A deterministic state-space model of intrinsic quantum uncertainties

Ciann-Dong Yang, Kuan Chang Su, Chung Hsuan Kuo

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

For an intrinsic quantum uncertainty described by |x - x(t)| ≤ Δx and |p - p(t)|≤ Δp, with ΔxΔp ≥ h/2, we establish a state-space model governed by the quantum Hamilton equations q = f(q, p) and p == g(q, p) such that their solutions (q(t), p(t)) satisfy the given uncertainty bound and meanwhile, the statistical distributions of the trajectory sets {q(t)} and {p(t)} exactly reproduce the probability density functions ψ (x)ψ(x) and ψ (p)ψ(p) prescribed a priori. Although actual quantum trajectories are random and non-differentiable, we point out that a complex trajectory q(t) solved from the state-space model provides an uncertainty boundary encompassing an ensemble of quantum trajectories in such a way that its real part qR (t) provides the mean trajectory, while its imaginary part q1 (t) gives the radius of deviation of the quantum trajectories from the mean traj ectory.

Original languageEnglish
Title of host publication2013 10th IEEE International Conference on Control and Automation, ICCA 2013
Pages1766-1771
Number of pages6
DOIs
Publication statusPublished - 2013 Aug 26
Event2013 10th IEEE International Conference on Control and Automation, ICCA 2013 - Hangzhou, China
Duration: 2013 Jun 122013 Jun 14

Publication series

NameIEEE International Conference on Control and Automation, ICCA
ISSN (Print)1948-3449
ISSN (Electronic)1948-3457

Other

Other2013 10th IEEE International Conference on Control and Automation, ICCA 2013
CountryChina
CityHangzhou
Period13-06-1213-06-14

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Computer Science Applications
  • Control and Systems Engineering
  • Electrical and Electronic Engineering
  • Industrial and Manufacturing Engineering

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  • Cite this

    Yang, C-D., Su, K. C., & Kuo, C. H. (2013). A deterministic state-space model of intrinsic quantum uncertainties. In 2013 10th IEEE International Conference on Control and Automation, ICCA 2013 (pp. 1766-1771). [6564959] (IEEE International Conference on Control and Automation, ICCA). https://doi.org/10.1109/ICCA.2013.6564959