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Simulating unusual phenomena in low dimensional systems

Palomares Báez, Juan Pedro

Published Dec 1, 2011• 0 citations
OpenAlex

Abstract

"This thesis deals with physics phenomena in low dimensional systems, i.e., systems that range between few atoms and the bulk. The work deals with well studied (in this sense, classical) phenomena such as quantum tunneling and the enhancement of tunneling, surface reconstructions on surfaces, stability of structures vs. shape and size of nanoparticles, the mechanical properties studied in classical elastic theory for metals (such as hardness, ductility, malleability, etc.). However, althouh we have used and applied "classical" theories from both quantum and mechanical physics, we studied new, unusual phenomena in low dimensional systems. Thus, the reader will find in this thesis work, theoretical developments, hypothesis and results that advance explanations in unusual physical phenomena. In quantum physics there are phenomena which do not have analogs in classical physics. One of these phenomena is quantum tunneling. The manifestation of this process is penetration of a particle or more complicated object through a potential barrier. Such process is forbidden by classical mechanics. Besides tunneling through static potential barriers there are many phenomena in labs and nature when tunneling occurs across nonstationary barriers. There are many examples of such processes, ionization of atoms by a nonstationary electric filed, ac electric current in junctions of metals or semiconductors, dissociation of molecules by a high-frequency fields, field emission from metals by the action of an ac field, decay of current states in Josephson junctions, alpha decay of nuclei initiated by an external flux of protons, etc. These processes of tunneling through nonstationary barriers require an adequate theoretical description. Regarding studies for nanoparticles, we have faced the shape, structure and mechanical properties of metallic nanoparticles. First, we studied a particular truncation operated on the regular icosahedron gives rise to a new (not reported before) particle with five-fold symmetry and external decahedral shape termed the decmon motif. These truncated icosahedra exposes internal facets (100) and (111)â˘AS¸ additional to the external (111) facets of the regular icosahedron. The uncovering of additional facets to the icosahedron gives rise to phenomena such as surface reconstructions and a delicate competition in the energy contribution coming from the new facets (100) and (111) to the total surface energy."

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N 1923, during the infancy of the quantum theory, de Broglie [ 11 introducted a new fundamental hypothesis that matter may be endowed with a dualistic natureparticles may also have the characteristics of waves. This hypothesis, in the hands of Schrodinger [2] found expression in the definite form now known as the Schrodinger wave equation, whereby an electron or a particle is assumed to be represented by a solution to this equation. The continuous nonzero nature of such solutions, even in classically forbidden regions of negative kinetic energy, implies an ability to penetrate such forbidden regions and a probability of tunneling from one classically allowed region to another. The concept of tunneling, indeed, arises from this quantum-mechanical result. The subsequent experimental manifestations of this concept can be regarded as one of the early triumphs of the quantum theory. In 1928, theoretical physicists believed that tunneling could occur by the distortion, lowering or thinning, of a potential barrier under an externally applied high electric field. Oppenheimer [3] attributed the autoionization of excited states of atomic hydrogen to the tunnel effect: The coulombic potential well which binds an atomic electron could be distorted by a strong electric field so that the electron would see a finite potential barrier through which it could tunnel. Fowler and Nordheim [4] explained, on the basis of electron tunneling, the main features of the phenomenon of electron emission from cold metals by high external electric fields, which had been unexplained since its observation by Lilienfeld [SI in 1922. They proposed a one-dimensional model. Metal electrons are confined by a potential wall whose height is determined by the work function 9 plus the Fermi energy E/, and the wall thickness is substantially decreased with an externally applied high electric field, allowing electrons to tunnel through the potential wall, as shown in Fig. 1. They successfully derived the well-known Fowler-Nordheim formula for the current as a function of electric field F: J = AF* exp [-4(2nr)1'*t$a'*/3kF]. An application of these ideas which followed almost immediately came in the model for a decay as a tunneling process put forth by Gamow [6] and Gurney and Condon [7]. Subsequently, Rice [8] extended this theory to the description of molecular dissociation. The next important development was an attempt to invoke tunneling in order to understand transport properties of electrical contacts between two solid conductors. The problems of metal-to-metal and semiconductor-to-metal contacts are important technically, because they are directly related to electrical switches and rectifiers or detectors.

