After substitution we find the voltage between the two sides M’ and M to be:
(104) VH= RHJ-Bh
Often this transverse voltage is measured at fixed current and the Hall resistance
recorded. It can easily be seen that this Hall resistance increases linearly with
magnetic field.
The Quantum Hall effect (QHE) is phenomenon occurring at low temperatures
(millikelvin range) and when strong magnetic fields (1-15 tesla) are applied upon
semiconductors. In the absence of magnetic field the density of states in 2D is
constant as a function of energy, but in field the available states clump into
Landau levels separated by the cyclotron energy, with regions of energy between
the Landau levels where there are no allowed states. As the magnetic field is
swept the Landau levels move relative to the Fermi energy. When the Fermi
energy lies in a gap between Landau levels electrons cannot move to new states
and so there is no scattering. Thus the transport is dissipationless and the
resistance falls to zero (Leadley, 1997).
It was supposed (Porter, 2003) that in neurons there is analogous situation
where the local magnetic field produced by the neuronal currents acts upon the
microtubules and that anyons could be formed via QHE. However the idea that
the local magnetic field generated by the neuronal cytoplasmatic currents inputs
information to the brain microtubules via classical Hall effect or QHE and that this
process is linked to our conscious experience is disproved by the calculations. It
is clear that local magnetic flux density varying from zero to 10-7 T makes the
idea untenable, because the brain is exposed to stronger magnetic fields and no
direct effects on consciousness are registered. It is interesting that strong
magnetic fields reaching flux density of 1T are used in the fMRI imaging. The
visualization of the brain with fMRI however has no impact on consciousness.
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