Classical vs quantum dynamics and the onset of chaos in a macrospin system

TL;DR

This paper compares classical and quantum dynamics of a driven macrospin system, revealing how chaos, bifurcations, and quantum effects interplay, with finite-size quantum effects suppressing some classical chaotic behaviors.

Contribution

It provides a detailed analysis of the transition from classical to quantum chaos in a macrospin system, highlighting finite-size effects and the conditions for quantum-classical convergence.

Findings

Classical system exhibits chaos, quasiperiodicity, and bifurcations.

Quantum simulations show suppression of some classical behaviors due to finite size.

Quantum chaos is characterized by delocalized density matrices and diffusive Hilbert space exploration.

Abstract

We study a periodically driven macrospin system with anisotropic long-range interactions and collective dissipation, described by a Lindblad master equation. In the thermodynamic limit ($N\to\infty$), a mean-field treatment yields classical equations of motion, whose dynamics are characterized via the maximal Lyapunov exponent (MLE). Focusing on the thermodynamic limit, we map out chaotic, quasiperiodic, and periodic phases via bifurcation diagrams, MLEs, and Fourier spectra of evolved observables, identifying classic period-doubling bifurcations and fractal boundaries in the regions of attractors. Finite-size quantum simulations in the Dicke basis reveal that while both quantum and classical systems exhibit diverse dynamical phases, finite-size effects suppress some behaviors present in the thermodynamic limit. The sign of $\lambda_{\mathrm{max}}$ serves as a key indicator of convergence between quantum and classical dynamics, which agree over timescales up to the Lyapunov time. Analysis of the density matrix shows that convergence occurs only when its nonzero elements are sharply localized. However, the nonconvergence does not imply a fundamental difference between quantum and classical dynamics: in chaotic regimes, although the evolution orbits of quantum and classical systems show significant differences, quantum evolution becomes mixed and diffusively explores the Hilbert space, signaling quantum chaos, which can be confirmed by the delocalized nature of the density matrix.