2019/07/09 by Komech, Alexander
#35B41 #35L70 #35P30 #35Q40 #37L05 #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.1907.04297
Our goal is the discussion of the problem of mathematical interpretation of basic postulates (or `principles') of Quantum Mechanics: transitions to quantum stationary orbits, the wave-particle duality, and the probabilistic interpretation, in the context of semiclassical self-consistent Maxwell--Schrödinger equations. We discuss possible relations of these postulates to the theory of attractors of Hamiltonian nonlinear PDEs and to a new general mathematical conjecture on global attractors of G-invariant nonlinear Hamiltonian partial differential equations with a Lie symmetry group G. This conjecture is inspired by our results on global attractors of nonlinear Hamiltonian PDEs obtained since 1990 for a list of model equations with three basic symmetry groups: the trivial group, the group of translations, and the unitary group U(1). We present sketchy these results.