An Introduction to Quantum Stochastic Calculus
K.R. Parthasarathy, "An Introduction to Quantum Stochastic Calculus "
English | ISBN: 3034805659 | 2012 | 301 pages | PDF | 4 MB
English | ISBN: 3034805659 | 2012 | 301 pages | PDF | 4 MB
An Introduction to Quantum Stochastic Calculus aims to deepen our understanding of the dynamics of systems subject to the laws of chance both from the classical and the quantum points of view and stimulate further research in their unification. This is probably the first systematic attempt to weave classical probability theory into the quantum framework and provides a wealth of interesting features:
The origin of Ito’s correction formulae for Brownian motion and the Poisson process can be traced to commutation relations or, equivalently, the uncertainty principle.
Quantum stochastic integration enables the possibility of seeing new relationships between fermion and boson fields.
Many quantum dynamical semigroups as well as classical Markov semigroups are realised through unitary operator evolutions.
The text is almost self-contained and requires only an elementary knowledge of operator theory and probability theory at the graduate level.