We consider a continuous measurement of a two-level system (double-dot) by
weakly coupled detector (tunnel point contact nearby). While usual treatment
leads to the gradual system decoherence due to the measurement, we show that
the knowledge of the measurement result can restore the pure wavefunction at
any time (this can be experimentally verified). The formalism allows to write a
simple Langevin equation for the random evolution of the system density matrix
which is reflected and caused by the stochastic detector output. Gradual
wavefunction ``collapse'' and quantum Zeno effect are naturally described by
the equation.Comment: 6 pages, 2 figure
