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Quantum Stochastic Calculus & Differential Equations
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Quantum stochastic calculus is a differential
calculus for the bewildering variety of noises in quantum world. The first quantum
stochastic calculus was introduced by R. L. Hudson and K. R. Parthasarathy
for Bose noises. Roughly speaking, this is a sort of Ito calculus for the
most fundamental noises in quantum theory. The study of stochastic calculi
for several types of noises (Bose, Fermi, free, Boolean, monotonic, …) is
still a hot topic. Quantum stochastic differential equations are
stochastic differential equations for operator processes driven by quantum
noises. They are applied in the study of the evolution of quantum open
systems, in the theory of quantum continual measurements, in the study of
quantum Markov processes and dilations of quantum Markov semigroups [Fa03a], [FW03], [Gr00], [Gr01], [Gr05a], [Gr05b]. |