TY - GEN

T1 - A deterministic state-space model of intrinsic quantum uncertainties

AU - Yang, Ciann-Dong

AU - Su, Kuan Chang

AU - Kuo, Chung Hsuan

PY - 2013/8/26

Y1 - 2013/8/26

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84882358905&partnerID=8YFLogxK

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U2 - 10.1109/ICCA.2013.6564959

DO - 10.1109/ICCA.2013.6564959

M3 - Conference contribution

AN - SCOPUS:84882358905

SN - 9781467347075

T3 - IEEE International Conference on Control and Automation, ICCA

SP - 1766

EP - 1771

BT - 2013 10th IEEE International Conference on Control and Automation, ICCA 2013

T2 - 2013 10th IEEE International Conference on Control and Automation, ICCA 2013

Y2 - 12 June 2013 through 14 June 2013

ER -