Speaker
Description
Classical chaos arises from the inherent non-linearity of dynamical systems. However, quantum maps are linear; therefore, the definition of chaos is not straightforward. To address this, we study a quantum system that exhibit chaotic behavior in their classical limits. One such system of interest is the kicked top model Haake, Ku ́s, and Scharf, Z. Phys. B 65, 381 (1987), where classical dynamics are governed by Hamilton’s equations on phase space, while quantum dynamics are described by the Schr ̈odinger equation in Hilbert space. In the kicked top model, non-linearity is introduced through the exponent of the angular momentum term, denoted as J^p. Notably, when p = 1, the system remains integrable. Extensive research has focused on the case where p = 2. In this study, we investigate the critical degree of non-linearity necessary for a system to exhibit chaotic behavior. This is done by modifying the original Hamiltonian such that a non-integer value of p is allowed. We categorize the modified kicked top into two regimes: 1 ≤ p ≤ 2 and p > 2, and analyze their distinct behaviors. Our findings reveal that the system loses integrability for any p > 1, leading to the emergence of chaos. Moreover, we observe that the intensity of chaos amplifies with increasing non-linearity. However, as we further increase p (> 2), we observe unexpected behavior, where chaos is suppressed, and regions of chaotic sea are confined to a small region in phase space. This study sheds light on the complex interplay between non-linearity and chaos, offering valuable insights into their dynamic behavior.
| Keyword-1 | Chaos |
|---|---|
| Keyword-2 | non-linear |
| Keyword-3 | dynamical systems |