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"This thesis deals with physics phenomena in low dimensional systems, i.e., systems that range between few atoms and the bulk. The work deals with well studied (in this sense, classical) phenomena such as quantum tunneling and the enhancement of tunneling, surface reconstructions on surfaces, stability of structures vs. shape and size of nanoparticles, the mechanical properties studied in classical elastic theory for metals (such as hardness, ductility, malleability, etc.). However, althouh we have used and applied "classical" theories from both quantum and mechanical physics, we studied new, unusual phenomena in low dimensional systems. Thus, the reader will find in this thesis work, theoretical developments, hypothesis and results that advance explanations in unusual physical phenomena. In quantum physics there are phenomena which do not have analogs in classical physics. One of these phenomena is quantum tunneling. The manifestation of this process is penetration of a particle or more complicated object through a potential barrier. Such process is forbidden by classical mechanics. Besides tunneling through static potential barriers there are many phenomena in labs and nature when tunneling occurs across nonstationary barriers. There are many examples of such processes, ionization of atoms by a nonstationary electric filed, ac electric current in junctions of metals or semiconductors, dissociation of molecules by a high-frequency fields, field emission from metals by the action of an ac field, decay of current states in Josephson junctions, alpha decay of nuclei initiated by an external flux of protons, etc. These processes of tunneling through nonstationary barriers require an adequate theoretical description. Regarding studies for nanoparticles, we have faced the shape, structure and mechanical properties of metallic nanoparticles. First, we studied a particular truncation operated on the regular icosahedron gives rise to a new (not reported before) particle with five-fold symmetry and external decahedral shape termed the decmon motif. These truncated icosahedra exposes internal facets (100) and (111)â˘AS¸ additional to the external (111) facets of the regular icosahedron. The uncovering of additional facets to the icosahedron gives rise to phenomena such as surface reconstructions and a delicate competition in the energy contribution coming from the new facets (100) and (111) to the total surface energy."
N 1923, during the infancy of the quantum theory, de Broglie [ 11 introducted a new fundamental hypothesis that matter may be endowed with a dualistic natureparticles may also have the characteristics of waves. This hypothesis, in the hands of Schrodinger [2] found expression in the definite form now known as the Schrodinger wave equation, whereby an electron or a particle is assumed to be represented by a solution to this equation. The continuous nonzero nature of such solutions, even in classically forbidden regions of negative kinetic energy, implies an ability to penetrate such forbidden regions and a probability of tunneling from one classically allowed region to another. The concept of tunneling, indeed, arises from this quantum-mechanical result. The subsequent experimental manifestations of this concept can be regarded as one of the early triumphs of the quantum theory. In 1928, theoretical physicists believed that tunneling could occur by the distortion, lowering or thinning, of a potential barrier under an externally applied high electric field. Oppenheimer [3] attributed the autoionization of excited states of atomic hydrogen to the tunnel effect: The coulombic potential well which binds an atomic electron could be distorted by a strong electric field so that the electron would see a finite potential barrier through which it could tunnel. Fowler and Nordheim [4] explained, on the basis of electron tunneling, the main features of the phenomenon of electron emission from cold metals by high external electric fields, which had been unexplained since its observation by Lilienfeld [SI in 1922. They proposed a one-dimensional model. Metal electrons are confined by a potential wall whose height is determined by the work function 9 plus the Fermi energy E/, and the wall thickness is substantially decreased with an externally applied high electric field, allowing electrons to tunnel through the potential wall, as shown in Fig. 1. They successfully derived the well-known Fowler-Nordheim formula for the current as a function of electric field F: J = AF* exp [-4(2nr)1'*t$a'*/3kF]. An application of these ideas which followed almost immediately came in the model for a decay as a tunneling process put forth by Gamow [6] and Gurney and Condon [7]. Subsequently, Rice [8] extended this theory to the description of molecular dissociation. The next important development was an attempt to invoke tunneling in order to understand transport properties of electrical contacts between two solid conductors. The problems of metal-to-metal and semiconductor-to-metal contacts are important technically, because they are directly related to electrical switches and rectifiers or detectors.
