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2 results

  • 5 - Continuous Measurement: Diffusive Case

  • Andrew N. Jordan, University of Rochester, New York, Irfan A. Siddiqi, University of California, Berkeley
  • Book:
    Quantum Measurement
    Published online:
    10 May 2024
    Print publication:
    15 February 2024, pp 90-128

  • Summary

    Chapter 5 considers the case of diffusive continuous measurements, where the measurement outcomes and quantum state dynamics are analogous to a Brownian noise process. We motivate this type of measurement by considering the example of a double quantum dot system being measured by a quantum point contact. The intrinsic shot noise of the measurement naturally brings about an effective time-continuous measurement. A second example of a superconducting circuit made from Josephson junctions readout with a microwave frequency electromagnetic wave is also discussed in detail. The mathematics of quantum trajectory theory is then pedagogically built up, resulting in the stochastic Schrodinger equation, the stochastic master equation, and the stochastic path integral. We also discuss experimental data and its comparison with this theoretical formalism. These experiments allow us to peer into the inner workings of wavefunction collapse, giving an empirical handle on the many philosophical issues that arise in quantum measurement.

  • The cost of a general stochastic epidemic

  • J. Gani, D. Jerwood
  • Journal:
    Journal of Applied Probability / Volume 9 / Issue 2 / June 1972
    Published online by Cambridge University Press:
    14 July 2016, pp. 257-269
    Print publication:
    June 1972

  • This paper is concerned with the cost Cis = aWis + bTis (a, b > 0) of a general stochastic epidemic starting with i infectives and s susceptibles; Tis denotes the duration of the epidemic, and Wis the area under the infective curve. The joint Laplace-Stieltjes transform of (Wis, Tis) is studied, and a recursive equation derived for it. The duration Tis and its mean Nis are considered in some detail, as are also Wis and its mean Mis. Using the results obtained, bounds are found for the mean cost of the epidemic.