Chapters authored
A Quantum Trajectory Interpretation of Magnetic Resistance in Quantum Dots
For a complete description of the electronic motion in a quantum dot, we need a method that can describe not only the trajectory behavior of the electron but also its probabilistic wave behavior. Quantum Hamilton mechanics, which possesses the desired ability of manifesting the wave-particle duality of electrons moving in a quantum dot, is introduced in this chapter to recover the quantum-mechanical meanings of the classical terms such as backscattering and commensurability and to give a quantum-mechanical interpretation of the observed oscillation in the magneto-resistance curve. Solutions of quantum Hamilton equations reveal the existence of electronic standing waves in a quantum dot, whose occurrence is found to be accompanied by a jump in the electronic resistance. The comparison with the experimental data shows that the predicted locations of the resistance jump match closely with the peaks of the measured magneto-resistance.
Part of the book: Nonmagnetic and Magnetic Quantum Dots
Complex Space Nature of the Quantum World: Return Causality to Quantum Mechanics
As one chapter, we about to begin a journey with exploring the limitation of the causality that rules the whole universe. Quantum mechanics is established on the basis of the phenomenology and the lack of ontology builds the wall which blocks the causality. It is very difficult to reconcile the probability and the causality in such a platform. A higher dimension consideration may leverage this dilemma by expanding the vision. Information may seem to be discontinuous or even so weird if only be viewed from a part of the degree of freedoms. Based on this premise, we reexamined the microscopic world within a complex space. Significantly, some knowledge beyond the empirical findings is revealed and paves the way for a more detailed exploration of the quantum world. The random quantum motion is essential for atomic particle and exhibits a wave-related property with a bulk of trajectories. It seems we can break down the wall which forbids the causality entering the quantum kingdom and connect quantum mechanics with classical mechanics. The causality returns to the quantum world without any assumption in terms of the quantum random motion under the optimal guidance law in complex space. Thereby hangs a tale, we briefly introduce this new formulation from the fundamental theoretical description to the practical technology applications.
Part of the book: Quantum Mechanics