Nonlinear Schrödinger-Poisson definition of fine-structure-constant's value ~1/137
Gilbert Reinisch
By numerically investigating the nonlinear Schrödinger-Poisson eigenstates of a condensed Bose gas of charged particles that is confined in a two-dimensional axisymmetric parabolic potential ½ m e ω 2 r 2 (e.g. quantum-dot helium), it is shown that the probability amplitude between two nonlinear—and hence non-orthogonal—eigenstates displays an interference pattern scaled (within 0.03 %) by Since α = e 2 /ℏ c ~ 1/137 is the fine structure constant, this stunning result—indeed velocity of light c does not enter the present non-relativistic model—is tentatively explained by the existence of a "nonlinear" bound state of the trapped particle-particle interaction Coulomb field whose energy defines the induced emission or absorption equilibrium processes between two appropriate chemical potentials. Besides, a non-decoherence quantum-classical transition with increasing nonlinearity is pointed out. As a possible experimental test for the present theory, the 0 s 2 → 1 s 2 nonlinear transition in an ℏω = 1.66meV GaAs quantum-dot helium is emphasized.
Journal of Physics Conference Series•Jun 1, 2010•2 citations