Bloch Motions and Spinning Tops
Albert Huber, Paul Schreivogl

TL;DR
This paper explores the dynamics of closed quantum systems using classical rigid body methods, deriving integrability and stability criteria, and constructing solutions that describe oscillating entanglement phenomena.
Contribution
It introduces a novel formalism linking quantum dynamics to classical spinning top models, revealing integrability, stability conditions, and entanglement oscillations.
Findings
Proves Liouville integrability of quantum Bloch dynamics.
Derives stability criteria analogous to classical mechanics.
Constructs solutions showing oscillating entanglement states.
Abstract
This work investigates the dynamics of closed quantum systems in the Bloch vector representation using methods from rigid body dynamics and the theory of integrable systems. To this end, equations of motion for Bloch components are derived from the von Neumann equation, which are mathematically equivalent to equations of motion for a distribution of point masses from classical mechanics. Furthermore, using the Heisenberg equation, another system of Bloch vector equations is derived, which forms an Euler-Poinsot system, as is commonly encountered in the theory of torque-free spinning tops. This is used to prove the Liouville integrability of the corresponding Hamilton equations of motion, whereby formal connections to the Neumann model of classical Hamiltonian dynamics and the Hamiltonian Euler-Poinsot model are drawn to identify the first integrals of motion. Within the same framework,…
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Taxonomy
TopicsQuantum Information and Cryptography · Quantum many-body systems · Quantum chaos and dynamical systems
