A new expansion scheme to evaluate the eigenvalues of the generalized evolution operator (Frobenius-Perron operator) Hq relevant to the fluctuation spectrum and poles of the order-q power spectrum is proposed. The “partition function” is computed in terms of unstable periodic orbits and then used in a finite pole approximation of the continued fraction expansion for the evolution operator. A so...

We study an approximation scheme based on a second quantization method for a chemical master equation. Small systems, such as cells, could not be studied by the traditional rate equation approach because fluctuation effects are very large in such small systems. Although a Fokker-Planck equation obtained by the system size expansion includes the fluctuation effects, it needs large computational ...

A formulation is developed for the calculation of the electromagnetic-fluctuation forces for dielectric objects of arbitrary geometry at small separations, as a perturbative expansion in the dielectric contrast. The resulting Lifshitz energy automatically takes on the form of a series expansion of the different many-body contributions. The formulation has the advantage that the divergent contri...

Advancement in the reduction of technical noise and isolation of seismic vibration has let a high-precision measurement device like the interferometric gravitational-wave detectors [1] be so sensitive that tiny thermal fluctuation of the measurement surface can limit the sensitivity. It is important to develop a method to estimate the thermalnoise level as accurately as possible. Our study with...