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The effective dynamics of interacting waves for coupled Schrödinger-Korteweg-de Vries
equations over a slowly varying random bottom is rigorously studied. One motivation for
studying such a system is better understanding the unidirectional motion of interacting
surface and internal waves for a fluid system that is formed of two immiscible layers. It
was shown recently by Craig-Guyenne-Sulem [1] that
in the regime where the internal wave has a large...
The analysis of dissipative transport equations within the framework of open quantum systems with Fokker-Planck-type scattering is carried out from the perspective of a Wigner function approach. In particular, the well-posedness of the self-consistent whole-space problem in 3D is analyzed: existence of solutions, uniqueness and asymptotic behavior in time, where we adopt the viewpoint of mild solutions in this paper. Also, the admissibility of a density matrix formulation in Lindblad form with Fokker-Planck...
Several situations of physical importance may be modelled by linear quantum fields propagating in fixed spacetime-dependent classical background fields. For example, the quantum Dirac field in a strong and/or time-dependent external electromagnetic field accounts for the creation of electron-positron pairs out of the vacuum. Also, the theory of linear quantum fields propagating on a given background curved spacetime is the appropriate framework for the derivation of black-hole evaporation (Hawking...
Questo lavoro costituisce un survey sui problemi di limite asintotico per le soluzioni delle equazioni di Ginzburg-Landau in dimensione due. Vengono presentati essenzialmente i risultati di [BBH] e [BR] sulla formazione ed il comportamento asintotico dei vortici in un dominio bidimensionale nel caso fortemente repulsivo (large limit).
This article studies the asymptotic behavior of the number of the negative eigenvalues as of the two dimensional Pauli operators with electric potential decaying at and with nonconstant magnetic field , which is assumed to be bounded or to decay at . In particular, it is shown that , when decays faster than under some additional conditions.
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