In Section 3 we have given just a few examples of simple models based on EEQT; more can
be found elsewhere. In [49] quantum Zeno effect is discussed within the framework
of EEQT. A quantum system is "observed" - that is coupled in an appropriate way - to a classical system. The intensity of observation is mathematically modelled by the
value of the coupling constant. We find that indeed, with the increase of the
coupling constant, the Hamiltonian part of the evolution effectively stops.
In [50] we examined the EPR paradox within EEQT, with the result that EPR
phenomenon alone can not be used for a superluminal signalling.
In [51, 52] we discussed the problem of whether the quantum state
itself can be determined by a measurement (as defined within EEQT)
In [53] we
applied EEQT to a SQUID-tank model, where a classical system has as its
manifold of pure states, the phase space of a radio-frquency oscillator. It is
interesting that in this case classical events are characterized by discontinuous
changes of velocity, while the position is changing in a continuous way. The back
action of the quantum circuit on the classical one leads to new terms in
semi-phenomenological evolution equation that, in principle, can be tested
experimentally.
Some mathematical problems arising in our models have been discussed
by Olkiewicz in [39], while in [55] we have examined in detail
the relevant probabilistic aspects of the piecewise deterministic Markov process
governing the behaviour of individual systems.
Quantum time-of-arival observables,
its non-linearity and dependence on the effectiveness of the detectors have been
discussed in [19], while in [17] we have shown that Born's
probabilistic interpretation of quantum wave function follows, in a special limit,
from our detector model. An entropy generating fuzzy clock is discussed in
[54]
Algorithm for cloud-chamber particle tracks formation,
resulting from EEQT have been developed in [5, 6].
Some projects we have started
are still in a state of incompletion for lack of time. One such project is deriving EEQT from quantum electrodynamics, where the classical parameter enters naturally as the index
of inequivalent non-Fock infrared representations. We believe that using
infinite tensor product representations of quantum systems with an infinite number
of degrees of freedom, we will arrive naturally at our 
operators
relating to Hilbert spaces of inequivalent representations of CCRCAR.
We also
started, but did not finish, modelling of a coupling of a quantum particle to
a classical (Newton) gravitational potential. The general idea is simple: a quantum particle,
having a mass, must back-react on the gravitational potential. The point is, however,
to model it, in a natural and possibly unique way, via Louville equation of the type demanded by EEQT. This would be only a first step towards a more ambitious project: coupling
of Quantum Electrodynamics to classical (relativistic) gravity, with - how else - a hope that
the back-action will smooth out divergencies of QED.
Some of the future project are
rather straightforward - here belongs the further study of chaos induced by quantum
measurement. We encourage all interested readers to contact us - we will try to help
as much as we can.
Acknowledgements
One of us (A.J) would like to thank L.K-J for invaluable help.