Practical considerations in estimating dimension from time series data

Eric Kostelich, Harry L. Swinney

Research output: Contribution to journalArticle

26 Citations (Scopus)

Abstract

A dissipative quantum system exhibiting chaos in its classical limit is constructed by coupling the quantum kicked rotator to a reservoir with exchange of action. A version of the quantized standard map that incorporates dissipation is derived from this model and iterated numerically to study the long-time behavior in various regions of the damping rate. It is found that even weak damping is capable of disrupting dynamical localization which suppresses chaotic motion in the conservative standard map, and thus restores diffusion in the action variable. On the time scale of classical relaxation, a steady state is reached which is the quantum analogue of a classical strange attractor. For strong dissipation, observable deviations from classical behavior both in the transients and in the steady state are due to quantum noise. They are reproduced by a classical stochastic map which is approached by the dissipative quantum map as its semi-classical limit.

Original languageEnglish (US)
Pages (from-to)436-441
Number of pages6
JournalPhysica Scripta
Volume40
Issue number3
DOIs
StatePublished - Sep 1 1989
Externally publishedYes

Fingerprint

Time Series Data
Standard Map
estimating
Dissipation
Damping
Quantum Noise
Semiclassical Limit
Strange attractor
dissipation
Chaotic Motion
Classical Limit
damping
Dissipative Systems
Long-time Behavior
disrupting
strange attractors
Quantum Systems
Chaos
Time Scales
Deviation

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mathematical Physics
  • Atomic and Molecular Physics, and Optics

Cite this

Practical considerations in estimating dimension from time series data. / Kostelich, Eric; Swinney, Harry L.

In: Physica Scripta, Vol. 40, No. 3, 01.09.1989, p. 436-441.

Research output: Contribution to journalArticle

@article{4857c593ae504c989261b571bb33f077,
title = "Practical considerations in estimating dimension from time series data",
abstract = "A dissipative quantum system exhibiting chaos in its classical limit is constructed by coupling the quantum kicked rotator to a reservoir with exchange of action. A version of the quantized standard map that incorporates dissipation is derived from this model and iterated numerically to study the long-time behavior in various regions of the damping rate. It is found that even weak damping is capable of disrupting dynamical localization which suppresses chaotic motion in the conservative standard map, and thus restores diffusion in the action variable. On the time scale of classical relaxation, a steady state is reached which is the quantum analogue of a classical strange attractor. For strong dissipation, observable deviations from classical behavior both in the transients and in the steady state are due to quantum noise. They are reproduced by a classical stochastic map which is approached by the dissipative quantum map as its semi-classical limit.",
author = "Eric Kostelich and Swinney, {Harry L.}",
year = "1989",
month = "9",
day = "1",
doi = "10.1088/0031-8949/40/3/030",
language = "English (US)",
volume = "40",
pages = "436--441",
journal = "Physica Scripta",
issn = "0031-8949",
publisher = "IOP Publishing Ltd.",
number = "3",

}

TY - JOUR

T1 - Practical considerations in estimating dimension from time series data

AU - Kostelich, Eric

AU - Swinney, Harry L.

PY - 1989/9/1

Y1 - 1989/9/1

N2 - A dissipative quantum system exhibiting chaos in its classical limit is constructed by coupling the quantum kicked rotator to a reservoir with exchange of action. A version of the quantized standard map that incorporates dissipation is derived from this model and iterated numerically to study the long-time behavior in various regions of the damping rate. It is found that even weak damping is capable of disrupting dynamical localization which suppresses chaotic motion in the conservative standard map, and thus restores diffusion in the action variable. On the time scale of classical relaxation, a steady state is reached which is the quantum analogue of a classical strange attractor. For strong dissipation, observable deviations from classical behavior both in the transients and in the steady state are due to quantum noise. They are reproduced by a classical stochastic map which is approached by the dissipative quantum map as its semi-classical limit.

AB - A dissipative quantum system exhibiting chaos in its classical limit is constructed by coupling the quantum kicked rotator to a reservoir with exchange of action. A version of the quantized standard map that incorporates dissipation is derived from this model and iterated numerically to study the long-time behavior in various regions of the damping rate. It is found that even weak damping is capable of disrupting dynamical localization which suppresses chaotic motion in the conservative standard map, and thus restores diffusion in the action variable. On the time scale of classical relaxation, a steady state is reached which is the quantum analogue of a classical strange attractor. For strong dissipation, observable deviations from classical behavior both in the transients and in the steady state are due to quantum noise. They are reproduced by a classical stochastic map which is approached by the dissipative quantum map as its semi-classical limit.

UR - http://www.scopus.com/inward/record.url?scp=0043035345&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0043035345&partnerID=8YFLogxK

U2 - 10.1088/0031-8949/40/3/030

DO - 10.1088/0031-8949/40/3/030

M3 - Article

AN - SCOPUS:0043035345

VL - 40

SP - 436

EP - 441

JO - Physica Scripta

JF - Physica Scripta

SN - 0031-8949

IS - 3

ER -