In this work, our prime focus is to study the one to one correspondence
between the conduction phenomena in electrical wires with impurity and the
scattering events responsible for particle production during stochastic
inflation and reheating implemented under a closed quantum mechanical
system in early universe cosmology. In this connection, we also present a
derivation of quantum corrected version of the Fokker Planck equation
without dissipation and its fourth-order corrected analytical solution for
the probability distribution profile responsible for studying the dynamical
features of the particle creation events in the stochastic inflation and
reheating stage of the universe. It is explicitly shown from our
computation that quantum corrected Fokker Planck equation describes the
particle creation phenomena better for Dirac delta type of scatterer. In
this connection, we additionally discuss Ito, Stratonovich prescription and
the explicit role of finite temperature effective potential for solving the
probability distribution profile. Furthermore, we extend our discussion of
particle production phenomena to describe the quantum description of
randomness involved in the dynamics. We also present computation to derive
the expression for the measure of the stochastic nonlinearity (randomness
or chaos) arising in the stochastic inflation and reheating epoch of the
universe, often described by Lyapunov Exponent. Apart from that, we
quantify the quantum chaos arising in a closed system by a more strong
measure, commonly known as Spectral Form Factor using the principles of
random matrix theory (RMT). Finally, we discuss the role of out of time
order correlation function (OTOC) to describe quantum chaos in early
universe cosmology.