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Egli, Daniel; Fröhlich, Jürg; Gang, Zhou; Shao, Arick; Sigal, Israel Michael

Hamiltonian dynamics of a particle interacting with a wave field. (English) Zbl 1281.35084

Commun. Partial Differ. Equations 38, No. 12, 2155-2198 (2013).
Summary: We study the Hamiltonian equations of motion of a heavy tracer particle interacting with a dense weakly interacting Bose-Einstein condensate in the classical (mean-field) limit. Solutions describing ballistic subsonic motion of the particle through the condensate are constructed. We establish asymptotic stability of ballistic subsonic motion.

Cited in 5 Documents

MSC:

35Q70 PDEs in connection with mechanics of particles and systems of particles
35B35 Stability in context of PDEs
70H14 Stability problems for problems in Hamiltonian and Lagrangian mechanics
35B40 Asymptotic behavior of solutions to PDEs
35C07 Traveling wave solutions

Keywords:

Bose-Einstein condensation; Gross-Pitaevskii equation; Hamiltonian dynamics; particle-field interaction; quantum trajectory; Schrödinger equation; tracer particle; traveling waves
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\textit{D. Egli} et al., Commun. Partial Differ. Equations 38, No. 12, 2155--2198 (2013; Zbl 1281.35084)
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