TY - JOUR
T1 - Mean-square displacement of a stochastic oscillator
T2 - Linear vs quadratic noise
AU - Gitterman, M.
PY - 2012/6/1
Y1 - 2012/6/1
N2 - Using the Langevin equations, we calculated the stationary second-order moment (mean-square displacement) of a stochastic harmonic oscillator subject to an additive random force (Brownian motion in a parabolic potential) and to different types of multiplicative noise (random frequency or random damping or random mass). The latter case describes Brownian motion with adhesion, where the particles of the surrounding medium may adhere to the oscillator for some random time after the collision. Since the mass of the Brownian particle is positive, one has to use quadratic (positive) noise. For all types of multiplicative noise considered, replacing linear noise by quadratic noise leads to an increase in stability.
AB - Using the Langevin equations, we calculated the stationary second-order moment (mean-square displacement) of a stochastic harmonic oscillator subject to an additive random force (Brownian motion in a parabolic potential) and to different types of multiplicative noise (random frequency or random damping or random mass). The latter case describes Brownian motion with adhesion, where the particles of the surrounding medium may adhere to the oscillator for some random time after the collision. Since the mass of the Brownian particle is positive, one has to use quadratic (positive) noise. For all types of multiplicative noise considered, replacing linear noise by quadratic noise leads to an increase in stability.
KW - Additive and multiplicative linear and quadratic random forces
KW - Stationary second moment
KW - Stochastic oscillator
UR - http://www.scopus.com/inward/record.url?scp=84858069573&partnerID=8YFLogxK
U2 - 10.1016/j.physa.2012.01.021
DO - 10.1016/j.physa.2012.01.021
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SN - 0378-4371
VL - 391
SP - 3033
EP - 3042
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
IS - 11
ER -