Non-linearity and chaos in the kicked top

Abstract

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 exhibits chaotic behavior in its classical limit: the kicked top model, whose classical dynamics are governed by Hamilton's equations on phase space, whereas its quantum dynamics are described by the Schrödinger equation in Hilbert space. We explore the critical degree of non-linearity signifying the onset of chaos in the kicked top by modifying the original Hamiltonian so that the non-linearity is parametrized by a quantity $p$. We find two distinct behaviors of the modified kicked top depending on the value of $p$. Chaos intensifies as $p$ varies within the range of $1\le p\le 2$, whereas it diminishes for $p>2$, eventually transitioning to a purely regular oscillating system as $p$ tends to infinity. We also comment on the complicated phase space structure for non-chaotic dynamics. Our investigation sheds light on the relationship between non-linearity and chaos in classical systems, offering insights into their dynamic behavior.

References in corpus (11)

• Ergodic dynamics and thermalization in an isolated quantum system
• Remarks on the notion of quantum integrability
• Energy gaps in quantum first-order mean-field-like transitions: The problems that quantum annealing cannot solve
• Quantum annealing correction at finite temperature: ferromagnetic $p$-spin models
• Hamiltonian mappings and circle packing phase spaces
• Nonlinear dynamics and quantum chaos of a family of kicked $p$-spin models
• Quantum-classical correspondence in the vicinity of periodic orbits
• Chaos in a Relativistic 3-body Self-Gravitating System
• Simulation of complex dynamics of mean-field $p$-spin models using measurement-based quantum feedback control
• A new model of variable-length coupled pendulums: from hyperchaos to superintegrability
• Hamiltonian mappings and circle packing phase spaces: numerical investigations

Cited by in corpus (1)

• Trotter transition in BCS pairing dynamics