Investigation Of Time Problem In Quantum Devices And Evanescent Fields' Physical Properties

Time in quantum mechanics and the physical properties of evanescent fields are two important and crossrelated issues in nanoelectronics, the former is concerned in how to understand and control the limiting speed of quantum devices' operation and response, while the latter is related to how to apply the physical properties of evanescent fields in nanotechnological manufactures and in the designs of quantum devices with novel function. Moreover, tunneling time in nanostructures, as a quantum-mechanical time problem, can be studied via the propagation experiment of evanescent fields. However, on the one hand, time in quantum mechanics is a parameter rather than a dynamical operator, such that it cannot represent an observable and has been a conundrum since the advent of quantum mechanics; on the other hand, the propagation of evanescent fields is due to a purely quantum-mechanical effect without any correspondence in classical mechanics, and it is difficult to define the propagation velocity of evanescent fields. As a result, in spite of the fact that both theoretical and experimental studies have obtained the same conclusion that evanescent waves propagate superluminally, recently there are many disputes about the physical meaning and validity of such superluminal phenomenon. Seeing that these issues have both theoretical and applied interests, this doctoral dissertation will focus on them, and contains several aspects as follows:1. General rules about how to introduce time operator and how to calculate the quantum-mechanical average of time are given; the theory of time-of-arrival is extended from nonrelativistic to relativistic quantum-mechanical case; a formal theory of time operator is presented via a dual theory of the traditional mechanics; in the sense of second quantization, the space-time position operator in relativistic quantum theory is studied.2. Based on the extrapolated phase time theory, we show that the group velocities of modified Bessel waves are superluminal; an alternative theory to describe photon tunneling is developed, and at the second-quantized level, a rigorous argument for the superluminality of evanescent modes is presented; a quantum Lorentz transformation between classical and quantum reference frames is studied, from which the conclusion that a particle can propagate over a space-like interval is obtained, which is due to the Heisenberg's uncertainty relation and in agreement with quantum field theory. Moreover, the first-quantized theory of photons is established, and a quantum-mechanical equation of photons inside a waveguide is presented, these are important for us to study photons' locality in three dimensional spaces.3. An equivalent description for electromagnetic waveguides is given by the image method, in particular, evanescent fields inside an undersized waveguide are described as near fields, such that evanescent fields are qualitatively studied from the point of view of virtual photons and phase transition; relativistic spintronics is developed by proposing that electron's spin states are manipulated and controlled via evanescent fields; a possible quantum bit from the splitting of energy levels induced by photon tunneling is presented.