Vsevolod SakbaevDynamics of quantum states generated by the nonlinear Schrodinger equationAbstract
We consider the transformation of the initial data space for the Schrodinger
equation. We study the phenomenon of global existence of a solution of the Cauchy
problem the phenomenon of rise of a solution gradient blow up during a finite time.
We define a solution extension through the moment of a gradient blow up using
the oneparameter family of probability measures on the initial data space of the
Cauchy problem. We show that this extension describes the destruction of a solution
as the destruction of a pure quantum state and the transition from the set of pure
quantum states
into the set of mixed quantum states.
