96-44 Dell'Antonio G.F., Figari R., Teta A.

A Limit Evolution Problem for Time-Dependent Point Interactions (59K, LaTeX) Feb 19, 96

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Abstract. We study the diffusion in $R^{3}$ of a particle interacting with N fixed points through point interactions whose strength varies in time. Under mild assumptions on the time-dependence of the strengths we prove existence for all times and uniqueness of the solution, for which we provide a rather explicit expression. We also prove that, under a suitable rescaling of the interaction strengths, the solution converges, when N goes to infinity, to the solution of a diffusion equation with a regular killing term (potential). We use properties of the local self-adjoint extensions of the laplacian and results from the theory of fractional integrals and derivatives.

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