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DOI 10.1007/s00601-015-0990-z

Few-body Syst, C. A. Bertulani

Published Jan 1, 2015• 0 citations
OpenAlex

Abstract

Abstract This is a brief review of few relevant topics on tunneling of composite particles and how the coupling to intrinsic and external degrees of freedom affects tunneling probabilities. I discuss the phenomena of resonant tunneling, different barriers seen by subsystems, damping of resonant tunneling by level bunching and continuum effects due to particle dissociation.

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Abstract This is a brief review of few relevant topics on tunneling of composite particles and how the coupling to intrinsic and external degrees of freedom affects tunneling probabilities. I discuss the phenomena of resonant tunneling, different barriers seen by subsystems, damping of resonant tunneling by level bunching and continuum effects due to particle dissociation.
A variety of physical phenomena have at their foundation the quantum tunneling of particles through potential barriers. Many of these phenomena can be associated with the tunneling of single inert particles. The tunneling of composite systems is more complex than for single particles due to the coupling of the tunneling coordinate with the internal degrees of freedom of the tunneling system. Reported here are the results of a study for the tunneling of a two-component projectile incident on a potential energy system which differs for the two components. A specific linkage is made to sub-Coulomb nuclear reactions.
Some aspects of quantum tunnelling of a composite particle are clarified by a simple model. We calculate the probability that a couple of point particles bound to each other by a square well potential with a hard core tunnel through a rectangular potential barrier. It is shown that resonance structures appear in the transmission spectrum in some cases, which reflects the existence of quasi-bound-states of the centre of mass motion around the potential barrier. It is also shown that an inelastic tunnelling occurs in which the transitions in the relative motion are induced by the tunnelling of the centre of mass.
Quantum tunnelling is a phenomenon in which a particle is able to traverse a potential barrier, even if said particle possesses less energy than the barrier. This process is highly important in many modern fields of physics, such as nuclear physics and semiconductor technology. In this thesis, this phenomenon was presented through analytical study, as well as the derivation of the transmission coefficient in one and three dimensions. Of even greater interest is the phenomenon of resonant tunnelling, where particles tunnel through two or more potential barriers, leading to the formation of quantum wells and quasi-bound energy levels that result in heightened transmission probabilities at certain energies. The transfer matrix method was used in order to find an expression for the resonant tunnelling transmission coefficient in double barrier systems. In addition, a programme was developed in Python in order to investigate resonant tunnelling in different barrier systems. The programme demonstrates how the probability of transmission fluctuates with the energy of the incoming particle, as well as how it is influenced by changes to the framework of the barrier system. Furthermore, effects caused by the inclusion of asymmetry into the system are studied. Finally, the process of spin-dependent tunnelling and the related Rashba spin-orbit coupling were discussed as an extension of the resonant tunnelling phenomenon.
Tunneling is a supreme quantum effect. Every introductory text [1] on quantum mechanics gives the paradigm example of a particle tunneling through a one-dimensional potential barrier despite having a total energy less than the barrier height. Indeed, the reader typically works through a number of exercises, all involving one-dimensional potential barriers of one form or another modeling several key physical phenomena ranging from atom transfer reactions to the decay of α-particles [2]. However, one seldom encounters coupled multidimenisonal tunneling in such texts since an analytical solution of the Schro¨dinger equation in such cases is not possible. Interestingly, the richness and complexity of the tunneling phenomenon manifest themselves in full glory in the case of multidimensional systems [3]. Thus, for instance, the usual one-dimensional expectation of increasing tunneling splittings as one approaches the barrier top from below is not necessarily true as soon as one couples another bound degree of freedom to the tunneling coordinate. In the context of molecular reaction dynamics, multidimensional tunneling can result in strong mode-specificity and fluctuations in the reaction rates [4]. In fact, a proper description of tunneling of electrons and hydrogen atoms is absolutely essential [5,6] even in molecular systems as large as enzymes and proteins. Although one usually assumes tunneling effects to be significant in molecules involving light atom transfers, it is worth pointing out that neglecting the tunneling of even a heavy atom like carbon is the difference between a reaction occurring or not occurring. In particular, one can underestimate rates by nearly hundred orders of magnitude [7]. Interestingly, and perhaps paradoxically, several penetrating insights into the nature and mechanism of multidimensional barrier tunneling have been obtained from a phase-space perspective [8,9]. The contributions by Creagh, Shudo and Ikeda, and Takahashi in the present volume provide a detailed account of the latest advances in the phasespace-based understanding of multidimensional barrier tunneling.
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.