https://doi.org/10.1140/epjb/s10051-021-00217-5
Regular Article - Statistical and Nonlinear Physics
Velocity auto correlation function of a confined Brownian particle
Department of Physics, University of Kerala, 695581, Kariavattom, Thiruvananthapuram, India
Received:
9
October
2020
Accepted:
16
September
2021
Published online:
11
October
2021
Motivated by the simple models of molecular motor obeying a linear force-velocity relation, we have studied the stochastic dynamics of a Brownian particle in the presence of a linear velocity dependent force, 
where 
is a constant. The position and velocity auto correlation functions in different situations of the dynamics are calculated exactly. We observed that the velocity auto correlation function shows an exponentially decaying behaviour with time and saturates to a constant value in the time asymptotic limit, for a fixed 
. It attains saturation faster with increase in the value. When the particle is confined in a harmonic well, the spectral density exhibits a symmetric behaviour and the corresponding velocity auto correlation function shows a damped oscillatory behaviour before decaying to zero in the long time limit. With viscous coefficient, a non-systematic variation of the velocity auto correlation function is observed. Further, in the presence of a sinusoidal driving force, the correlation in velocities increases with increase in the amplitude of driving in the transient regime. For the particle confined in a harmonic well, the correlation corresponding to the shift relative to the average position is basically the thermal contribution to the total position correlation. Moreover, in the athermal regime, the total correlation is entirely due to the velocity dependent force.
© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2021
