We study the critical points of a nonlocal free energy functional. The functional has two minimizers (ground states) m(±) with zero energy. We prove that there is a first excited state identified as the instanton mathL, and that above the energy of the instanton there is a gap. We also characterize parts of the basin of attraction of m(±) and mathL under a dynamics associated to the free energy functional. The result completes the analysis of tunneling from m(−) to m(+).

Energy levels of a non local functional

DE MASI, Anna;
2005

Abstract

We study the critical points of a nonlocal free energy functional. The functional has two minimizers (ground states) m(±) with zero energy. We prove that there is a first excited state identified as the instanton mathL, and that above the energy of the instanton there is a gap. We also characterize parts of the basin of attraction of m(±) and mathL under a dynamics associated to the free energy functional. The result completes the analysis of tunneling from m(−) to m(+).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/5263
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