### Abstract

We study the analytical structure of corrections to perfect adiabatic evolution associated with an ensemble of classical ergodic Hamiltonians with specific correlation properties, distributed at inital time, e.g., over a single energy shell. In particular, we aim to check the prediction of the multiple-time-scale method concerning the structure of energy moments that measure the extent of violation of an ergodic adiabatic invariant when the slowness parameter is small but finite. Solving exactly for the evolution of the phase space density, we find the explicit form of the energy moments for an infinite one-dimensional system of harmonic oscillators with time-decaying couplings. A comparison with the multiple-time-scale method shows its restricted applicability to a marginal limit of a vanishing slow time scale.

Original language | English (US) |
---|---|

Pages (from-to) | 80-91 |

Number of pages | 12 |

Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 53 |

Issue number | 1 SUPPL. A |

State | Published - 1996 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Condensed Matter Physics
- Statistical and Nonlinear Physics

### Cite this

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,

*53*(1 SUPPL. A), 80-91.

**Adiabatic propagation of distributions : Exactly solvable models.** / Percus, Jerome; Šamaj, L.

Research output: Contribution to journal › Article

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, vol. 53, no. 1 SUPPL. A, pp. 80-91.

}

TY - JOUR

T1 - Adiabatic propagation of distributions

T2 - Exactly solvable models

AU - Percus, Jerome

AU - Šamaj, L.

PY - 1996

Y1 - 1996

N2 - We study the analytical structure of corrections to perfect adiabatic evolution associated with an ensemble of classical ergodic Hamiltonians with specific correlation properties, distributed at inital time, e.g., over a single energy shell. In particular, we aim to check the prediction of the multiple-time-scale method concerning the structure of energy moments that measure the extent of violation of an ergodic adiabatic invariant when the slowness parameter is small but finite. Solving exactly for the evolution of the phase space density, we find the explicit form of the energy moments for an infinite one-dimensional system of harmonic oscillators with time-decaying couplings. A comparison with the multiple-time-scale method shows its restricted applicability to a marginal limit of a vanishing slow time scale.

AB - We study the analytical structure of corrections to perfect adiabatic evolution associated with an ensemble of classical ergodic Hamiltonians with specific correlation properties, distributed at inital time, e.g., over a single energy shell. In particular, we aim to check the prediction of the multiple-time-scale method concerning the structure of energy moments that measure the extent of violation of an ergodic adiabatic invariant when the slowness parameter is small but finite. Solving exactly for the evolution of the phase space density, we find the explicit form of the energy moments for an infinite one-dimensional system of harmonic oscillators with time-decaying couplings. A comparison with the multiple-time-scale method shows its restricted applicability to a marginal limit of a vanishing slow time scale.

UR - http://www.scopus.com/inward/record.url?scp=4243922312&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4243922312&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:4243922312

VL - 53

SP - 80

EP - 91

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 1 SUPPL. A

ER -