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Rotating Charge Coupled to the Maxwell Field: Scattering Theory and Adiabatic Limit

In: Nonlinear Differential Equation Models

Author

Listed:
  • Valery Imaikin

    (University of Vienna, Institute of Mathematics)

  • Alexander Komech

    (University of Vienna, Institute of Mathematics)

  • Herbert Spohn

    (TU München, Zentrum Mathematik)

Abstract

We consider a spinning charge coupled to the Maxwell field. Through the appropriate symmetry in the initial conditions the charge remains at rest. We establish that any time-dependent finite energy solution converges to a sum of a soliton wave and an outgoing free wave. The convergence holds in global energy norm. Under a small constant external magnetic field the soliton manifold is stable in local energy seminorms and the evolution of the angular velocity is guided by an effective finite-dimensional dynamics. The proof uses a non-autonomous integral inequality method.

Suggested Citation

  • Valery Imaikin & Alexander Komech & Herbert Spohn, 2004. "Rotating Charge Coupled to the Maxwell Field: Scattering Theory and Adiabatic Limit," Springer Books, in: Ansgar Jüngel & Raul Manasevich & Peter A. Markowich & Henrik Shahgholian (ed.), Nonlinear Differential Equation Models, pages 143-156, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7091-0609-9_11
    DOI: 10.1007/978-3-7091-0609-9_11
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