A quantum stochastic model for the Markovian dynamics of an open system under the nondemolition unsharp observation which is continuous in time, is given. A stochastic equation for the posterior evolution of a quantum continuously observed system is derived and the spontaneous collapse (stochastically continuous reduction of the wave packet) is described. The quantum Langevin evolution equation is solved for the case of a quasi-free Hamiltonian in the initial CCR algebra with a linear output channel, and the posterior dynamics corresponding to an initial Gaussian state is found. It is shown for an example of the posterior dynamics of a quantum oscillator that any mixed state under a complete nondemolition measurement collapses exponentially to a pure Gaussian one.
Communications in Mathematical Physics
- Pub Date:
- June 1992
- Mathematical Physics;
- Mathematics - Mathematical Physics
- 25 pages. See also related papers at http://www.maths.nott.ac.uk/personal/vpb/research/fil_con.html and http://www.maths.nott.ac.uk/personal/vpb/research/evo_equ.html