Zero-field fluctuations

The third application is to velocity field fluctuations. For an equilibrium fluid the velocity field is, on average, zero everywhere but it does fluctuate. The correlations trim out to be... 

The origin of this force can be traced back to the zero-point fluctuations of the electromagnetic field which are modified by the addition of the two plates relative to the free case. This induces the following change in the energy of the vacuum ... 

The NMRD profile of the hexaaqua nickel(II) complex is independent of the magnetic field up to about 100 MHz, as shown in Fig. 15. An increase in the proton relaxivity is then observed for higher fields, ascribed to a field dependence of the electron relaxation time, caused by fluctuations of the zero-field splitting. A value of Tig around 3 x 10 s can be estimated from the SBM theory, or, more appropriately, around 10 s if ZFS, expected to be around 3 cm 52), is taken into account in the fit. Data have been analyzed using the slow-motion theory (see Section IV of Chapter 2), which does not provide any value for the electron relaxation time, and indicates... 

Since a small arbitrary inhomogeneous field must affect the correlations like small fluctuations from zero-field equilibrium, we may use Eq. (71) in Section III to linearize Eq. (32). 

The proton relaxivity for the hexaaqua Ni(II) complex is independent on the magnetic field up to 140 MHz, as shown in Fig. 5.48. The increase noted at higher fields is due to a field dependence of the electron relaxation time, caused by fluctuations of the quadratic zero field splitting (Table 5.6). From this inflection, a value of Tjo around 3 x 10-12 s is calculated in the Solomon limit, or around 10-11 s if ZFS is taken into account. ZFS is estimated to be around 3 cm-1 [130]. No complexes with large ZFS [131-134]. The >/ dispersion occurs outside the accessible frequency range. No... 

For this reason, the Casimir formulation had another far-reaching effect. It made us recognize that "zero-point" electromagnetic-field fluctuations in a vacuum are as valid as fluctuations viewed in terms of charge motions.11 As clearly predicted by the... 

Figure 15 (a) The 4.2 K Mossbauer spectra of [(Fe(IV)=0)(TMC)(NCCH3)](0Tf)2 in acetonitrile recorded in (A) zero field and (B)a parallel field of 6.5 T. The solid line represents a spin Hamilton simulation with the parameters described in the text, (b) Mossbauer spectra of [Fe(lV)=(0)(TMCS)] recorded at temperatures and applied fields that are indicated. The solid lines represent spin Hamiltonian simulations with parameters described in the text. The spectra were simulated in the slow (at 4.2 K) and fast (at 30 K) spin fluctuation limit. The applied field was directed parallel to the observed y radiation. The doublet drawn above the topmost experimental spectrum (0 T, 4 K) represents a 7% Fe(ll) contribution from the starting complex. (From J. U. Rohde et al. (2003) Science 299 1037-1039. Reprinted with permission from AAAS)... 

Fluctuations of the Molecular Fields. The second right-hand term of Kerr s constant (191), in the case of dipolar molecules, leads directly to the result (178). We shall now show that this part of the Kerr constant is non-zero even in liquids composed of non-dipolar molecules. This is due to the circumstance that in dense media, even if no external field is applied, intense molecular fields fluctuating in time and space have to be considered locally. The molecular fields Fm induce electric dipoles in the molecules in such regions, giving rise in the medium to the non-zero total dipole moment A/q occurring in the second part of the constant (191). In fact, we have in a linear approximation ... 

M. Odelius, C. Ribbing, and J. Kowalewski, Molecular Dynamics Simulation of the Zero-field Splitting Fluctuations in Aqueous Ni(II), J. Chem. Phys., 103 (1995), 1800-1811. 

T superparamagnetic reversal fluctuation time (zero field)... 

Here Vhas the same meaning as in (21). Thus, the zero-point fluctuations of the electric field strength of plane waves have the same magnitude at any space point. By construction, (28) describes the zero-point fluctuations in empty space. 

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