Semi-classical Analysis of Spin Systems near Critical Energies

Details Semi-classical Analysis of Spin Systems near Critical Energies Semi-classical Analysis of Spin Systems near Critical Energies

2008-06-19

arxiv.org/abs/0806.3192v1

Physics

Quantum Physics

3 figures

Scientific paper

10.1103/PhysRevA.79.032107

The spectral properties of $su(2)$ Hamiltonians are studied for energies near the critical classical energy $\epsilon_c$ for which the corresponding classical dynamics presents hyperbolic points (HP). A general method leading to an algebraic relation for eigenvalues in the vicinity of $\epsilon_c$ 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 $\epsilon_c$, are also computed and shown to be in agreement with the numerical results.

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