Neurons, Cooperativity and the Role of Noise in Brain

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 using the results of quantum mechanics. We have developed a scheme to investigate this situation in this paper by taking into consideration the Schrödinger 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 commutatively and noise inside the circuit scheme. The behaviour of the circuit elements with interesting limits is 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.