319 (2005)]

Antonio S. M. de Castro, J. F. Peruzzo, V. V. Dodonov

Physical Review AApr 7, 20050 citations

Publisher's Note: Quantum-mechanical cumulant dynamics near stable periodic orbits in phase space: Application to the classical-like dynamics of quantum accelerator modes [Phys. Rev. A71, 033417 (2005)]

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Publisher's Note: Quantum-mechanical cumulant dynamics near stable periodic orbits in phase space: Application to the classical-like dynamics of quantum accelerator modes [Phys. Rev. A71, 033417 (2005)]

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