Brownian colloids in underdamped and overdamped regimes with nonhomogeneous temperature

The motion of Brownian particles when temperature is spatially dependent is studied by stochastic simulations and theoretical analysis. Nonequilibrium steady probability distributions $P_{st}(z,v)$ for both underdamped and overdamped regimes are analyzed. The existence of local kinetic energy equipartition theorem is also discussed. The transition between both regimes is characterized by a dimensionless friction parameter. This study is applied to three physical systems of colloidal particles.

Figure 1

(a) Simulation results of the steady distribution $P_{st}\left(z\right)$ for different values of ${\widehat{\gamma }}_0$ (see inset). Simulation data (symbols). Continuous line is the analytical expression (25). (b) Local second moment $\langle v^2\left(z\right)\rangle$ for the values of previous figure. Continuous line corresponds to the energy equipartition theorem. Dashed lines are polynomial fits as a guide.

Figure 2

(a) Simulation results of the steady distribution $P_{st}\left(z\right)$ for the harmonic potential. Simulation data (symbols) and the continuous line is the analytical expression (30). (b) Local second moment $\langle v^2\left(z\right)\rangle$ for the harmonic potential. Continuous line corresponds to the energy equipartition theorem (13), and the dashed line is a guide.

Figure 3

(a) Simulation results of the steady distribution $P_{st}\left(z\right)$ for the bistable system. Simulation data (symbols). Continuous line is the numerical calculation of (9) for this system. (b) Local second moment $\langle v^2\left(z\right)\rangle$ for the values of previous figure. Continuous line corresponds to the energy equipartition theorem (13).

Figure 4

Simulation results for the difference functions (18) and (19) in a log-log plot. Vertical dashed line separates the two regimes.