zum Hauptkapitel Emerging Quantum Mechanics:

## Calculations with coupling to the environment

The Phonon energy is \hbar\omega=0.1 (see below the diagonal matrix elements in the 32x32-matrix); coupling matrix element of phonon to 3rd qubit=0.1 (see lower triangle of 32x32-matrix) The time dependence of the phonon coupling is: 0.07\cdot e^{-0.005(t-10)^2}\cdot \sqrt{\pi /0.005} (see last line of input). It lives for roughly t=\sqrt{1/0.005}=sqrt{200}=15=1.5\cdot 10^{-6} seconds.

The width of the environmental band is 0.001=10^{-8}eV; it contains 29 energy levels (see line below diagonal matrix elements). The coupling of the third qubit to the environmental band is 0.001=10^{-8} eV, i.e., the coupling of the 3rd qubit to a single environmental level is 3.5x10^{-10} eV (see next line).