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WORLD SCIENTIFIC eBooks

Quantum Mechanical Tunnelling and Its Applications

D Roy

Published Dec 1, 1986• 68 citations
Publisher

Abstract

This book presents a new approach to quantum mechanical tunnelling and its applications to various fields of physics. The conventional concepts of this phenomenon, which are based on a time-dependent or time-independent approach, are inadequate in providing explanations for 1) the limit of resolution of field-emission microscope, 2) the Esaki-Integral representation the tunnelling I-V characteristics of tunnel diodes, 3) the Josephson effect, 4) the tunnelling time, etc. The new theory presented here not only provides adequate explanation for all the above-mentioned effects but also gives an accurate expression for tunnelling current density which predicts results closer to the experimentally observed values. The new presentation also provides a more comprehensive description of the results obtained using older treatment.

DOI
10.1142/0217

Related papers

A Quantum Measurement Approach to Tunnelling

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This book presents a new approach to analyze quantum mechanical tunnelling of particles across potential barriers. The conventional concepts of this phenomenon, which are based on a time-in-dependent or a time-dependent perturbation approach are inadequate in furnishing explanations to a number of effects, e.g. (i) the limit of resolution of a field emission macroscope (FEM), (ii) Esaki integral, representing the I-V characteristics of solid-state junctions, (iii) Josephson effect, (iv) tunnelling time, (v) tunnelling current density etc. The new analysis presented here not only provides adequate explanations to all the above mentioned effects but also furnishes an appropriate expression for the tunnelling current density which yields results closer to experimentally observed values

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It has been observed experimentally that the tunneling current across pn tunnel diodes decreases when a magnetic field is applied to it at liquid helium temperatures. Such a decrease is noticed both for longitudinal and transverse applications of magnetic fields relative to the direction of the current flow. Classically, tunneling of particles is regarded to propagate with the speed of light. Therefore, on the basis of the postulates of special theory of relativity tunneling of a potential barrier by particles should be independent of the state of motion of an observer relative to the tunneling system. In other words, the tunneling rate should remain unaffected of the motion of the observer. Therefore, to explain tunneling of particles in a crossed configuration of electric and magnetic fields, a suitable frame of reference for an observer can always be chosen so that the magnetic flux density observed from the new frame reduces to zero. The tunneling along the reduced electric field intensity may then be studied on established laws. The resultant electric field intensity in such a case becomes a function of the original magnetic flux density and it shows a steady decline with the increase in the magnitude of the latter. Therefore, a reduction in the tunneling probability and the tunneling current density is expected when the magnetic flux density normal to the current flow is increased. Finally, at a particular magnetic field intensity the tunneling current density drops to zero. It then turns out that the cyclotron frequency corresponding to this cut off magnetic field is proportional to the reciprocal of the tunneling time derived on the ideas of quantum measurement and observations. Therefore, by recording the normal magnetic flux density required to cut off the tunneling current across pn tunnel diodes immersed in a liquid helium bath, it may be possible to make an estimate of the tunneling time across a potential barrier. The working expression of the calculation of the tunneling time also follows independently of the relativistic treatment outlined above. The identity of results derived on the two approaches seems to justify the fact that the speed Of tunneling is really high enough so that the relativistic treatments may be applied to it as an approximation although tunneling may not propagate with the exact speed of light.

