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

Bellettini, G., De Masi, A., Presutti, E. (2005). Energy levels of a non local evolution equations. JOURNAL OF MATHEMATICAL PHYSICS, 46(8), 1-31 [10.1063/1.1990107].

Energy levels of a non local evolution equations

BELLETTINI, GIOVANNI;
2005-01-01

Abstract

We study the critical points of a nonlocal free energy functional. The functional has two minimizers (ground states) m(±)m(±) with zero energy. We prove that there is a first excited state identified as the instanton m̂ Lm̂L, and that above the energy of the instanton there is a gap. We also characterize parts of the basin of attraction of m(±)m(±) and m̂ Lm̂L under a dynamics associated to the free energy functional. The result completes the analysis of tunneling from m(−)m(−) to m(+)m(+)
2005
Bellettini, G., De Masi, A., Presutti, E. (2005). Energy levels of a non local evolution equations. JOURNAL OF MATHEMATICAL PHYSICS, 46(8), 1-31 [10.1063/1.1990107].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/1017448