Exactly Solvable Quantum State Reduction Models with Time-Dependent Coupling

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Brody, D C; Constantinou, I C; Dear, J D C and Hughston, L P. 2006. Exactly Solvable Quantum State Reduction Models with Time-Dependent Coupling. Journal of Physics A: Mathematical and General, 39(35), pp. 11029-11051. ISSN 0305-4470 [Article]

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Official URL: https://doi.org/10.1088/0305-4470/39/35/006

Abstract or Description

A closed-form solution to the energy-based stochastic Schrödinger equation with a time-dependent coupling is obtained. The solution is algebraic in character, and is expressed directly in terms of independent random data. The data consist of (i) a random variable H and (ii) an independent Brownian motion. When the coupling is time independent, it is known that state reduction occurs asymptotically—that is to say, over an infinite time horizon. In the case of a time-dependent coupling, we show that if the magnitude of the coupling decreases sufficiently rapidly, then the energy variance will be reduced under the dynamics, but the state need not reach an energy eigenstate. This situation corresponds to the case of a 'partial' or 'incomplete' measurement of the energy. We also construct an example of a model where the opposite situation prevails, in which complete state reduction is achieved after the passage of a finite period of time.

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https://doi.org/10.1088/0305-4470/39/35/006