Title:
Probing Dynamical Sensitivity of a Non-KAM System Through Out-of-Time-Order Correlators
Abstract:
Non-KAM systems, when perturbed by weak time-dependent fields, offer a fast route to classical chaos through an abrupt breaking of invariant phase space tori. In this work, we employ OTOCs to study the dynamical sensitivity of a perturbed non-KAM system in the quantum limit as the parameter that characterizes the resonance condition is slowly varied. For this purpose, we consider a quantized kicked harmonic oscillator model, which displays stochastic webs resembling Arnold's diffusion that facilitate large-scale diffusion in the phase space. Motivated by this, we study the OTOCs when the system is in resonance and contrast the results with the non-resonant case. At resonances, we observe that the long-time dynamics of the OTOCs are sensitive to these structural changes, where they grow quadratically as opposed to linear or stagnant growth at non-resonances. On the other hand, our findings suggest that the short-time dynamics remain relatively more stable and show the exponential growth found in the literature for unstable fixed points. The numerical results are backed by analytical expressions derived for a few special cases. We will then extend our findings concerning the non-resonant cases to a broad class of near-integrable KAM systems.
Key finding:
Our findings provide a complementary perspective to previous studies that have primarily focused on the systems displaying classical chaos and the unstable fixed points, where exponential growth of OTOCs is expected over a short time. However, our work highlights the intricate nature of the system under quantum resonances, showcasing their ability to modulate the growth even in systems with significant classical chaos with positive Lyapunov exponents.
In collaboration with
Abinash sahu, Arul Lakshminarayan, and Vaibhav Madhok.
ArXiv Link:
Journal ref:
Will be updated soon.
To discuss more about our work, write to me at vndileep@physics.iitm.ac.in