Amplification Induced by White Noise(Condensed Matter and Statistical Physics)

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概要

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• We investigate the amplification of a field induced by white noise. In the present study, we study a stochastic equation which has two parameters, the energy ω(k^^→) of a free particle and the coupling strength D between the field and the white noise, where the quantity k^^→ represents the momentum of the free particle. This equation is reduced to an equation with one parameter α(k^^→), which is defined as α[numerical formula]. We obtain an expression of the exponent statistically averaged over a unit time and derive an approximate expression of it. In addition, the exponent is obtained numerically by solving the stochastic equation. We find that the amplification increases with α(k^^→). This indicates that when the energy ω(k^^→) is equal to [numerical formula], white noise can amplify the fields for soft modes if the mass m of the field is sufficiently small and if the strength of the coupling between the field and white noise is sufficiently strong. We show that the α(k^^→) dependence of the exponent statistically averaged is qualitatively similar to that of the exponent obtained by solving the stochastic equation numerically, and that for small values of α(k^^→) these two exponents are quantitatively similar.

• 理論物理学刊行会の論文
• 2006-07-25

著者

• Ishihara Masamichi

  Department Of Human Life Studies Koriyama Women's University

関連論文

• Effects of Nonlinear Terms on Parametric Resonance in the λφ^4 Model(Nuclear Physics)
• Amplification Induced by White Noise(Condensed Matter and Statistical Physics)
• Effects of White Noise on Parametric Resonance in λφ^4 Theory(Nuclear Physics)

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