Direct approach for the fluctuation-dissipation theorem under nonequilibrium steady-state conditions

Kentaro Komori, Yutaro Enomoto, Hiroki Takeda, Yuta Michimura, Kentaro Somiya, Masaki Ando, Stefan Ballmer

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

The test mass suspensions of cryogenic gravitational-wave detectors such as the KAGRA project are tasked with extracting the heat deposited on the optics. These suspensions have a nonuniform temperature, requiring the calculation of thermal noise in nonequilibrium conditions. While it is not possible to describe the whole suspension system with one temperature, the local temperature at every point in the system is still well defined. We therefore generalize the application of the fluctuation-dissipation theorem to mechanical systems, pioneered by Saulson and Levin, to nonequilibrium conditions in which a temperature can only be defined locally. The result is intuitive in the sense that the thermal noise in the observed degree of freedom is given by averaging the temperature field, weighted by the dissipation density associated with that particular degree of freedom. After proving this theorem, we apply the result to examples of increasing complexity: a simple spring, the bending of a pendulum suspension fiber, and a model of the KAGRA cryogenic suspension. We conclude by outlining the application to nonequilibrium thermoelastic noise.

Original languageEnglish (US)
Article number102001
JournalPhysical Review D
Volume97
Issue number10
DOIs
StatePublished - May 15 2018

Fingerprint

dissipation
theorems
nonequilibrium conditions
thermal noise
cryogenics
theorem proving
degrees of freedom
temperature
pendulums
gravitational waves
temperature distribution
optics
heat
fibers
detectors

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

Cite this

Direct approach for the fluctuation-dissipation theorem under nonequilibrium steady-state conditions. / Komori, Kentaro; Enomoto, Yutaro; Takeda, Hiroki; Michimura, Yuta; Somiya, Kentaro; Ando, Masaki; Ballmer, Stefan.

In: Physical Review D, Vol. 97, No. 10, 102001, 15.05.2018.

Research output: Contribution to journalArticle

Komori, Kentaro ; Enomoto, Yutaro ; Takeda, Hiroki ; Michimura, Yuta ; Somiya, Kentaro ; Ando, Masaki ; Ballmer, Stefan. / Direct approach for the fluctuation-dissipation theorem under nonequilibrium steady-state conditions. In: Physical Review D. 2018 ; Vol. 97, No. 10.
@article{a2a95b36bf1d4d8dae65999fa2d633f1,
title = "Direct approach for the fluctuation-dissipation theorem under nonequilibrium steady-state conditions",
abstract = "The test mass suspensions of cryogenic gravitational-wave detectors such as the KAGRA project are tasked with extracting the heat deposited on the optics. These suspensions have a nonuniform temperature, requiring the calculation of thermal noise in nonequilibrium conditions. While it is not possible to describe the whole suspension system with one temperature, the local temperature at every point in the system is still well defined. We therefore generalize the application of the fluctuation-dissipation theorem to mechanical systems, pioneered by Saulson and Levin, to nonequilibrium conditions in which a temperature can only be defined locally. The result is intuitive in the sense that the thermal noise in the observed degree of freedom is given by averaging the temperature field, weighted by the dissipation density associated with that particular degree of freedom. After proving this theorem, we apply the result to examples of increasing complexity: a simple spring, the bending of a pendulum suspension fiber, and a model of the KAGRA cryogenic suspension. We conclude by outlining the application to nonequilibrium thermoelastic noise.",
author = "Kentaro Komori and Yutaro Enomoto and Hiroki Takeda and Yuta Michimura and Kentaro Somiya and Masaki Ando and Stefan Ballmer",
year = "2018",
month = "5",
day = "15",
doi = "10.1103/PhysRevD.97.102001",
language = "English (US)",
volume = "97",
journal = "Physical Review D",
issn = "2470-0010",
publisher = "American Physical Society",
number = "10",

}

TY - JOUR

T1 - Direct approach for the fluctuation-dissipation theorem under nonequilibrium steady-state conditions

AU - Komori, Kentaro

AU - Enomoto, Yutaro

AU - Takeda, Hiroki

AU - Michimura, Yuta

AU - Somiya, Kentaro

AU - Ando, Masaki

AU - Ballmer, Stefan

PY - 2018/5/15

Y1 - 2018/5/15

N2 - The test mass suspensions of cryogenic gravitational-wave detectors such as the KAGRA project are tasked with extracting the heat deposited on the optics. These suspensions have a nonuniform temperature, requiring the calculation of thermal noise in nonequilibrium conditions. While it is not possible to describe the whole suspension system with one temperature, the local temperature at every point in the system is still well defined. We therefore generalize the application of the fluctuation-dissipation theorem to mechanical systems, pioneered by Saulson and Levin, to nonequilibrium conditions in which a temperature can only be defined locally. The result is intuitive in the sense that the thermal noise in the observed degree of freedom is given by averaging the temperature field, weighted by the dissipation density associated with that particular degree of freedom. After proving this theorem, we apply the result to examples of increasing complexity: a simple spring, the bending of a pendulum suspension fiber, and a model of the KAGRA cryogenic suspension. We conclude by outlining the application to nonequilibrium thermoelastic noise.

AB - The test mass suspensions of cryogenic gravitational-wave detectors such as the KAGRA project are tasked with extracting the heat deposited on the optics. These suspensions have a nonuniform temperature, requiring the calculation of thermal noise in nonequilibrium conditions. While it is not possible to describe the whole suspension system with one temperature, the local temperature at every point in the system is still well defined. We therefore generalize the application of the fluctuation-dissipation theorem to mechanical systems, pioneered by Saulson and Levin, to nonequilibrium conditions in which a temperature can only be defined locally. The result is intuitive in the sense that the thermal noise in the observed degree of freedom is given by averaging the temperature field, weighted by the dissipation density associated with that particular degree of freedom. After proving this theorem, we apply the result to examples of increasing complexity: a simple spring, the bending of a pendulum suspension fiber, and a model of the KAGRA cryogenic suspension. We conclude by outlining the application to nonequilibrium thermoelastic noise.

UR - http://www.scopus.com/inward/record.url?scp=85048098663&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85048098663&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.97.102001

DO - 10.1103/PhysRevD.97.102001

M3 - Article

VL - 97

JO - Physical Review D

JF - Physical Review D

SN - 2470-0010

IS - 10

M1 - 102001

ER -