Semi-classical Analysis of Spin Systems near Critical Energies
Résumé
The spectral properties of $su(2)$ Hamiltonians are studied for energies near the critical classical energy $\varepsilon_c$ for which the corresponding classical dynamics presents hyperbolic points (HP). A general method leading to an algebraic relation for eigenvalues in the vicinity of $\varepsilon_c$ is obtained in the thermodynamic limit, when the semi-classical parameter $n^{-1}=(2s)^{-1}$ goes to zero (where $s$ is the total spin of the system). Two applications of this method are given and compared with numerics. Matrix elements of observables, computed between states with energy near $\varepsilon_c$, are also computed and shown to be in agreement with the numerical results.
Domaines
Physique Quantique [quant-ph]Origine | Fichiers produits par l'(les) auteur(s) |
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