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•Feb 5, 2026•0 citations
This book presents a new approach to quantum mechanical tunnelling and its applications to various fields of physics. The conventional concepts of this phenomenon, which are based on a time-dependent or time-independent approach, are inadequate in providing explanations for 1) the limit of resolution of field-emission microscope, 2) the Esaki-Integral representation the tunnelling I-V characteristics of tunnel diodes, 3) the Josephson effect, 4) the tunnelling time, etc. The new theory presented here not only provides adequate explanation for all the above-mentioned effects but also gives an accurate expression for tunnelling current density which predicts results closer to the experimentally observed values. The new presentation also provides a more comprehensive description of the results obtained using older treatment.
This book presents a new approach to analyze quantum mechanical tunnelling of particles across potential barriers. The conventional concepts of this phenomenon, which are based on a time-in-dependent or a time-dependent perturbation approach are inadequate in furnishing explanations to a number of effects, e.g. (i) the limit of resolution of a field emission macroscope (FEM), (ii) Esaki integral, representing the I-V characteristics of solid-state junctions, (iii) Josephson effect, (iv) tunnelling time, (v) tunnelling current density etc. The new analysis presented here not only provides adequate explanations to all the above mentioned effects but also furnishes an appropriate expression for the tunnelling current density which yields results closer to experimentally observed values
It has been observed experimentally that the tunneling current across pn tunnel diodes decreases when a magnetic field is applied to it at liquid helium temperatures. Such a decrease is noticed both for longitudinal and transverse applications of magnetic fields relative to the direction of the current flow. Classically, tunneling of particles is regarded to propagate with the speed of light. Therefore, on the basis of the postulates of special theory of relativity tunneling of a potential barrier by particles should be independent of the state of motion of an observer relative to the tunneling system. In other words, the tunneling rate should remain unaffected of the motion of the observer. Therefore, to explain tunneling of particles in a crossed configuration of electric and magnetic fields, a suitable frame of reference for an observer can always be chosen so that the magnetic flux density observed from the new frame reduces to zero. The tunneling along the reduced electric field intensity may then be studied on established laws. The resultant electric field intensity in such a case becomes a function of the original magnetic flux density and it shows a steady decline with the increase in the magnitude of the latter. Therefore, a reduction in the tunneling probability and the tunneling current density is expected when the magnetic flux density normal to the current flow is increased. Finally, at a particular magnetic field intensity the tunneling current density drops to zero. It then turns out that the cyclotron frequency corresponding to this cut off magnetic field is proportional to the reciprocal of the tunneling time derived on the ideas of quantum measurement and observations. Therefore, by recording the normal magnetic flux density required to cut off the tunneling current across pn tunnel diodes immersed in a liquid helium bath, it may be possible to make an estimate of the tunneling time across a potential barrier. The working expression of the calculation of the tunneling time also follows independently of the relativistic treatment outlined above. The identity of results derived on the two approaches seems to justify the fact that the speed Of tunneling is really high enough so that the relativistic treatments may be applied to it as an approximation although tunneling may not propagate with the exact speed of light.
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.
The tunnel effect, commonly defined as the phenomenon in which a microparticle overcomes a potential barrier that exceeds its total energy, is often cited in quantum mechanics. However, this effect does not actually occur in its described form in nature, and the quantum mechanical interpretation of tunneling does not accurately represent the real physical processes involved, but rather provides a mathematical model. The true physical mechanism of the tunnel effect remains unidentified. An analysis of the tunnel effect reveals that its manifestation creates a “paradox” in classical physics. Explanations based on the Heisenberg uncertainty principle and the wave nature of particles fail to offer a comprehensive understanding of the actual physical process.This study proposes a new explanation of the tunneling phenomenon based on the principles of classical physics and electrodynamics. It is shown that the overcoming of the Coulomb barrier by low-energy microparticles occurs exclusively due to brief localized decreases in potential within the Coulomb barrier, allowing certain charged microparticles to penetrate. The formation mechanism of these short-lived localized regions, which manifest as volume channels with lower potential within the Coulomb barrier, is examined.It is established that the creation of these channels is linked to the properties of atomic nuclear and their associated electric fields. This facilitates the supra barrier penetration of the Coulomb barrier by individual low-energy microparticles that pass through these channels while experiencing a reduction in their total energy. This explanation resolves the “paradox” of the tunneling effect, eliminating the contradiction with classical physics laws.Moreover, the derived estimates of the tunneling process parameters are in qualitative agreement with the results obtained from quantum-mechanical models. The proposed framework aligns with nuclear physics findings, is supported by experimental evidence, and provides a new mechanism for controlling the tunneling effect in various energy-related applications.
The quantum tunneling phenomenon has long been explained by quantum mechanics using abstract concepts such as probability waves and wave function collapse. However, the essence of its microscopic physical mechanism—how and why a particle can traverse a classically forbidden region—has never been clearly elucidated, leading to a schism between the physical laws governing the micro- and macro-worlds. Based on the Great Tao Model and the Unified Theory of Atomic and Molecular Structure, this paper, for the first time, constructs a complete, self-consistent, and quantifiable framework for a classical physical explanation. The core of this framework clarifies the microscopic physical mechanisms of "local weakening of the Existence Field" and "formation of a directional field channel", reducing the tunneling process to a deterministic sequence of events: "information coupling → field weakening → channel formation → classical penetration". The study rigorously derives the quantitative relationships between the field strength weakening coefficient, the field channel width, and the penetration probability. Its mathematical form is compatible with the empirical formula of quantum mechanics, but its physical connotation is fundamentally different. Case studies demonstrate that this theory can uniformly explain the atomic-scale resolution of scanning tunneling microscopy (STM), the deterministic energy release in α-decay, and the physical necessity for the impossibility of macroscopic object tunneling. Starting from the first principles of classical physics, this paper provides a new paradigm for understanding tunneling that aligns with physical intuition, has a clear mechanism, and is subject to experimental verification, achieving a logical unification of micro- and macro-physical laws.