  In view of some recent results in case of the dopaminergic neurons exhibiting
long range correlations in VTA of the limbic brain we are interested to find
out whether any stochastic nonlinear response may be reproducible in the nano
scales usimg the results of quantum mechanics. We have developed a scheme to
investigate this situation in this paper by taking into consideration the
Schrodinger equation (SE) in an arbitrary manifold with a metric, which is in
some sense a special case of the heat kernel equation. The special case of this
heat kernel equation is the diffusion equation, which may reproduce some key
phenomena of the neural activities. We make a dual equivalent circuit model of
SE and incorporate non commutativity and noise inside the circuit scheme. The
behaviour of the circuit elements with interesting limits are investigated. The
most bizarre part is the long range response of the model by dint of the
Central Limit Theorem, which is responsible for coherent behaviour of a large
assembly of neurons.
