Abstract:
Quantum dynamics of particles in time-dependent random potential field with
Gaussian distribution of realisations probabilities in unbounded space is studied.
A constant absorption and monoenergetic extended source of particles are introduced
into the Schrödinger equation. The moment of switching-on the source is shifted to the
infinite past. Assuming that the fluctuations of the random potential are stationary, the
existence of stationary limit for the density matrix averaged over potential realisations
is proved. It is checked that in the weak interaction approximation, when additionally
the absorption length and spatial scale of the source of particles are of the same order
as the free run length, the limit mentioned satisfies the usual stationary equation of
radiation transport in scattering medium.
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