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Fluctuation-dissipation theorem for thermo-refractive noise

Fluctuation-dissipation theorem for thermo-refractive noise. Formulation Some applications Proof Discussion. Y. Levin, Leiden University. Physics Letters A, 372, 1941 (2008). Thermo-refractive noise. Braginsky, Gorodetsky, & Vyatchanin 2000. medium. Index of refraction:.

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Fluctuation-dissipation theorem for thermo-refractive noise

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  1. Fluctuation-dissipation theorem for thermo-refractive noise • Formulation • Some applications • Proof • Discussion Y. Levin, Leiden University Physics Letters A, 372, 1941 (2008)

  2. Thermo-refractive noise Braginsky, Gorodetsky, & Vyatchanin 2000 medium Index of refraction: δn(r,t)=k δT(r,t) beam δφ(t)= ∫ I(r)k δT(r,t) d r 3 temperature fluctuation phaseshift intensity readout variable

  3. Thermo-mechanical noise Callen and Welton 51, L. 98 Readout variable: Interaction 1. oscillatingpressure 2. Compute/measuredissipatedpower 3.

  4. Thermo-refractive noise Readout variable: 1. oscillatingentropy injection 2. Compute/measuredissipatedpower, e.g. 3.

  5. Application 1: coating thermo-refractive noise. readout: heatwave Mental experiment: Answer: Identical to Braginsky, Gorodetsky, & Vyatchanin 2000

  6. Application 2: coating thermo-optical noise Evans, et al. 08 surface displacement δT negative correlation! refractive index

  7. Proof: • Thermometers-ensembles of identical harmonic oscillators, x , ω • Choose ω >>ω • Assume fast (<<1/ω) thermal coupling • Consider dynamical coordinate: i 0 0 for dense packing, this becomes density but so by choosing becomes

  8. Proof (continued): • Introduce interaction Hamiltonian • This amounts to slow sinusoidal change in spring constant. • From adiabatic theorem, • On average, oscillator energy stays constant=kT. Therefore, • Heat input can be reformulated as entropy input: QED

  9. Conclusions: FdT theorem is just as easy to use for thermal variable as for mechanical one.

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