2008/02/20 by Vyacheslav V. Stepanov, Gerhard Müller, Gerhard Muller +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Boson #Classical limit #Eigenvalues and eigenvectors #Hamiltonian (control theory) #Integrable system #Lambda #Mathematical physics #Mathematics #Physics #Quantum #Quantum Information and Cryptography #Quantum chaos and dynamical systems #Quantum mechanics #Quantum number #Spectroscopy and Quantum Chemical Studies #Spin (aerodynamics) #cond-mat.other #nlin.SI
paper · pdf · doi:10.1103/physreve.77.066202
published as Phys. Rev. E 77, 066202 (2008)
arxiv created 2008/02/20 · openalex publication_date 2008/06/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the spectral properties of a spin-boson Hamiltonian that depends on two continuous parameters 0 < or = Lambda < infinity (interaction strength) and 0 < or = alpha < or = pi/2 (integrability switch). In the classical limit, this system has two distinct integrable regimes, alpha=0 and alpha=pi/2 . For each integrable regime we can express the quantum Hamiltonian as a function of two action operators. Their eigenvalues (multiples of variant Planck's over 2pi ) are the natural quantum numbers for the complete level spectrum. This functional dependence cannot be extended into the nonintegrable regime (0<alpha<pi/2) . Here level crossings are prohibited and the level spectrum is naturally described by a single (energy sorting) quantum number. In consequence, the tracking of individual eigenstates along closed paths through both regimes leads to conflicting assignments of quantum numbers. This effect is a useful and reliable indicator of quantum chaos-a diagnostic tool that is independent of any level-statistical analysis.