Quantum trajectory of an individual particle in the presence of chaos

We study the quantum trajectory of an individual particle in the presence of chaos by virtue of the de Broglie–Bohmian causal formulation of quantum mechanics. It is shown that the single quantum trajectory can be obtained by numerically solving an auxiliary differential equation. The present results show that, corresponding to the chaotic motion of the individual particle in the classical limit, a stochastic quantum trajectory can be obtained. Moreover, it is found that pure quantum phenomena such as chaos-assisted tunnelling can also be directly exhibited by means of the method developed here. A driven anharmonic oscillator model is taken as an example to illustrate the main results described above.