Codice QDD 3 Titolo Some stochastic differential equations in quantum optics and measurement theory: the case of counting processes Data 2006-10-02 Autore/i Barchielli, A. Link Download full text Pubblicato In L. Diosi, B. Lukacs (eds.), Stochastic Evolution of Quantum States in Open Systems and in Measurement (Plenum Press, New York, 1997) pp. 243-252 Abstract Stochastic differential equations of jump type are used in the theory of measurements continuous in time in quantum mechanics and have a concrete application in describing direct detection in quantum optics (counting of photons). In the paper the connections are explained among various types of stochastic equations: linear for Hilbert-space unnormalized vectors, non-linear for Hilbert space normalized vectors, linear for trace-class operators, non-linear for density matrices. These equations allow to construct a posteriori states and probabilities for the counting process describing the direct detection. Relations with master equations and a priori states are also explained. Two concrete applications related to a two-level atom are presented.