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

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)).Comment: 3 pages, to appear in Physics Letters

Topological spin transport of photons: the optical Magnus Effect and Berry Phase

The paper develops a modified geometrical optics (GO) of smoothly inhomogeneous isotropic medium, which takes into account two topological phenomena: Berry phase and the optical Magnus effect. By using the analogy between a quasi-classical motion of a quantum particle with a spin and GO of an electromagnetic wave in smoothly inhomogeneous media, we have introduced the standard gauge potential associated with the degeneracy in the wave momentum space. This potential corresponds to the Dirac-monopole-like field (Berry curvature), which causes the topological spin (polarization) transport of photons. The deviations of waves of right-hand and left-hand helicity occur in the opposite directions and orthogonally to the principal direction of motion. This produces a spin current directed across the principal motion. The situation is similar to the anomalous Hall effect for electrons. In addition, a simple scheme of the experiment allowing one to observe the topological spin splitting of photons has been suggested.Comment: 4 pages, 1 figur

On spin evolution in a time-dependent magnetic field: post-adiabatic corrections and geometric phases

We examine both quantum and classical versions of the problem of spin evolution in a slowly varying magnetic field. Main attention is given to the first- and second-order adiabatic corrections in the case of in-plane variations of the magnetic field. While the first-order correction relates to the adiabatic Berry phase and Coriolis-type lateral deflection of the spin, the second-order correction is shown to be responsible for the next-order geometric phase and in-plain deflection. A comparison between different approaches, including the exact (non-adiabatic) geometric phase, is presented.Comment: 10 pages, 1 figure, to appear in Phys. Lett.

Weak antilocalization of ultrarelativistic fermions

The paper discusses the Berry phase influence on the weak localization phenomenon at the adiabatic backscattering of ultrarelativistic particles in a random medium. We demonstrate that bosons that pass along a certain closed path in opposite directions come back always in phase (an example: the backscattering enhancement of electromagnetic waves), whereas fermions come exactly in antiphase. This produces a "complete weak antilocalization" of ultrarelativistic fermions: the backscattering field intensity vanishes.Comment: 5 pages, 3 figures, to appear in Physics Letters

Spin-orbit interaction of photons and fine splitting of levels in ring dielectric resonator

We consider eigenmodes of a ring resonator made of a circular dielectric waveguide. Taking into account the polarization corrections, which are responsible for the interaction of polarization and orbital properties of electromagnetic waves (spin-orbit interaction of photons), results in fine splitting of the levels of scalar approximation. The basic features of this fine structure of the levels are similar to that of electron levels in an atom. Namely: 1) sublevels of the fine structure are defined by an additional quantum number: product of helicity of the wave and its orbital moment; 2) for a waveguide with a parabolic profile of the refractive index each level of the scalar approximation splits into N sublevels (N is the principal quantum number), while for any other profile it splits into 2 sublevels; 3) each level of the fine structure remains twice degenerated due to local axial symmetry of the waveguide. Numerical estimations show that the described fine splitting of levels may be observed in optic-fiber ring resonators.Comment: 8 pages, 1 figure, final version with jornal misprints correcte

Spin Gauge Fields: from Berry Phase to Topological Spin Transport and Hall Effects

The paper examines the emergence of gauge fields during the evolution of a particle with a spin that is described by a matrix Hamiltonian with n different eigenvalues. It is shown that by introducing a spin gauge field a particle with a spin can be described as a spin multiplet of scalar particles situated in a non-Abelian pure gauge (forceless) field U(n). As the result, one can create a theory of particle evolution that is gauge invariant with regards to the group U^n(1). Due to this, in the adiabatic (Abelian) approximation the spin gauge field is an analogue of n electromagnetic fields U(1) on the extended phase space of the particle. These fields are force ones, and the forces of their action enter the particle motion equations that are derived in the paper in the general form. The motion equations describe the topological spin transport, pumping and splitting. The Berry phase is represented in this theory analogously to the Dirac phase of a particle in an electromagnetic field. Due to the analogy with the electromagnetic field, the theory becomes natural in the four-dimensional form. Besides the general theory the article considers a number of important particular examples, both known and new.Comment: 28 pages, the final (journal) versio