Year: 2008
Type: article
Abstract: We study the spectral properties of a spin-boson Hamiltonian that depends on two continuous parameters $0\ensuremath{\le}\ensuremath{\Lambda}<\ensuremath{\infty}$ (interaction strength) and $0\ensuremath{\le}\ensuremath{\alpha}\ensuremath{\le}\ensuremath{\pi}/2$ (integrability switch). In the classical limit, this system has two distinct integrable regimes, $\ensuremath{\alpha}=0$ and $\ensuremath{\alpha}=\ensuremath{\pi}/2$. For each integrable regime we can express the quantum Hamiltonian as a function of two action operators. Their eigenvalues (multiples of $\ensuremath{\hbar}$) are the natural quantum numbers for the complete level spectrum. This functional dependence cannot be extended into the nonintegrable regime $(0<\ensuremath{\alpha}<\ensuremath{\pi}/2)$. 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.
Source: Physical Review E
Institutions: University of Rhode Island, TU Dortmund University
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1990994179