Nondemolition observation of a free quantum particle.

@article{Belavkin1992NondemolitionOO,
  title={Nondemolition observation of a free quantum particle.},
  author={Belavkin and Staszewski},
  journal={Physical review. A, Atomic, molecular, and optical physics},
  year={1992},
  volume={45 3},
  pages={
          1347-1356
        }
}
  • Belavkin, Staszewski
  • Published 1 February 1992
  • Physics, Medicine
  • Physical review. A, Atomic, molecular, and optical physics
A stochastic model of a continuous nondemolition observation of a free quantum Brownian motion is presented. The nonlinear stochastic wave equation describing the posterior dynamics of the observed quantum system is solved in a Gaussian case for a free particle of mass m > 0. It is shown that the dispersion of the wave packet does not increase to in…nity like for the free unobserved particle but tends to the …nite limit 1 = (~=2 m) where is the accuracy coe¢ cient of an indirect nondemolition… 

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References

SHOWING 1-10 OF 46 REFERENCES
A posterior Schrödinger equation for continuous nondemolition measurement
A continuous model for a nondemolition observation of an atom is given. An equation for the corresponding instrument is found and a stochastic dissipative Schrodinger equation for the unnormalized
Quantum stochastic calculus and quantum nonlinear filtering
A *-algebraic indefinite structure of quantum stochastic (QS) calculus is introduced and a continuity property of generalized nonadapted QS integrals is proved under the natural integrability
in Modeling and Control of Systems in Engineering
  • Quantum Mechanics, Economics, and Biosciences, ed. by A. Blaquiere
  • 1989
Commun
  • Math. Phys. 93, 301
  • 1984
Phys
  • Rev. A 31, 3761
  • 1985
Commun. Math. Phys
  • Commun. Math. Phys
  • 1984
Quantum theory of open systems
Commun
  • Math. Phys. 17, 239
  • 1970
A continuous diffusion observation and posterior quantum dynamics
  • submitted to J. of Phys. A, Preprint N Phys. Dep. University of Roma “La Sapienza”
  • 1989
...
1
2
3
4
5
...