Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apdo. Postal 70-543, C.P. 04510 Cd. Mx., México.
Physikalisches Institut, Albert-Ludwigs-Universitat Freiburg, Hermann-Herder-Str. 3, Freiburg D-79104, Germany.
Phys Rev Lett. 2019 Jan 18;122(2):024101. doi: 10.1103/PhysRevLett.122.024101.
The exponential growth of the out-of-time-ordered correlator (OTOC) has been proposed as a quantum signature of classical chaos. The growth rate is expected to coincide with the classical Lyapunov exponent. This quantum-classical correspondence has been corroborated for the kicked rotor and the stadium billiard, which are one-body chaotic systems. The conjecture has not yet been validated for realistic systems with interactions. We make progress in this direction by studying the OTOC in the Dicke model, where two-level atoms cooperatively interact with a quantized radiation field. For parameters where the model is chaotic in the classical limit, the OTOC increases exponentially in time with a rate that closely follows the classical Lyapunov exponent.
时移无序相关函数（OTOC）的指数增长被提出作为经典混沌的量子标志。增长率预计与经典的 Lyapunov 指数一致。这种量子-经典对应关系已经在踢转子和体育场 billiard 中得到了证实，它们是一维混沌系统。这个猜想还没有在具有相互作用的现实系统中得到验证。我们通过研究 Dicke 模型中的 OTOC 在这方面取得了进展，在这个模型中，两个能级的原子与一个量子化的辐射场协同相互作用。对于模型在经典极限中是混沌的参数，OTOC 随时间呈指数增长，增长率与经典 Lyapunov 指数密切相关。
