Adiabatic propagation of distributions

Exactly solvable models

Jerome Percus, L. Šamaj

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)80-91
Number of pages12
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume53
Issue number1 SUPPL. A
StatePublished - 1996

Fingerprint

Exactly Solvable Models
Multiple Time Scales
Propagation
propagation
Energy
Adiabatic Invariant
Moment
One-dimensional System
Infinite Systems
Harmonic Oscillator
Phase Space
Shell
Time Scales
Ensemble
moments
space density
Prediction
harmonic oscillators
energy
predictions

ASJC Scopus subject areas

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

Cite this

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

In: Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 53, No. 1 SUPPL. A, 1996, p. 80-91.

Research output: Contribution to journalArticle

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