The kink cannot decay even if it is perturbed, this is guaranteed by the winding
number. In fact, the sine-Gordon model is peculiar in that a kink-anti-kink
configuration does not decay to the vacuum either, in short, if a kink is
superimposed with an anti-kink at a different position they will move towards
each other but they will not annihilate, they will pass through each other. In fact,
there is an oscillating solution known as a breather. This solution has winding
number zero but is stable, at least to small perturbations. Kink-anti-kink
annihilation is allowed by the conservation of winding number and occurs in
similar models. It does not occur in the sine-Gordon model because the
sine-Gordon model is integrable.
In the quantized sine-Gordon model the field quanta behave like particles in the
normal way, what isn't normal is that the solitons also behave like particles. This
means there are two different particle spectra: a soliton spectrum and a spectrum
arising out of quantization (Houghton, 2000).
The water molecule superradiance (Jibu et al., 1996; Jibu & Yasue, 1997) could
be part of the tubulin C-termini conformational soliton picture if the
conformational states of the tubulin tails are coupled with the dynamics of their
hydratation shells. In contrast with the intra-cavital soliton propagation (Abdalla et
al., 2001) the C-termini - water molecule solitons are formed on the microtubular
surface and could have direct intraneuronal effects such as control of MAP
binding and motor protein associated cargo trafficking.
The flexible tubulin tails could explain the electric sensitivity and could account
for direct translation of the EPSP and IPSPs into quantum states. The model is
attractive because the proposed microtubular solitons could have direct effect
upon the presynaptic scaffold protein function and exocytosis as supposed by
Georgiev (2003) and because the tubulin tails are prone to extensive biochemical
modification - providing link to GPCRs intraneuronal signalling!
75
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