Fluctuations phase

Wlren a nematic phase is cooled towards a smectic A phase, fluctuations of smectic order build up. These fluctuations were called cybotactic clusters in tire early literature. Regardless of tire physical picture of such fluctuations. 

Figure 2. Intensity and phase fluctuations measured over a 1.3 km path at the same time.-...

Such problems can be circumvented if the local oscillator co-travels with the pump and Stokes excitation beams into the microscope, as depicted in Figure 9.7. In this configuration, the local oscillator is generated either in-line (Andresen et al. 2006 Lee et al. 2007 Yacoby et al. 1980) or in a compact interferometer (Potma et al. 2006), which minimizes phase fluctuations. An active stabilization scheme is relatively easily incorporated into the interferometer (Krishnamachari et al. 2006). Because the local oscillator propagates through the same optics as the pump and Stokes beams, no temporal phase differences are accumulated beyond the interferometer. 

The Fraunhofer approximation is useful when sF 5 1, i.e. well beyond the Fresnel distance F = a jX. Closer to the transducer the field must be calculated numerically (Zemanek 1971). If aj/X > 1, the amplitude and phase fluctuate considerably in the region between the face of the transducer and the plane sF = 1 in particular there are nulls along the axis in the region 0 < s <0.5. The final maximum in the amplitude on the axis occurs at sp = 1, i.e. F = a /X, which is known as the Fresnel length. In the plane perpendicular to the axis at sp = 1 the field is reasonably well behaved in both amplitude and phase. 

Several comparisons can be made between the solution- and solid-phase approaches. Yields of oligomers formed on the solid phase fluctuate more than solution methods, though both are similar. Solution yield calculations were compiled from isolated yields for each of the three transformations,... 

If one includes the effect of Coulomb interaction in d = 1 dimension, phase fluctuations of the free phase field increase only as (T = 0)... 

As a result, phase fluctuations are too weak to suppress the disorder even for large values of K and the system is always in the pinned phase. The phase diagram is therefore similar to that in d > 1 dimensions. 

Figure 61 shows the ZFC and FC M(T) curves for the FMM phase II, which show a first-order transition at 7c where the bond-length fluctuations become frozen out to restore the phonon contribution to the thermal conductivity, fig. 62. In the I + II two-phase samples t = 0.973 and t = 0.974, phase II is suppressed and phase fluctuations inhibit phonon formation below Tco or 7c. Tokura et al. (1996) applied hydrostatic pressure to the FM phase II of (Ndo.i25Smo.875)o.5Sro.5Mn03 having / /c they reported the appearance of a CE AFI second phase having a volume fraction that increased with pressure below Too = 7n- Since pressure... 

A more complex analysis of the effect of laser phase diffusion has been appli fS the case of one-photon vs. three-photon absoiption (i.e., simultaneous absorption 3a)j and third-harmonic generation frqnt>t coi laser. As discussed in Section 3.3.2, current experiments vary the relative ph of two laser beams by passing co3 and co, through a gas. If the laser frequcnc somewhat unstable, then the relative phase of the two beams will acquire a fhtct y ing phase that is a source of phase loss in the system. The phase fluctuations q ... 

Key words Superconducting Y123, the diffusion controlled topo-chemical decomposition of Y123, the standard oxygenation treatment, a phase fluctuation-like effect... 

In the present study, the thermodynamic analysis6,7 of such processes in the cuprates has been carried out with the aim of finding the rate-controlling steps, the nature of the SFs-like precipitates, the role of the lattice defects regions in the internal topo-chemical reactions, and finally - to show a possibility of a manifestation of a phase fluctuation-like effect. 

The results of the data analysis show the possibility of a manifestation of a phase fluctuation-like effect with respect to physical properties of HTSC cuprates, which can be evaluated for different oxygenation regimes. 

Rulfier-Albenque, F., Alloul, H., and Tourbot, R. (2003). Influence of pair breaking and phase fluctuations on disordered high tc cuprate superconductors. Phy. Rev. Lett., 91 047001. 

A Possibility of a Phase Fluctuation-Like Effect in HTSC Cuprates 91... 

The fluctuations of a self-exdted osdllator have been studied via a model based on the Van der Pol equation. Such an equation has been used to account for the ampUtude and phase fluctuations. A growth of the time coherence of phase above threshold is attributed to a decrease in an apparent diffusion coefficient for phase fluctuations. 

In many physical systems the situation becomes simpler due to the inherent stochastic nature of the driving field itself. To see the possible significance of this effect, consider a conventional COj-laser pulse with 10-ns duration and a bandwidth of 1 cm incident on a diatomic molecule characterized by an environment-induced energy relaxation time of 100 ns. The laster pulse is obviously not uncertainty limited, and its width is associated with the random fluctuations in its phase and/or amplitude. For simplicity we consider random phase fluctuations, whence the external field is... 

---