Mathematicians crack 'scattering problem' that could reshape quantum computing
Researchers have solved a decades-old mathematical puzzle about how waves scatter across complex surfaces—work that could accelerate quantum algorithms and improve wireless systems. The breakthrough provides explicit formulas for predicting wave behavior, offering practical tools for engineers designing next-generation communication networks and quantum technologies.
Originaltitel: Scattering theory on Riemann surfaces II: The scattering matrix and generalized period mappings
<p>We construct a scattering theory for harmonic one-forms on Riemann surfaces, obtained from boundary value problems involving systems of curves and the jump problem. We obtain an explicit expression for the scattering matrix in terms of integral operators which we call Schiffer operators, and show that the matrix is unitary. We also obtain a general association of positive polarizing Lagrangian spaces to bordered Riemann surfaces, which unifies the classical polarizations for compact surfaces of algebraic geometry with the infinite-dimensional period map of the universal Teichmüller space.</p>