| Abstract: |
| This work investigates the inverse interior scattering problem for quantum Bunimovich billiards subject to small boundary perturbations. We consider billiards whose boundaries are piecewise $C^2$ perturbations of the original domain, satisfying the generalized defocusing mechanism. An incident field is generated from the center of each perturbed circular arc, and the resulting scattered field is measured on an auxiliary arc. By synthesizing the transformed field expansion method with Fourier analysis and mathematical induction, we develop a procedure to reconstruct the perturbation`s shape. We establish that, when the billiard boundary and the auxiliary arc are sufficiently close, the perturbation is uniquely determined by the imaginary part of the total field, yielding an explicit reconstruction formula. |
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