Diagonal Representation for a Generic Matrix Valued Quantum Hamiltonian

Pierre Gosselin (1) , Herve Mohrbach (2, 3)

1 IF - Institut Fourier
2 FCN - Fédération de Chimie de Nancy
3 LPMC - Laboratoire de physique moléculaire et des collisions

A general method to deduce the diagonal representation for a generic matrix valued quantum Hamiltonian is proposed. This method can be applied to any kind of quantum system which has an energy band spectrum. In particular it would be useful for the study of relativistic Dirac particles in strong external fields as well as for Bloch electrons in solids. In this approach the diagonal energy operator and the dynamical operators which depend on Berry phase terms can be expanded in power series in the planck constant. The connection with previous less general approaches is also presented. As an example, the case of a Dirac electron in an external electric field is considered.

Domaines: Physique mathématique [math-ph]; Autre [cond-mat.other]; Physique des Hautes Energies - Théorie [hep-th]; Physique Quantique [quant-ph]

Pierre Gosselin, Herve Mohrbach. Diagonal Representation for a Generic Matrix Valued Quantum Hamiltonian. 2008. ⟨hal-00202491v1⟩