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We prove explicit asymptotics for the location of semiclassical scattering resonances in the setting of -dependent delta-function potentials on . In the cases of two or three delta poles, we are able to show that resonances occur along specific lines of the form More generally, we use the method of Newton polygons to show that resonances near the real axis may only occur along a finite collection of such lines, and we bound the possible number of values of the parameter We present numerical evidence of the existence of more and more possible values of for larger numbers of delta poles.
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We compute resonance width asymptotics for the delta potential on the half-line, by deriving a formula for resonances in terms of the Lambert W function and applying a series expansion. This potential is a simple model of a thin barrier, motivated by physical problems such as quantum corrals and leaky quantum graphs.more » « less
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Abstract We consider the initial‐value problem for a one‐dimensional wave equation with coefficients that are positive, constant outside of an interval, and have bounded variation (BV). Under the assumption of compact support of the initial data, we prove that the local energy decays exponentially fast in time, and provide the explicit constant to which the solution converges. The key ingredient of the proof is a high‐frequency resolvent estimate for an associated Helmholtz operator with a BV potential.more » « less
