What Really Matters in Hilbert-Space Stochastic Processes

Forrest G. Hall

O. Nicrosini, A. Rimini

祐一郎 垣原

Alexander Semenovich Holevo

G. C. Ghirardi, O. Nicrosini, A. Rimini

The relationship between discontinuous and continuous stochastic processes in Hilbert space is investigated. It is shown that for any continuos process there is a parent discontinuous process, that becomes the continuous one in the proper infinite frequency limit. From the point of view of solving the quantum measurement problem, what really matters is the choice of the set of operators whose value distributions are made sharp. In particular, the key role of position sharping is emphasized.

Heinz‐Peter Breuer, Francesco Petruccione

A Hilbert space path integral for the dissipative dynamics of matter in thermal radiation fields is derived from the Hamiltonian of quantum electrodynamics. This path integral represents the conditional transition probability of a stochastic Markov process as a sum over sample trajectories in Hilbert space. The realizations of the process are piecewise deterministic paths broken by instantaneous quantum jumps. It is shown that the operators which define the possible quantum jumps form a continuous family parametrized by the polarization vector of the emitted or absorbed photons. The stochastic process is shown to be representation-independent and to be invariant with respect to space rotations. The precise physical interpretation of the stochastic process is given. In particular, the expansion of the density matrix in terms of quantum jumps is derived for finite temperatures from the Hilbert space path integral.