2005/08/31 by Masamichi Ishihara · 1 citation
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Coupling (piping) #Exponent #Field (mathematics) #Field strength #Momentum (technical analysis) #Noise (video) #Theoretical and Computational Physics #White noise #cond-mat.stat-mech #hep-ph #stochastic dynamics and bifurcation
paper · pdf · doi:10.1143/ptp.116.37
published in Progress of Theoretical Physics 116(1), 37-46 (Oxford University Press) · 9 pages, 4 eps figures; Changed content
arxiv created 2006/03/01 · openalex publication_date 2006/07/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 of a free particle and the coupling strength D between the field and the white noise, where the quantity represents the momentum of the free particle. This equation is reduced to an equation with one parameter , which is defined as . 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 . This indicates that when the energy is equal to , 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 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 these two exponents are quantitatively similar.