Generalized geometric phase of a classical oscillator

@article{Bliokh2003GeneralizedGP,
  title={Generalized geometric phase of a classical oscillator},
  author={Konstantin Y. Bliokh},
  journal={Journal of Physics A},
  year={2003},
  volume={36},
  pages={1705-1710}
}
  • K. Bliokh
  • Published 29 January 2003
  • Physics, Mathematics
  • Journal of Physics A
The equation of a linear oscillator with adiabatically varying eigenfrequency ω(et) (e 1 is the adiabaticity parameter) is considered. The asymptotic solutions to the equation have been obtained to terms of order e3. It is shown that imaginary terms of order e2 form a generalized geometric phase determined by the geometry of the system's contour in the plane (ω, ω'). The real terms of orders e and e3, as predicted (Bliokh K Yu 2002 J. Math. Phys. 43 5624), do not form geometric amplitudes but… 
View via Publisher
wwwrsphysse.anu.edu.au
3 Citations

Figures from this paper

3 Citations

On spin evolution in a time-dependent magnetic field: Post-adiabatic corrections and geometric phases
On the change in electromagnetic wave polarization in a smooth one-dimensionally inhomogeneous medium
Propagation of an electromagnetic wave in a smooth one-dimensionally inhomogeneous isotropic medium is considered in the second approximation of geometrical optics. The polarization evolution is…
Modified geometrical optics of a smoothly inhomogeneous isotropic medium: the anisotropy, Berry phase, and the optical Magnus effect.
  • K. Bliokh, Y. Bliokh
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2004
TLDR
The Hamilton ray equations giving a unified description for both the optical Magnus effect and the Berry phase have been derived and also a novel splitting effect for a ray of noncircular polarization has been predicted.

References

SHOWING 1-10 OF 11 REFERENCES
Geometric amplitude, adiabatic invariants, quantization, and strong stability of Hamiltonian systems
Considered is a linear set of ordinary differential equations with a matrix depending on a set of adiabatically varying parameters. Asymptotic solutions have been constructed. As has been shown, an…
Generalization of Berry's geometric phase, equivalence of the Hamiltonian nature, quantizability and strong stability of linear oscillatory systems, and conservation of adiabatic invariants
A linear set of ordinary differential equations with a matrix depending on a set of adiabatically varying parameters is considered. Its asymptotic solutions are constructed to an arbitrary accuracy…
Geometric Phases in Physics
During the last few years, considerable interest has been focused on the phase that waves accumulate when the equations governing the waves vary slowly. The recent flurry of activity was set off by a…
Quantal phase factors accompanying adiabatic changes
  • M. Berry
  • Physics
    Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1984
A quantal system in an eigenstate, slowly transported round a circuit C by varying parameters R in its Hamiltonian Ĥ(R), will acquire a geometrical phase factor exp{iγ(C)} in addition to the familiar…
Angle variable holonomy in adiabatic excursion of an integrable Hamiltonian
If an integrable classical Hamiltonian H describing bound motion depends on parameters which are changed very slowly then the adiabatic theorem states that the action variables I of the motion are…
J. Math. Phys
  • J. Math. Phys
  • 2002
Izv. Vuzov: Appl. Nonlinear Dyn
  • Izv. Vuzov: Appl. Nonlinear Dyn
  • 2001
Advanced Mathematical Methods for Scientists and Engineers
Proc. R. Soc. A
  • Proc. R. Soc. A
  • 1984
J. Phys. A: Math. Gen
  • J. Phys. A: Math. Gen
  • 1985
...
...