Constraint dependence of average potential energy of a passive particle in an active bath

We quantify the mean potential energy of a passive colloidal particle harmonically confined in a bacterial solution using optical traps.We find that the average potential energy of the passive particle depends on the trap stiffness,in contrast to the equilibrium case where energy partition is independent of the external constraints.The constraint dependence of the mean potential energy originates from the fact that the persistent collisions between the passive particle and the active bacteria are influenced by the particle relaxation dynamics.Our experimental results are consistent with the Brownian dynamics simulations,and confirm the recent theoretical prediction.

Analytical solution of the Boltzmann-Poisson equation and its application to MIS tunneling junctions

In order to consider quantum transport under the influence of an electron-electron （e-e） interaction in a mesoscopic conductor,the Boltzmann equation and Poisson equation are investigated jointly.The analytical expressions of the distribution function for the Boltzmann equation and the self-consistent average potential concerned with e-e interaction are obtained,and the dielectric function appearing in the self-consistent average potential is naturally generalized beyond the Thomas-Fermi approximation.Then we apply these results to the tunneling junctions of a metal-insulator-semiconductor （MIS） in which the electrons are accumulated near the interface of the semiconductor,and we find that the e-e interaction plays an important role in the transport procedure of this system. The electronic density,electric current as well as screening Coulombic potential in this case are studied,and we reveal the time and position dependence of these physical quantities explicitly affected by the e-e interaction.