... [*]
On leave of absence from Institute of Theoretical Physics, University of Wroclaw 
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
... process[*]
The Markovian property is not really important. 
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
... catastrophe.[*]
The term instantaneously in the last sentence may suggest that our formalism is incompatible with Einstein's relativity. That this is not so has been demonstrated in Ref.[10]. The point is that for a relativistic theory the role of time is being played by the Fock-Schwinger "proper time" as a Floquet variable. The reader should bear in mind that the EEQT algorithm is explicitly nonlocal: to simulate a history of an individual system integrations over entire space (or space-time) are needed. 
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
... fractals[*]
The term quantum fractals has been used before by Casati et al. [18,19] in a different context. 
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
... place.[*]
The operators for different spin directions do not commute, but this does not contradicts Heisenberg's uncertainty relations as these deal with statistical ensembles averages, while here we are describing an individual quantum system. In fact, realizing the chaotic behavior of a quantum state vector, when several noncommuting observables are being simultaneously monitored, can help us to understand the mechanisms of statistical uncertainties. 
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
... configurations:[*]
There is no good reason why we chose these configurations - simplicity and beauty are the main reasons here. Notice that, to enable easy zooming onto the attractor, we have chosen the orientations in such a way that in each case the North Pole, with coordinates (0,0,1), of the sphere is occupied by one of the vertices. 
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
... EEQT.[*]
It is of interest that Born's probabilistic interpretation of quantum mechanics as well as the standard formula for quantum mechanical transition probabilities, can be derived in this way and there is no need of adding it as a separate postulate. 
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
... matrices.[*]
In fact, by using Cayley transform, this relation identifies the space of unitary matrices with the compactified Minkowski space. 
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.