We investigate the impact of noise on a two-dimensional simple paradigmatic piecewise-smooth dynamical system. For that purpose, we consider the motion of a particle subjected to dry friction and colored noise. The finite correlation time of the noise provides an additional dimension in phase space, causes a nontrivial probability current, and establishes a proper nonequilibrium regime. Furthermore, the setup allows for the study of stick-slip phenomena, which show up as a singular component in the stationary probability density. Analytic insight can be provided by application of the unified colored noise approximation, developed by Jung and Hänggi [Phys. Rev. A 35, 4464(R) (1987)0556-279110.1103/PhysRevA.35.4464]. The analysis of probability currents and of power spectral densities underpins the observed stick-slip transition, which is related with a critical value of the noise correlation time.
[1]
J. Elgin.
The Fokker-Planck Equation: Methods of Solution and Applications
,
1984
.
[2]
John B. Shoven,et al.
I
,
Edinburgh Medical and Surgical Journal.
[3]
Aleksej F. Filippov,et al.
Differential Equations with Discontinuous Righthand Sides
,
1988,
Mathematics and Its Applications.
[4]
G. G. Stokes.
"J."
,
1890,
The New Yale Book of Quotations.
[5]
C. Gardiner.
Stochastic Methods: A Handbook for the Natural and Social Sciences
,
2009
.
[6]
R. Kubo.
Statistical Physics II: Nonequilibrium Statistical Mechanics
,
2003
.
[7]
Thomas Hellman.
PHIL
,
2018,
Encantado.
[8]
Ericka Stricklin-Parker,et al.
Ann
,
2005
.
[9]
B. M. Fulk.
MATH
,
1992
.