dorsal/arxiv
View SchemaExactly solvable quantum state reduction models with time-dependent coupling
| Authors | Dorje C. Brody, Irene C. Constantinou, James D. C. Dear, Lane P. Hughston |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0511046 |
| URL | https://arxiv.org/abs/quant-ph/0511046 |
| DOI | 10.1088/0305-4470/39/35/006 |
| Journal | Journal of Physics A39, 11029-11051 (2006) |
Abstract
A closed-form solution to the energy-based stochastic Schrodinger 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 which has the distribution P(H=E_i) = pi_i, where pi_i is the transition probability from the initial state to the Luders state with energy E_i; and (ii) an independent P-Brownian motion, where P is the physical probability measure associated with the dynamics of the reduction process. 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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"abstract": "A closed-form solution to the energy-based stochastic Schrodinger equation\nwith a time-dependent coupling is obtained. The solution is algebraic in\ncharacter, and is expressed directly in terms of independent random data. The\ndata consist of (i) a random variable H which has the distribution P(H=E_i) =\npi_i, where pi_i is the transition probability from the initial state to the\nLuders state with energy E_i; and (ii) an independent P-Brownian motion, where\nP is the physical probability measure associated with the dynamics of the\nreduction process. When the coupling is time-independent, it is known that\nstate reduction occurs asymptotically--that is to say, over an infinite time\nhorizon. In the case of a time-dependent coupling, we show that if the\nmagnitude of the coupling decreases sufficiently rapidly, then the energy\nvariance will be reduced under the dynamics, but the state need not reach an\nenergy eigenstate. This situation corresponds to the case of a ``partial\u0027\u0027 or\n``incomplete\u0027\u0027 measurement of the energy. We also construct an example of a\nmodel where the opposite situation prevails, in which complete state reduction\nis achieved after the passage of a finite period of time.",
"arxiv_id": "quant-ph/0511046",
"authors": [
"Dorje C. Brody",
"Irene C. Constantinou",
"James D. C. Dear",
"Lane P. Hughston"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/39/35/006",
"journal_ref": "Journal of Physics A39, 11029-11051 (2006)",
"title": "Exactly solvable quantum state reduction models with time-dependent coupling",
"url": "https://arxiv.org/abs/quant-ph/0511046"
},
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