On the Hamiltonian nature of semiclassical equations of motion in the presence of an electromagnetic field and Berry curvature
arXiv:cond-mat/0507499 · doi:10.1016/j.physleta.2005.10.087
Abstract
We consider the semiclassical equations of motion of a particle when both an external electromagnetic field and the Berry gauge field in the momentum space are present. It is shown that these equations are Hamiltonian and relations between the canonical and covariant variables are determined through a consistent account of all components of the Berry connection. The Jacobian of the canonical-to-covariant-variables transformation describes the nonconservation of the 'naive' phase space volume in the covariant coordinates (D.Xiao, J.Shi, and Q.Niu, Phys. Rev. Lett. 95, 137204 (2005)).
arXiv comment3 pages, to appear in Physics Letters A
References in corpus (14)
- Dissipationless Quantum Spin Current at Room Temperature
- Hall Effect of Light
- Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects
- First Principles Calculation of Anomalous Hall Conductivity in Ferromagnetic bcc Fe
- Berry phase correction to electron density of states in solids
- Semiclassical theory of spin transport in spin-orbit coupled systems
- Exotic galilean symmetry in the non-commutative plane, and the Hall effect
- Topological spin transport of photons: the optical Magnus Effect and Berry Phase
- Modified geometrical optics of a smoothly inhomogeneous isotropic medium: the anisotropy, Berry phase, and the optical Magnus effect
- Topological spin transport of relativistic electron
- Spin Gauge Fields: from Berry Phase to Topological Spin Transport and Hall Effects
- Topological spin transport of photons: "magnetic monopole" gauge field in Maxwell equations and polarization splitting of rays in periodically inhomogeneous media
- Enlarged Galilean symmetry of anyons and the Hall effect
- Topological spin pumps I
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