Exponential return to equilibrium for hypoelliptic quadratic systems

M. Ottobre; G. A. Pavliotis; K. Pravda-Starov

doi:10.1016/j.jfa.2012.02.008

Exponential return to equilibrium for hypoelliptic quadratic systems

M. Ottobre, G. A. Pavliotis^*, K. Pravda-Starov

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

35 Citations (Scopus)

Abstract

We study the problem of convergence to equilibrium for evolution equations associated to general quadratic operators. Quadratic operators are non-selfadjoint differential operators with complex-valued quadratic symbols. Under appropriate assumptions, a complete description of the spectrum of such operators is given and the exponential return to equilibrium with sharp estimates on the rate of convergence is proven. Some applications to the study of chains of oscillators and to the generalized Langevin equation are given. (C) 2012 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	4000-4039
Number of pages	40
Journal	Journal of Functional Analysis
Volume	262
Issue number	9
DOIs	https://doi.org/10.1016/j.jfa.2012.02.008
Publication status	Published - 1 May 2012

Keywords

Quadratic operators
Hypoellipticity
Return to equilibrium
Rate of convergence
Chains of oscillators
Generalized Langevin equation
FOKKER-PLANCK EQUATION
NONEQUILIBRIUM STATISTICAL-MECHANICS
DIFFERENTIAL-OPERATORS
ANHARMONIC CHAINS
BEHAVIOR

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10.1016/j.jfa.2012.02.008

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title = "Exponential return to equilibrium for hypoelliptic quadratic systems",

abstract = "We study the problem of convergence to equilibrium for evolution equations associated to general quadratic operators. Quadratic operators are non-selfadjoint differential operators with complex-valued quadratic symbols. Under appropriate assumptions, a complete description of the spectrum of such operators is given and the exponential return to equilibrium with sharp estimates on the rate of convergence is proven. Some applications to the study of chains of oscillators and to the generalized Langevin equation are given. (C) 2012 Elsevier Inc. All rights reserved.",

keywords = "Quadratic operators, Hypoellipticity, Return to equilibrium, Rate of convergence, Chains of oscillators, Generalized Langevin equation, FOKKER-PLANCK EQUATION, NONEQUILIBRIUM STATISTICAL-MECHANICS, DIFFERENTIAL-OPERATORS, ANHARMONIC CHAINS, BEHAVIOR",

author = "M. Ottobre and Pavliotis, {G. A.} and K. Pravda-Starov",

year = "2012",

month = may,

day = "1",

doi = "10.1016/j.jfa.2012.02.008",

language = "English",

volume = "262",

pages = "4000--4039",

journal = "Journal of Functional Analysis",

issn = "0022-1236",

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TY - JOUR

T1 - Exponential return to equilibrium for hypoelliptic quadratic systems

AU - Ottobre, M.

AU - Pavliotis, G. A.

AU - Pravda-Starov, K.

PY - 2012/5/1

Y1 - 2012/5/1

N2 - We study the problem of convergence to equilibrium for evolution equations associated to general quadratic operators. Quadratic operators are non-selfadjoint differential operators with complex-valued quadratic symbols. Under appropriate assumptions, a complete description of the spectrum of such operators is given and the exponential return to equilibrium with sharp estimates on the rate of convergence is proven. Some applications to the study of chains of oscillators and to the generalized Langevin equation are given. (C) 2012 Elsevier Inc. All rights reserved.

AB - We study the problem of convergence to equilibrium for evolution equations associated to general quadratic operators. Quadratic operators are non-selfadjoint differential operators with complex-valued quadratic symbols. Under appropriate assumptions, a complete description of the spectrum of such operators is given and the exponential return to equilibrium with sharp estimates on the rate of convergence is proven. Some applications to the study of chains of oscillators and to the generalized Langevin equation are given. (C) 2012 Elsevier Inc. All rights reserved.

KW - Quadratic operators

KW - Hypoellipticity

KW - Return to equilibrium

KW - Rate of convergence

KW - Chains of oscillators

KW - Generalized Langevin equation

KW - FOKKER-PLANCK EQUATION

KW - NONEQUILIBRIUM STATISTICAL-MECHANICS

KW - DIFFERENTIAL-OPERATORS

KW - ANHARMONIC CHAINS

KW - BEHAVIOR

U2 - 10.1016/j.jfa.2012.02.008

DO - 10.1016/j.jfa.2012.02.008

M3 - Article

SN - 0022-1236

VL - 262

SP - 4000

EP - 4039

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 9

ER -

Exponential return to equilibrium for hypoelliptic quadratic systems

Abstract

Keywords

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