Finite-time stochastic reduction models
Dorje C. Brody, Lane P. Hughston
Abstract
A new energy-based stochastic extension of the Schrodinger equation for which the wave function collapses after the passage of a finite amount of time is proposed. An exact closed-form solution to the dynamical equation, valid for all finite-dimensional quantum systems, is presented and used to verify explicitly that reduction of the state vector to an energy eigenstate occurs. A time-change technique is introduced to construct a `clock' variable that relates the asymptotic and the finite-time collapse models by means of a nonlinear transformation.
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