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.
Attractors of nonlinear Hamiltonian PDEs
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abstract
This is a survey of results on long time behavior and attractors for nonlinear Hamiltonian partial differential equations, considering the global attraction to stationary states, stationary orbits, and solitons, the adiabatic effective dynamics of the solitons, and the asymptotic stability of the solitary manifolds. The corresponding numerical results and relations to quantum postulates are considered.
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math-ph 1years
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.