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arXiv:2211.16369 · Journal of Applied Physics

Electromagnetic analogs of quantum mechanical tunneling

Jeanne M. Riga, Rebecca Seviour

Published Nov 23, 2022• 9 citations
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Abstract

In this paper, we introduce the theoretical framework underlying our proposed methodology of verification and validation (V&V) for quantum mechanical emission models using analogous macroscopic electromagnetic systems. We derive the correspondence between quantum mechanics and electromagnetism using the transfer matrix approach and describe the electromagnetic analog that will be used to anchor the atomistic quantum tunneling simulations. Finally, we illustrate this correspondence by comparing the quantum mechanical and electromagnetic systems for some simple, analytically soluble examples and outline future V&V work based on the framework presented here.

DOI
10.1063/5.0118308

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In this paper, we introduce the theoretical framework underlying our proposed methodology of verification and validation (V&V) for quantum mechanical emission models using analogous macroscopic electromagnetic systems. We derive the correspondence between quantum mechanics and electromagnetism using the transfer matrix approach and describe the electromagnetic analog that will be used to anchor the atomistic quantum tunneling simulations. Finally, we illustrate this correspondence by comparing the quantum mechanical and electromagnetic systems for some simple, analytically soluble examples and outline future V&V work based on the framework presented here.
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This research paper explores the theoretical foundations of quantum tunneling, explaining how particles can pass through potential barriers despite lacking the classical energy to do so. It develops the mathematical framework using the Schrödinger equation, derives the transmission coefficient for a rectangular potential barrier, introduces the WKB approximation for more realistic barriers, and examines key applications such as alpha decay, scanning tunneling microscopy (STM), and the Josephson effect. The paper also reviews the historical development, experimental verification, and limitations of quantum tunneling, highlighting its significance as one of the most fundamental and experimentally validated predictions of quantum mechanics.
This paper explores a novel approach to algorithm acceleration by leveraging the principles of quantum tunneling. The core idea is to map specific computational steps within classical algorithms onto simulated quantum tunneling processes. By employing probability calculations and sampling techniques, we aim to achieve significant speedups for certain algorithms. This work presents a theoretical framework and outlines a methodology for implementing this approach, focusing on the potential advantages offered by quantum mechanics in overcoming limitations inherent in classical computation. The exploration includes detailed mathematical formulations and conceptual descriptions, offering a foundation for future research and development in this area. We demonstrate the feasibility of this method through illustrative examples, highlighting the potential for transformative gains in computational efficiency. The focus remains on the theoretical aspects and algorithmic design, without requiring experimental validation. ---
This paper introduces a novel quantum computing model predicated on the principles of dynamic quantum tunneling. Traditional quantum computing models often rely on static quantum tunneling, limiting their ability to accurately simulate complex quantum systems. This research develops a dynamic quantum tunneling framework to mimic energy transfer and quantum entanglement, paving the way for exploring the potential applications of quantum computation. The model's core mechanism involves simulating energy transitions and entanglement driven by the dynamic nature of quantum tunneling, offering a more robust and flexible approach to quantum system modeling. We explore potential applications in various quantum algorithms and demonstrate the model's capabilities through illustrative examples.
In this revised and expanded edition, in addition to a comprehensible introduction to the theoretical foundations of quantum tunneling based on different methods of formulating and solving tunneling problems, different semiclassical approximations for multidimensional systems are presented. Particular attention is given to the tunneling of composite systems, with examples taken from molecular tunneling and also from nuclear reactions. The interesting and puzzling features of tunneling times are given extensive coverage, and the possibility of measurement of these times with quantum clocks are critically examined. In addition by considering the analogy between evanescent waves in waveguides and in quantum tunneling, the times related to electromagnetic wave propagation have been used to explain certain aspects of quantum tunneling times. These topics are treated in both non-relativistic as well as relativistic regimes. Finally, a large number of examples of tunneling in atomic, molecular, condensed matter and nuclear physics are presented and solved.
Analysis of the interaction of the electromagnetic field and matter is a topical area of research in modern physics. The goal of this paper is to move from mathematical postulates and formalisms of quantum mechanics to equations that include macroscopic variables. In this case, the macroscopic observables are determined by the mean values of the operator corresponding to the observable value, and the mean value is deter-mined by the density matrix. Then the equations are written only through the mean values, by substituting equivalent expressions for the density matrix. As a result, we come to a system of equations expressed in terms of such macroscopic variables as polarization and electromagnetic field. In the semi-classical approach, when the electromagnetic field is not quantized, it is necessary to add the Maxwell's equations of the electromagnetic field to the equations for the mean values. This forms a self-consistent system of equations.