Download PDF by FRANCIS BERNARDEAU: Cosmologie : Des fondements théoriques aux observations

By FRANCIS BERNARDEAU

ISBN-10: 2868839541

ISBN-13: 9782868839541

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2. 3 Magnetic Neutron Scattering [k fixed) ei r pi 0 &;, Bf Aw, fk G Fig. 2 Fig. 3 The spectrum of these fluctuations will therefore determine the inelastic scattering cross section. This is shown in the Appendix. For the moment, it will suffice to note that the intensity of the scqflered beam 1 Iscatf' is given by B+ d- nt Iscott = {factors times JSMM(-k’w ). (2. 30) e, + e, - fw i i Eq. 25) tells us to expect a Lorentzian line shape for this process, see fig. 3. The width of the Lorentzian, at half maximum, is given by Dk2.

For hydrodynamic modes, the frequency is so small that the prefactor in Eq. 62) is, effectively, unity. 58). 7 The Fluctuation-Dissipation Theorem [no < 5;;(0 = - < A, (0)>» (2. 640) x,, = . (2. 64b) We have subtracted the equilibrium averages in (2. 64a) so that Sii(f) + 0 as p + c, and thus its Fourier transform Sii(m) presumably exists. Of course, is independent of time. Let us perform the average over a canonical ensemble p=e-‘3H/fr e-BH. -BH .

22) z+iDk Note, however, that the initial condition is now not arbitrary but is perfectly well defined by eq. 14). 23) and therefore, for small k, S(kz) =fi2 , ' (2. 24) To extract the spectral density, we cannot use (2. 24) holds, by derivation, only for Imz >O0. 20) and obtain the final ku) = S pL (lb—u) + (Dk") "Tol h result x, whose experimental significance we shall discuss below. (2. 2 Spin Correlation Function Of course, eq. 25) is an approximation to the real world. It is valid only for small k and w which means, in the loose language that is common, it is valid when k-l is much larger than all "natural lengths in the system," and when w'] is much larger than all "natural times in the system".

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Cosmologie : Des fondements théoriques aux observations (Broché) by FRANCIS BERNARDEAU


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