Semiclassical Diagonalization of Quantum Hamiltonian and Equations of Motion with Berry Phase Corrections

Abstract

It has been recently found that the equations of motion of several semiclassical systems must take into account terms arising from Berry phases contributions. Those terms are responsible for the spin Hall effect in semiconductor as well as the Magnus effect of light propagating in inhomogeneous media. Intensive ongoing research on this subject seems to indicate that a broad class of quantum systems may be affected by Berry phase terms. It is therefore important to find a general procedure allowing for the determination of semiclassical Hamiltonian with Berry Phase corrections. This article presents a general diagonalization method at order $\hslash$ for a large class of quantum Hamiltonians directly inducing Berry phase corrections. As a consequence, Berry phase terms on both coordinates and momentum operators naturally arise during the diagonalization procedure. This leads to new equations of motion for a wide class of semiclassical system. As physical applications we consider here a Dirac particle in an electromagnetic or static gravitational field, and the propagation of a Bloch electrons in an external electromagnetic field.

15 pages

References in corpus (4)

• Dissipationless Quantum Spin Current at Room Temperature
• Topological spin transport of relativistic electron
• Spin Gauge Fields: from Berry Phase to Topological Spin Transport and Hall Effects
• On the Hamiltonian nature of semiclassical equations of motion in the presence of an electromagnetic field and Berry curvature

Cited by in corpus (6)

• Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium
• Berry Curvature in Graphene: A New Approach
• Recursive Diagonalization of Quantum Hamiltonians to all order in $\hslash$
• Berry Phase Effects in the dynamics of Dirac Electrons in Doubly Special Relativity Framework
• Semiclassical quantization of electrons in magnetic fields: the generalized Peierls substitution
• Diagonal Representation for a Generic Matrix Valued Quantum Hamiltonian