Stochastic fluctuation induced

The stochastic fluctuation induced extra resonances allow careful investigation of different noise models. It would be Interesting to compare the predictions of various noise models and find out if these extra resonances are useful for distinguishing between different noise processes. Work on this question is in progress. 

In general, fluctuations in any electron Hamiltonian terms, due to Brownian motions, can induce relaxation. Fluctuations of anisotropic g, ZFS, or anisotropic A tensors may provide relaxation mechanisms. The g tensor is in fact introduced to describe the interaction energy between the magnetic field and the electron spin, in the presence of spin orbit coupling, which also causes static ZFS in S > 1/2 systems. The A tensor describes the hyperfine coupling of the unpaired electron(s) with the metal nuclear-spin. Stochastic fluctuations can arise from molecular reorientation (with correlation time Tji) and/or from molecular distortions, e.g., due to collisions (with correlation time t ) (18), the latter mechanism being usually dominant. The electron relaxation time is obtained (15) as a function of the squared anisotropies of the tensors and of the correlation time, with a field dependence due to the term x /(l + x ). 

Ellis et al. [30] discussed the quantum fluctuations about the mean-field solution that would correspond in field theory to quantum fluctuations in the lightcone and could be induced by higher-genus effects in the string approach. Such effects would result in stochastic fluctuations in the velocity of light as of the order of... 

It has been suggested that weak interactions could be responsible for driving racemates towards homochirality via a deterministic process. However, it is difficult to deduce conclusions regarding the role played by these forces in chemical reactions for ensembles of molecules, since they induce a chiral bias of only 106 molecules per mole six orders of magnitude lower than the stochastic fluctuations present in a racemate. 

The fundamentals of NMR relaxation theory have been presented in many places [6-9], and there is no space here to give more than a taste of whaf is involved. The rate of ref urn of a spin system to equilibrium is determined by the time-dependent magnetic fields experienced at each atomic nucleus, arising from molecular motions. The ability of this stochastic, fluctuating field fo induce spin... 

The dynamic disorder stems from the stochastic coupling of the exciton states to the thermal bath. We describe this coupling in the framework of the Kubo-Anderson s theory of the stochastic resonance [20,21]. The stochastic fluctuations in the site energies are induced by the exciton-phonon coupling to the bath. They are assumed to be comparable or smaller than the energy difference in the eigenstates. We add to the excitonic Hamiltonian Hq of Eq. (1) a time... 

It will be apparent from the above discussion that the double-cavity membrane system is ideally suited to investigations of fluctuations and fluctuational transition phenomena. Stochastic resonance and huge noise-induced amplification of a heterodyne signal have been observed. We would emphasize that noise-protected heterodyning is a general phenomenon that may occur in bistable systems of various sorts, and that it may therefore be of interest for applications in engineering. 

In order to calculate ensemble averages the explicit time-dependence of the exciton Hamiltonian is replaced by stochastic processes. If drastic changes of Jmn appear due to CC conformational transitions it is hard to apply this approach (Refs. [33] and [34] introduced a dichotomically fluctuating transfer coupling to cover such large conformational transitions). Instead, as it will be demonstrated here, it is more appropriate to directly generate the time-dependence of the exciton parameters Em and Jmn by MD simulations. Then, a microscopic account for solvent effects as well as a detailed description of solvent induced conformational transitions is possible. 

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... 

Furthermore, it has recently been found that the discrete nature of a molecule population leads to qualitatively different behavior than in the continuum case in a simple autocatalytic reaction network [29]. In a simple autocatalytic reaction system with a small number of molecules, a novel steady state is found when the number of molecules is small, which is not described by a continuum rate equation of chemical concentrations. This novel state is first found by stochastic particle simulations. The mechanism is now understood in terms of fluctuation and discreteness in molecular numbers. Indeed, some state with extinction of specific molecule species shows a qualitatively different behavior from that with very low concentration of the molecule. This difference leads to a transition to a novel state, referred to as discreteness-induced transition. This phase transition appears by decreasing the system size or flow to the system, and it is analyzed from the stochastic process, where a single-molecule switch changes the distributions of molecules drastically. 

Modeling intracellular phenomena therefore demands an a priori choice of methods. As long as fluctuations are negligible, deterministic equations correctly capture the dynamics [10, 17]. However, these approaches break down in the presence of noise. Comparisons between stochastic models and their deterministic counterparts have revealed that noise can induce a dynamical behavior that is not present in the absence of fluctuations. For instance, the MinCDE system only oscillates if the experimentally observed small number of interacting molecules is respected [16]. The deterministic equations decay to a fixed point. 

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