标题： 非平衡随机过程中的复概率振荡与耗散动力学 显示英文标题

标题： Oscillatory and dissipative dynamics of complex probability in non-equilibrium stochastic processes

摘要： 对于由著名的经典主方程描述的马尔可夫和平稳随机过程，我们引入复数转移速率而不是实数转移速率，以研究复概率中的预热振荡行为。 此外，对于纯虚数转移速率，我们在复概率中获得了持续无限长寿命的振荡，其性质取决于状态空间的维度。 我们还探讨了对二元过程的松弛矩阵进行扰动的情况，其中振荡驱动的角频率的相对符号决定了复概率中是否会存在耗散。 显示英文摘要

摘要： For a Markov and stationary stochastic process described by the well-known classical master equation, we introduce complex transition rates instead of real transition rates to study the pre-thermal oscillatory behaviour in complex probabilities. Further, for purely imaginary transition rates we obtain persistent infinitely long lived oscillations in complex probability whose nature depends on the dimensionality of the state space. We also take a peek into cases where we perturb the relaxation matrix for a dichotomous process with an oscillatory drive where the relative sign of the angular frequency of the drive decides whether there will be dissipation in the complex probability or not.