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Keywords:entropy,chaos,quantum,quantum measurement,continuous measurement,event enhanced quantum theory,eeqt,lyapunov,mixing,noncommuting,zeno,zeno effect,markov,classical,spin,tetrahedron,jump,iterated function system,ifs,nonlinear ifs,fractal
Computer simulations of a continuous simultaneous monitoring of four (distributed at the edges of a regular tetrahedron, with all four coupling constants equal to the same parameter value alpha) noncommuting spin projections produced the following quantum state trajectories:
Note: interesting pictures culminate around alpha=0.6. For smaller alpha points are distributed evenly on the sphere. For alpha approaching 1 they tent to concentrate at the four veritces. Selfsimilarity is clearly seen for alpha=0.7
Fig. 0. Quantum state trajectory for alpha=0.1, 10000000 points.
Fig. 1. Quantum state trajectory for alpha=0.2, 10000000 points.
Fig. 1a. Quantum state trajectory for alpha=0.3, 10000000 points.
Fig. 2. Quantum state trajectory for alpha=0.4, 10000000 points.
Fig. 2a. Quantum state trajectory for alpha=0.5, 10000000 points.
Fig. 3. Quantum state trajectory for alpha=0.6, 10000000 points.
Fig. 4a. Quantum state trajectory for alpha=0.7, 1000000000 points.
Fig. 4b. Quantum state trajectory for alpha=0.7, zoom=2x, 1000000000 points.
Fig. 4c. Quantum state trajectory for alpha=0.7, zoom=4x, 1000000000 points.
Fig. 4d. Quantum state trajectory for alpha=0.7, zoom=16x, 1000000000 points.
Fig. 5. Quantum state trajectory for alpha=0.8, 10000000 points.
Fig. 5. Quantum state trajectory for alpha=0.9, 10000000 points.
Fig. 6. Animation through different coupling constants
New
paper: "How Events Come Into Being: EEQT, Particle
Tracks, Quantum Chaos, and Tunneling Time." This paper has graphics
displaying iterated Markov operator .
Homepage: http://www.cassiopaea.org/quantum_future/homepage.htm
.