Generalized-moment-expansion method for intensity correlation functions of the single-mode laser

Noriega, J. M.; Pesquera, L.; Rodrguez, M. A.

doi:10.1103/physreva.44.6087

Cited by 3 publications

(1 citation statement)

References 14 publications

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“…Generalized moment analysis is an extension of the first passage time approximation [28] and has been used to study, for instance, (non-)reactive processes that involve Brownian motion [29,30], finite Ising systems [31], single-mode lasers [32], or to generally approximate autocorrelation functions [30]. In fact, the mean relaxation time approximation represents the lowest order approximation of the generalized moment expansion method and could be shown to better approximate the exact correlation function than the high-frequency i.e., shorttime approximation used in conventional Padé approximations [30,33].…”

Section: Introductionmentioning

confidence: 99%

Generalized Moment Analysis of Magnetic Field Correlations for Accumulations of Spherical and Cylindrical Magnetic Perturbers

et al. 2016

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In biological tissue, an accumulation of similarly shaped objects with a susceptibility difference to the surrounding tissue generates a local distortion of the external magnetic field in magnetic resonance imaging. It induces stochastic field fluctuations that characteristically influence proton spin dephasing in the vicinity of these magnetic perturbers. The magnetic field correlation that is associated with such local magnetic field inhomogeneities can be expressed in the form of a dynamic frequency autocorrelation function that is related to the time evolution of the measured magnetization. Here, an eigenfunction expansion for two simple magnetic perturber shapes, that of spheres and cylinders, is considered for restricted spin diffusion in a simple model geometry. Then, the concept of generalized moment analysis, an approximation technique that is applied in the study of (non-)reactive processes that involve Brownian motion, allows deriving analytical expressions of the correlation function for different exponential decay forms. Results for the biexponential decay for both spherical and cylindrical magnetized objects are derived and compared with the frequently used (less accurate) monoexponential decay forms. They are in asymptotic agreement with the numerically exact value of the correlation function for long and short times.

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Section: Introductionmentioning

confidence: 99%

Generalized Moment Analysis of Magnetic Field Correlations for Accumulations of Spherical and Cylindrical Magnetic Perturbers

et al. 2016

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Decay of metastable states: Mean relaxation time formulation

Дроздов

Brey

1999

The Journal of Chemical Physics

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Fractional power dependence of the mean lifetime of a first order reaction on the time scale of environment relaxation in the slow diffusion limitThe mean relaxation time formalism introduced by Nadler and Schulten ͓J. Chem. Phys. 82, 151 ͑1985͔͒ in their generalized moment expansion method is extended to a general diffusion process in arbitrary dimensions. The utility of the approach is demonstrated by calculating analytically the rate of noise-induced transitions in a bistable system with an isolated transition point. The rate formula obtained summarizes in a uniform manner much of what had been done before in this field. Limitations of its validity are discussed and a perturbation procedure to systematically improve it is proposed. The validity of our theoretical predictions for the rate is confirmed by comparing with exact numerical results.

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Time mapping in power series expansions for the time evolution operator

Дроздов

1997

Phys. Rev. E

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Generalized-moment-expansion method for intensity correlation functions of the single-mode laser

Cited by 3 publications

References 14 publications

Generalized Moment Analysis of Magnetic Field Correlations for Accumulations of Spherical and Cylindrical Magnetic Perturbers

Generalized Moment Analysis of Magnetic Field Correlations for Accumulations of Spherical and Cylindrical Magnetic Perturbers

Decay of metastable states: Mean relaxation time formulation

Time mapping in power series expansions for the time evolution operator

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