Chaos-non chaos transition caused by the quantum continuous measurement

仅基于量子力学的经典李雅普诺夫指数的推导一直是量子-经典对应的重要公开问题之一。最近Bhattacharya等人取得了重大进展，证明了在Caves-Milburn型连续测量下的波包轨迹在经典极限下与经典波包轨迹具有相同的李雅普诺夫指数（其中“测量强度”k很大，Plack常数足够小）。回想一下酉演化（k=0）给出零李雅普诺夫指数，他们的回答表明，由于连续测量，存在“非混沌到混沌”的转变。在这个研究项目中，我们通过计算李雅普诺夫指数，并构建频闪映射，Duffing系统的各种值的k，特别是小值的k（太小，是在经典极限）的性质，这种转变。我们发现，即使当波包被扩展，它的运动可以用一个有限（>0）的李雅普诺夫指数。值得注意的是，我们的结果意味着混沌的存在，即使在量子动力学制度。

The derivation of classical Lyapunov exponents based only on quantum mechanics has till recently been one of the important open questions of quantum-classical correspondence. Recently Bhattacharya and other authors made great progress by showing that the trajectories of wave packets under continuous measurement of the Caves-Milburn type have the same Lyapunov exponents as the classical one in the classical limit (where "measurement strength" k is large, and Plack constant is small enough).Recalling that unitary evolution (k=0) gives zero Lyapunov exponent, their answer suggests the existence of "non-chaos to chaos" transition due to the continuous measurement. In this research project, we investigated the nature of this transition by computing the Lyapunov exponents, and constructing the stroboscopic maps, of the Duffing system with various values of k, especially small values of k (too small to be in the classical limit). We found that even when the wave packet is extended, its motion can be characterized by a finite (>0) Lyapunov exponent. Remarkably, our result implies the existence of chaos even in a quantum dynamical regime.