We consider the motion of a randomly accelerated particle in one dimension under stochastic resetting mechanism. Denoting the position and velocity by x and v respectively, we consider two different resetting protocols—(i) complete resetting: here both x and v reset to their initial values x 0 and v 0 at a constant rate r , (ii) partial resetting: here only x resets to x 0 while v evolves without interruption. For complete resetting, we find that the particle attains stationary state in both x and v . We compute the non-equilibrium joint stationary state of x and v from which we obtain the stationary state distribution for position by integrating over v . We also study the late time relaxation of the position distribution function. On the other hand, for partial resetting, the joint distribution is always in the transient state. At large t ...

中文翻译：

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随机重置下的随机加速过程

我们考虑随机复位机制下一维随机加速粒子的运动。分别用x和v表示位置和速度，我们考虑两种不同的重置协议-（i）完全重置：此处x和v均以恒定速率r重置为其初始值x 0和v 0，（ii）部分重置：这里，只有x重置为x 0，而v不断发展而没有间断。为了完全重置，我们发现粒子在x和v处都达到稳态。我们计算x和v的非平衡关节稳态，从中通过对v积分获得位置的稳态分布。我们还研究了位置分布函数的后期时间松弛。另一方面，对于部分重置，关节分布始终处于过渡状态。总的来说...