Frydel Derek
Department of Chemistry, <a href="https://ror.org/05510vn56">Universidad Técnica Federico Santa María</a>, Campus San Joaquin, 8940897 Santiago, Chile.
Phys Rev E. 2024 Aug;110(2-1):024613. doi: 10.1103/PhysRevE.110.024613.
We consider passive Brownian particles trapped in an "imperfect" harmonic trap. The trap is imperfect because it is randomly turned off and on, and as a result particles fail to equilibrate. Another way to think about this is to say that a harmonic trap is time dependent on account of its strength evolving stochastically in time. Particles in such a system are passive and activity arises through external control of a trapping potential, thus, no internal energy is used to power particle motion. A stationary Fokker-Planck equation of this system can be represented as a third-order differential equation, and its solution, a stationary distribution, can be represented as a superposition of Gaussian distributions for different strengths of a harmonic trap. This permits us to interpret a stationary system as a system in equilibrium with quenched disorder.
我们考虑被困在“不完美”谐振子势阱中的被动布朗粒子。该势阱是不完美的，因为它会随机开启和关闭，结果粒子无法达到平衡。另一种看待此问题的方式是说，由于谐振子势阱的强度随时间随机演化，所以它是时间依赖的。这种系统中的粒子是被动的，且通过对捕获势的外部控制产生活性，因此，没有内能用于驱动粒子运动。该系统的稳态福克 - 普朗克方程可表示为三阶微分方程，其解即稳态分布，可表示为不同强度谐振子势阱的高斯分布的叠加。这使我们能够将一个稳态系统解释为一个处于淬火无序平衡态的系统。
