Multiplicative Noise Induces Zero Critical Frequency

TL;DR

This paper investigates how multiplicative noise affects the critical frequency in stochastic Bloch systems, revealing that even weak noise can significantly alter system stability and induce zero critical frequency, impacting dynamical behavior.

Contribution

It provides exact solutions and cumulant expansion analysis showing the profound influence of multiplicative noise on critical frequencies in stochastic systems.

Findings

Weak noise can double or triple critical frequencies

Strong noise can induce zero critical frequency

Noise impacts system stability and phase transitions

Abstract

Stochastic Bloch equations which model the fluorescence of two level molecules and atoms, NMR experiments and Josephson junctions are investigated to illustrate the profound effect of multiplicative noise on the critical frequency of a dynamical system. Using exact solutions and the cumulant expansion we find two main effects: (i) even very weak noise may double or triple the number of critical frequencies, which is related to an instability of the system and (ii) strong multiplicative noise may induce a non-trivial zero critical frequency thus wiping out the over-damped phase.