Concepedia

Multiplicity of Resonances in Black Box Scattering

Canadian Mathematical Bulletin · 2004 · 11 citations · 7 references

Open access

Concepts

Spectral TheoryBlack BoxScattering MatrixPhysicsNatural ProofEngineeringWave ScatteringMagnetic ResonanceResonanceLight ScatteringDouble ResonanceInverse Scattering TransformsHigh-frequency ApproximationComplex Scaling

Abstract

Abstract We apply the method of complex scaling to give a natural proof of a formula relating the multiplicity of a resonance to the multiplicity of a pole of the scattering matrix.

References

7

Scattering Asymptotics for Riemann Surfaces

Laurent Guillopé, Maciej Zworski · Annals of Mathematics · 1997 · 176 citations

Elliptic Equation, Riemann-hilbert Problem, Potential Theory +8

Complex Scaling and the Distribution of Scattering Poles

Johannes Sjöstrand, Maciej Zworski · Journal of the American Mathematical Society · 1991 · 150 citations

Physics, Wave Scattering, High-frequency Approximation +2

Semi-classical Estimates on the Scattering Determinant

Vesselin Petkov, Maciej Zworski · Annales Henri Poincaré · 2001 · 78 citations · Full text

Spectral Theory, Scattering Determinant, Engineering +4

Scattering poles for asymptotically hyperbolic manifolds

David Borthwick, Peter Perry · Transactions of the American Mathematical Society · 2001 · 47 citations

Generic Potential Perturbations, Continued Resolvent Kernel, Lie Group +8

Semi-classical estimates for resolvents and asymptotics for total scattering cross-sections

Didier Robert, Hideo Tamura · French digital mathematics library (Numdam) · 1987 · 41 citations

Spectral Theory, Quantum Dynamic, Engineering +13