Localization fluctuation-induced

The local or extended nature of molecular-ion (or exciton) states in molecular solids is determined by a competition between fluctuations in the local site energies of these states (which tend to localize them) and the hopping integrals for inter-site excitation transfer (which tend to delocalize them). In order to define this fluctuation-induced localization concept more precisely, consider the model defined by the one-electron Hamiltonian... 

A spin system placed in a constant homogeneous magnetic field B0 finally attains thermal equilibrium with the lattice. This relaxation is induced by fluctuations of local magnetic fields which result from molecular motions. At equilibrium, the spin system is described by the equilibrium density matrix p0 ... 

Spin relaxation in a nucleus is induced by random fluctuations of local magnetic fields. These result from time-dependent modulation of the coupling energy of the resonating nuclear spin with nearby nuclear spins, electron spins, quadrupole moments, etc. Any time-dependent phenomenon able to modulate these couplings can contribute to nuclear relaxation. The distribution of the frequencies contained in these time-dependent phenomena is described by a correlation function, characterized by a parameter Tc, the correlation time. Its reciprocal can be considered as the maximum frequency produced by the fluctuations in the vicinity of the nuclear spin. If more than one process modulates the coupling between the nuclear spin and its surroundings, the reciprocal of the effective correlation time is the sum of the reciprocals of the various contributions... 

The influence of wake motion on bulk turbulence induced in the liquid is understood more clearly by inspecting oscillograms which show the fluctuation of local liquid velocity. Figure 43 shows such oscillograms taken by Kikuchi (K30) with a hot-wire probe. The bubble column is 8.0 cm in diameter, water-filled to a 170-cm height, with the probe 115 cm above the bottom gas distributor. In the column bubbles of constant volume (100 cc) are injected successively at constant time intervals, either at 2.1 sec (case a) or 0.50 sec (case b). Case c is an example of continuous bubbling at f/c = 6.45 cm/sec. 

As a last feature, it is worth mentioning another solvent effect of general occurrence. The solvent molecules possess an intrinsic thermal motion which may induce local fluctuations in their equilibrium distribution around... 

Fig. 4.35. Particle size-dependent bistability and hysteresis. On model system I (500-nm EBL-fabricated particles), the CO oxidation shows a perfectly stable bistability behavior. On the time scale accessible by the experiment (>10 s), we can arbitrarily switch between the two states by pulsing either pure CO or O2 (a and d). For the model system II (6-nm particles), a very slow transition toward a single global state is observed in the transition region between the CO- and O-rich reaction regimes (b and e). This behavior is assigned to fluctuation-induced transitions, which are accelerated by the presence of defect sites. For the smallest particles of the model system III (1.8 nm), a globally monostable kinetics is rapidly established under all conditions (c and f). For all experiments, the total flux of CO and O2 beams at the sample position was equivalent to a local pressure of 10" Pa. The surface temperature in (a-c) was 400 K and in (d-f) 415 K (from [147])...

This Brazovskii [327] mechanism for a fluctuation induced first order transition hence means that the strong increase of local fluctuations drives the fourth order coefficient of the Landau expansion negative, and thus a critical divergence of the local fluctuation is prevented. 

As a matter of fact, there are systems that cannot be easily characterized in terms of localized molecular orbitals, and thus not easily understood using localized bonds. An extreme example is provided by the fluxional behavior of CHs", where quantum-mechanical fluctuations induce delocalization phenomena and thus fluctuating bonds [16-20]. 

Summary YbPdSb is magnetically unstable. The [xSR data on a sample that does not develop long-range AFM order show that the material enters a spin-liquid state instead. This state is characterized by dynamic short-range correlations whose fluctuation rate becomes temperature independent below 0.3 K at the comparatively low value of 60 MHz. Probably one deals with quantum fluctuations that are interpreted here as local moment fluctuations induced by the dynamics of fluctuating bonds of Kondo spin pairs. 

Tucker (these proceedings, and [13]) reasons that in addition to the local density enhancement due to the direct inlermolecular interaction, an additional enhancement must be due to the critical-fluctuation induced long-range inhomogeneity of the fluid. 

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