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cond-mat.other2025
When can phonon modes be trapped by arbitrarily weak local defects? Rigorous sufficient conditions in a monatomic lattice
Jaden Thomas-Markarian, Jaden Thomas, Rodrigo Arrieta +3
Although many studies have shown that localized defects in vibrational lattices can trap localized phonon modes for particular geometries, there has been no general proof of locali…
cond-mat.other2010★ 21 cited
Sufficient conditions for two-dimensional localization by arbitrarily weak defects in periodic potentials with band gaps
Arthur Parzygnat, Karen K. Y. Lee, Yehuda Avniel +1
We prove, via an elementary variational method, 1d and 2d localization within the band gaps of a periodic Schrodinger operator for any mostly negative or mostly positive defect pot…