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Noise from Quantum Field Theory

**Bei-Lok Hu**
We discuss how noise as classical stochastic source can be defined
precisely from quantum field theory via coarse graining. For open
systems where the system and environment are cleary and ab initio
separated, one can use the Feynman-Vernon influcence functional to
capture the effect of the coarse-grained environment on the system.
We show the physical meaning of the noise and dissipation kernels
and derive expressions for the noise correlators for different
sample field theories, and the functional stochastic equations
such as the master, Langevin and Fokker-Planck equations.
For a close system such as molecular gas, we start with the
Schwinger-Dyson equation but view them in the light of a BBGKY
hierarchy. We point out that in realistic physical situations
because of the limitation in the measurement accuracy, usually
it is the low-order correlation functions which partake in
defining the physical system, which we call effectively open
systems. We discuss how truncation and factorization without causal
initial condition give rise to time-reversal invariant equations of
motion of the Vlasov type, where there is no noise and (Landau) `damping'
is due to special choices of initial conditions and representation.
When causal factorizable (`slaving') conditions such as molecular
chaos assumption is imposed, dissipation in the Boltzmann
equation appears. We point out that there should also be a noise
term accompanying this, arising from the coarse-grained information
of the higher order correlations. We derive explicit expressions
for such correlation noise via the CTP nPI effective action
and arrive at a Boltzmann-Langevin equation. Finally we show
under special conditions of near-equilibrium how one can use
fluctuation theory in linear response to derive noise in both
the open and effectively open systems.