Abstract
When the system gets coupled to the bath, the system dynamics gets altered by this system-bath interaction. In quantum theory, there are basically two kinds of noise introduced into the system dynamics from the bath, these are Brownian motion and Poisson processes. Classical Brownian motion can be described using creation and annihilation processes from the bath while the Poisson process can be described using the conservation process from the bath. Both quantum Brownian motion (i.e. superpositions of creation and annihilation processes) and quantum Poisson processes (i.e. the conservation process) in different states of the bath have statistics same as that of classical Brownian motion and the classical Poisson process and both of these quantum processes satisfy quantum Ito’s formula which specializes to classical Ito’s formula for Brownian motion and Poisson process.
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