2006/11/30 by Pierre Gosselin, Jocelyn Hanssen, Herve Mohrbach +1 · 5 citations
Physics and Astronomy · #Quantum Mechanics and Non-Hermitian Physics #Quantum and electron transport phenomena #Quantum, superfluid, helium dynamics #cond-mat.mes-hall #hep-th
paper · pdf · doi:10.1103/physrevd.77.085008
published as Phys.Rev.D77:085008,2008
arxiv created 2007/07/28 · openalex publication_date 2008/04/11 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We present a diagonalization method for generic matrix valued Hamiltonians based on a formal expansion in power of \ensuremathℏ. Considering \ensuremathℏ as a running parameter, a differential equation connecting two diagonalization processes for two very close values of \ensuremathℏ is derived. The integration of this differential equation allows the recursive determination of the series expansion in powers of \ensuremathℏ for the diagonalized Hamiltonian. This approach results in effective Hamiltonians with Berry-phase corrections of higher order in \ensuremathℏ, and deepens previous works on the semiclassical diagonalization of quantum Hamiltonians, which led notably to the discovery of the intrinsic spin Hall effect. As physical applications we consider spinning massless particles in isotropic inhomogeneous media and show that both the energy and the velocity get quantum corrections of order \ensuremathℏ2. We also derive formally to all orders in \ensuremathℏ the energy spectrum and the equations of motion of Bloch electrons in an external electric field.