Lectures on QM for mathematicians conjecture that quantum transitions and duality emerge from attractors in nonlinear Hamiltonian PDEs, supported by model cases since 1990 but open for Maxwell-Schrödinger, plus Kirchhoff-approximation calculations for diffraction and Aharonov-Bohm shift.
Aharonov-Bohm effect revisited
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abstract
Aharonov-Bohm effect is a quantum mechanical phenomenon that attracted the attention of many physicists and mathematicians since the publication of the seminal paper of Aharonov and Bohm [1] in 1959. We consider different types of Aharonov-Bohm effect such as magnetic AB effect, electric AB effect, combined electromagnetic AB effect, AB effect for the Schr\"odinger equations with Yang-Mills potentials, and the gravitational analog of AB effect. We shall describe different approaches to prove the AB effect based on the inverse scattering problems, the inverse boundary value problems in the presence of obstacles, spectral asymptotics, and the direct proofs of the AB effect.
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2019 1verdicts
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Lectures on Quantum Mechanics for mathematicians
Lectures on QM for mathematicians conjecture that quantum transitions and duality emerge from attractors in nonlinear Hamiltonian PDEs, supported by model cases since 1990 but open for Maxwell-Schrödinger, plus Kirchhoff-approximation calculations for diffraction and Aharonov-Bohm shift.