On the Hamiltonian nature of semiclassical equations of motion in the presence of an electromagnetic field and Berry curvature

2005/07/31 by Konstantin Y. Bliokh, K. Yu. Bliokh · 29 citations
Mathematics · Physics and Astronomy · #Berry connection and curvature #Canonical coordinates #Canonical transformation #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Covariant Hamiltonian field theory #Covariant transformation #Curvature #Electromagnetic field #Equations of motion #Geometric phase #Geometry #Hamiltonian (control theory) #Hamiltonian system #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Phase space #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Semiclassical physics #cond-mat.mes-hall #cond-mat.other

paper · pdf · doi:10.1016/j.physleta.2005.10.087

published in Physics Letters A 351(3), 123-124 (Elsevier BV) · 3 pages, to appear in Physics Letters A

arxiv created 2005/10/26 · openalex publication_date 2005/11/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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)).

Citations

• Modified geometrical optics of a smoothly inhomogeneous isotropic medium: The anisotropy, Berry phase, and the optical Magnus effect
• Topological spin transport of photons: the optical Magnus effect and Berry phase
• Dissipationless Quantum Spin Current at Room Temperature
• Topological spin transport of a relativistic electron
• Topological spin transport of photons: Magnetic monopole gauge field in Maxwell's equations and polarization splitting of rays in periodically inhomogeneous media
• Spin gauge fields: From Berry phase to topological spin transport and Hall effects

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• Relativistic Quantum Dynamics of Twisted Electron Beams in Arbitrary Electric and Magnetic Fields
• Berry curvature-induced transport signature for altermagnetic order