Quantum integrability and nonintegrability in the spin-boson model

Details Quantum integrability and nonintegrability in the spin-boson model Quantum integrability and nonintegrability in the spin-boson model

2008-02-20

arxiv.org/abs/0802.2815v1

Phys. Rev. E 77, 066202 (2008)

Physics

Condensed Matter

Other Condensed Matter

Scientific paper

10.1103/PhysRevE.77.066202

We study the spectral properties of a spin-boson Hamiltonian that depends on two continuous parameters $0\leq\Lambda<\infty$ (interaction strength) and $0\leq\alpha\leq\pi/2$ (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 $\hbar$) 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.

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