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IEEE International Symposium on Circuits and Systems proceedings

Probabilistic particle modeling of quantum wave propagation with excitation and refraction

Yuma Kawabata, Hisato Fujisaka, Takeshi Kamio

Published Jun 1, 2014• 1 citation
Publisher

Abstract

Quantum particles possess both wave and particle natures. When quantum effect devices exploiting the wave nature and the devices described from the view point of particle nature coexist in a system, the following advantages are gained by representing former devices in the same way as we describe the latter devices: First, it is not necessary to compute probability distribution from wave functions and sample device states in accordance with the probability distribution. Secondly, the particle models of the devices are suitable models for conventional circuit simulators. In this paper, simple particle models of an electromagnetic wave detector and an electron lens are constructed by applying Nelson's stochastic quantization theory. The device characteristics obtained from the wave functions and from the behavior of the particle models were almost equal.

DOI
10.1109/iscas.2014.6865175

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Quantum particles possess both wave and particle natures. When quantum effect devices exploiting the wave nature and the devices described from the view point of particle nature coexist in a system, the following advantages are gained by representing former devices in the same way as we describe the latter devices: First, it is not necessary to compute probability distribution from wave functions and sample device states in accordance with the probability distribution. Secondly, the particle models of the devices are suitable models for conventional circuit simulators. In this paper, simple particle models of an electromagnetic wave detector and an electron lens are constructed by applying Nelson's stochastic quantization theory. The device characteristics obtained from the wave functions and from the behavior of the particle models were almost equal.
Quantum particles possess both wave and particle natures. When quantum effect devices exploiting the wave nature and the devices described from the view point of particle nature coexist in a system, the following advantages are gained by representing former devices in the same way as we describe the latter devices: First, it is not necessary to compute probability distribution from wave functions and sample device states in accordance with the probability distribution. Secondly, the particle models of the devices are suitable models for conventional circuit simulators. In this paper, simple particle models of two quantum systems operating as wave filters are constructed by applying Nelson's stochastic quantization theory. The filter characteristics obtained from the wave functions and from the behavior of the particle models were almost equal.
This paper presents a method of computing sample trajectories of particle models of electrons on symmetric electron-wave stub-filters. The time-independent Schrödinger equation describing the electron-wave filters is transformed to a system of linear algebraic equations. The Fourier series expansion transforms the eigenvalues of the system to continuous and differentiable eigenfunctions. A electron wave packet is constructed from the obtained smooth eigenfunctions and a nonlinear stochastic ordinary differential equation (NSODE) which governs the behavior of the electron particle model is established by applying the stochastic quantization to the wave packet. Sample trajectories of the particles are computed by integrating the NSODE. Numerical experiments have shown that the statistical behavior of the particles is almost equal to that of the wave packets.
The wave-particle duality is one of the most mysterious phenomena of the quantum theory, in this paper first it's studied the rise of the wave properties of matter from the theory of stochastic electrodynamics (SED), in which de Broglie's idea of a guiding wave that follows the particle and determine its trajectory is taken back. In the frame of the theory (SED) this wave is of electromagnetic character and is a traveling wave that propagates within the zero point field (ZPF) which according the SED is a classic electromagnetic field that permeates all universe. The wave rise from the interaction between the background field and the particle that moves with certain velocity. Then, I expose the results of numerical simulations in which the behavior of the ZPF in a two slit diffraction experiment is calculated and a series of macroscopic experiments that shows behaviors similar to the ones described by the SED. Both, simulations and experiments give us a better physical understanding of the guiding wave and of the wave properties of quantum particles
Electrons possess both wave and particle natures. In this paper, we represent an electron on multi-stage coupled electron waveguides both by a wave function and by a probabilistic particle. We show first that time evolution of the wave function can be obtained by the combined use of the tight-binding method and two-port circuit theory. The wave function is in variable-separable form when wave propagation on the coupled electron waveguides is single mode. We present secondly that the variable separation simplifies the general Langevin equation describing behavior of the probabilistic particle. According to these two schemes, wave functions and sample particle trajectories on single and two-stage coupled electron waveguides were exemplified.
This paper proposes a probabilistic particle model of single-electrons on graphene. The behavior of a single-electron on graphene is described approximately by the massless Dirac equation. The electron is non-relativistic and given pseudo-spin. The Dirac equation originally describes the motion of a relativistic quantum particle with actual spin. Then, it has seemed difficult that the Nelson's stochastic quantization theory could build a particle model of the electron on graphene since the theory can deal with only non-relativistic quantum particles with spin not being taken into account. In this paper, Nelson's theory is interpreted by using probability density function and probability density current so that it can build a particle model of a single-electron on graphene. Single-electrons on a graphene nano-ribbon and on a graphene sheet in constant magnetic field were modeled as probabilistic particles. The models were described by nonlinear stochastic ordinary differential equations. It has been numerically confirmed that probability distributions of the electron models coincide with distributions derived from the wave functions.
This paper presents a realistic model that describes radiation-matter interactions. This is achieved by a generalization of first quantization, where the Maxwell equations are interpreted as the electromagnetic component of the Schroedinger equation. This picture is complemented by the consideration of electrons and photons as real particles in three-dimensional space, following guiding conditions derived from the particle-wave-functions to which they are associated. The guiding condition for the electron is taken from Bohmian mechanics, while the photon velocity is defined as the ratio between the Poynting vector and the electromagnetic energy density. The case of many particles is considered, taking into account their statistical properties. The formalism is applied to a two level system, providing a satisfactory description for spontaneous emission, Lamb shift, scattering, absorption, dispersion, resonance fluorescence and vacuum fields. This model adequately describes quantum jumps by the entanglement between the photon and the atomic system and it will prove to be very useful in the simulation of quantum devices for quantum computers and quantum information systems. A possible relativistic generalization is presented, together with its relationship to QED.