arXiv subjects

Ciann-Dong Yang

Publications and source records attributed to Ciann-Dong Yang.

5 recordsLinked to original sources

arXiv2026

An Ontological Interpretation of Photon Wave-Particle Duality via Complex-Space Trajectories

Wave particle duality remains a central interpretational challenge in quantum theory. In this work, we develop a trajectory-based description of photon dynamics formulated in an extended complex space within the relativistic quantum Hamilton Jacobi framework. In this approach, photon motion is represented by complex trajectories whose real projections describe propagation, while imaginary components encode oscillatory structure. We show that momentum eigenstates correspond to straight line trajectories with uniform propagation at the speed of light, whereas superposition states lead to nontrivial quantum potentials and oscillatory motion in the complex plane. Extending the analysis to complex two dimensional space reveals richer dynamical behavior, including propagating wave like trajectories and standing wave like patterns in real projections. Energy momentum consistency is verified through an internal coherence analysis based on projected standing wave wavelengths. Rather than introducing new dynamical laws or additional physical dimensions, the complex space is employed as an interpretational framework that renders wave like and particle like aspects as complementary projections of a single underlying motion. The results suggest a unified geometric perspective on wave particle duality, while remaining fully compatible with standard quantum mechanics.

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arXiv2024

Generation of Maximally Entangled States by Lyapunov Control Based on Entanglement Measure

Maximally entangled states (MES) are highly valued in quantum information processing. In quantum control, the creation of MES is typically treated as a state transfer problem with a predefined MES as the target. However, this approach is limited by the requirement to predetermine the MES structure. This paper introduces an improved quantum Lyapunov control approach that relies on the quantum entanglement measure to construct the Lyapunov function, instead of using the distance between quantum states. This strategy enables the preparation of any MES, regardless of whether its structure is known beforehand, using a single control scheme. The proposed entanglement control technique is unaffected by the number of entangled subsystems since it targets the entanglement measure as a scalar. Initially applied to bipartite pure states, this method demonstrates its capability to generate Bell states and their equivalents. Subsequent applications to bipartite mixed states and multipartite systems illustrate that the technique can produce MES with unspecified structures.

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arXiv2022

Quantum Chaos Control by Complex Trajectories

In recent years, analysis and control of quantum chaos are increasingly important, but the lack of the concept of trajectory makes it impossible to analyze quantum chaos by the methods used in classical chaos. This research aims to connect Newton's world to the quantum world by the complex mechanics so that quantum chaos can be analyzed and controlled by the complex-extended Newtonian mechanics. Through the bridge of complex mechanics, in this article, we model quantum motions for 2D charged anisotropic harmonic oscillator by complex-valued dynamic equations, based on which quantum chaos can be analyzed by using well-known methods used in classical chaos. With the established quantum dynamic model, we then apply the sliding-mode control method to control the chaotic quantum behavior of the considered quantum system. The simulation results show that chaotic motions can be changed into periodic motions by the proposed chaos control and meanwhile, chaos synchronization can be achieved in the presence of variations of initial conditions. Several signatures of chaos are introduced here to justify the chaos of the periodicity process under the sliding-mode control law.

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arXiv2021

Extending Quantum Probability from Real Axis to Complex Plane

Probability is an important question in the ontological interpretation of quantum mechanics. It has been discussed in some trajectory interpretations such as Bohmian mechanics and stochastic mechanics. New questions arise when the probability domain extends to the complex space, including the generation of complex trajectory, the definition of the complex probability, and the relation of the complex probability to the quantum probability. The complex treatment proposed in this article applies the optimal quantum guidance law to derive the stochastic differential equation governing a particle random motion in the complex plane. The probability distribution of the particle position over the complex plane is formed by an ensemble of the complex quantum random trajectories, which are solved from the complex stochastic differential equation. Meanwhile, this probability distribution is verified by the solution of the complex Fokker Planck equation. It is shown that quantum probability and classical probability can be integrated under the framework of complex probability, such that they can both be derived from the same probability distribution by different statistical ways of collecting spatial points.

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arXiv2020

Trajectory Interpretation of Correspondence Principle: Solution of Nodal Issue

The correspondence principle states that the quantum system will approach to the classical system in high quantum numbers. Indeed, the average of the probability density distribution reflects a classical-like distribution. However, the likelihood of finding a particle at node of the wave function is zero. This condition is recognized as the nodal issue. In this paper, we propose a solution for this issue by means of complex quantum random trajectories which are obtained by solving the stochastic differential equation under the optimal guidance law. It turns out that point set A which is collected by the intersections of complex random trajectories and the real axis can present the quantum mechanical compatible distribution of the quantum harmonic oscillator system. Meanwhile, the projections of complex quantum random trajectories on the real axis form point set B that gives a distribution without appearance of nodes. Moreover, point set B can represent the classical compatible distribution in high quantum numbers. Furthermore, the statistical distribution of point set B is verified by the solution of the Fokker-Planck equation.

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