N 1923, during the infancy of the quantum theory, de Broglie [ 11 introducted a new fundamental hypothesis that matter may be endowed with a dualistic natureparticles may also have the characteristics of waves. This hypothesis, in the hands of Schrodinger [2] found expression in the definite form now known as the Schrodinger wave equation, whereby an electron or a particle is assumed to be represented by a solution to this equation. The continuous nonzero nature of such solutions, even in classically forbidden regions of negative kinetic energy, implies an ability to penetrate such forbidden regions and a probability of tunneling from one classically allowed region to another. The concept of tunneling, indeed, arises from this quantum-mechanical result. The subsequent experimental manifestations of this concept can be regarded as one of the early triumphs of the quantum theory. In 1928, theoretical physicists believed that tunneling could occur by the distortion, lowering or thinning, of a potential barrier under an externally applied high electric field. Oppenheimer [3] attributed the autoionization of excited states of atomic hydrogen to the tunnel effect: The coulombic potential well which binds an atomic electron could be distorted by a strong electric field so that the electron would see a finite potential barrier through which it could tunnel. Fowler and Nordheim [4] explained, on the basis of electron tunneling, the main features of the phenomenon of electron emission from cold metals by high external electric fields, which had been unexplained since its observation by Lilienfeld [SI in 1922. They proposed a one-dimensional model. Metal electrons are confined by a potential wall whose height is determined by the work function 9 plus the Fermi energy E/, and the wall thickness is substantially decreased with an externally applied high electric field, allowing electrons to tunnel through the potential wall, as shown in Fig. 1. They successfully derived the well-known Fowler-Nordheim formula for the current as a function of electric field F: J = AF* exp [-4(2nr)1'*t$a'*/3kF]. An application of these ideas which followed almost immediately came in the model for a decay as a tunneling process put forth by Gamow [6] and Gurney and Condon [7]. Subsequently, Rice [8] extended this theory to the description of molecular dissociation. The next important development was an attempt to invoke tunneling in order to understand transport properties of electrical contacts between two solid conductors. The problems of metal-to-metal and semiconductor-to-metal contacts are important technically, because they are directly related to electrical switches and rectifiers or detectors.
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.
Everyday macroscopic objects follow the laws of classical mechanics. For microscopic objects, such as atoms or nuclei, the wave character of their dynamics has to be taken into account within the framework of quantum mechanics. While wave-like behaviour can show up in various ways, one of the most striking is the tunnelling effect: some events that are classically forbidden for energetic reasons happen because the quantum particles can tunnel under a potential barrier. Similarly, events that are prohibited due to some other dynamical constraints can occur via a process known as dynamical tunnelling. Indeed, tunnelling plays a major role in a variety of physical phenomena, ranging from α-particle radioactivity to the current–voltage characteristics of transistors.
Since the early days of quantum mechanics, tunneling has been recognized as one of the hallmarks of the wave character of microscopic physics. The possibility of a quantum particle to penetrate an energetic barrier represents certainly one of the most spectacular implications of quantum theory and has led to various applications in nuclear, atomic, and molecular physics as well as in mesoscopic science. Typical scenarios in which tunneling manifests are the escape route of a quantum particle from a quasibounded region, the transition between two or more symmetry-related, but classically disconnected wells (which we shall focus on in the following), as well as scattering or transport through potential barriers. The spectrum of scenarios becomes even richer when the concept of tunneling is generalized to any kind of classically forbidden transitions in phase space, that is, to transitions that are not necessarily inhibited by static potential barriers but by some other constraints of the underlying classical dynamics (such as integrals of motion). Such “dynamical tunneling” processes arise frequently in molecular systems [1] and were realized with cold atoms propagating in periodically modulated optical lattices [2-4]. Moreover, the electromagnetic analog of dynamical tunneling was also obtained with microwaves in billiards [5].
This paper focuses on the quantum tunneling effect, which describes how a particle may penetrate barriers or obstructions using the Schrödinger equation. If a particle makes a barrier tunneling, it means that a particle with low energy goes through the barrier whose energy level is much higher. It is a basis or background for the entire theory of this part. The particle transport probability is explained using both single- and multi-barrier system models. The paper studies the relationship between barrier parameters and particle transmission probability for both single- and multiple-barrier system models.The aim of the study is the provision of the theoretical devices and algorithms via a quantum operational efficiency.Particularly, the paper deals with the multipath barrier tunneling effect, and it connects the transmission coefficients with the system parameters. The goal of this article is to come up with the new strategies and procedures that one can use the quantum phenomenon of the tunneling effect in the contemporary physical th applications, cutting the gap between theoretical physics and technology.This will be done by studying and analyzing theoretical processes and mathematics of this phenomenon along with the technological applications it has.