Quantum Tunneling Ashley Gnoss & Kyle Kucker Physics 43/ May 10th, 2011 Santa Rosa Junior College Spring ‘11 Image:

Introduction to the concept Quantum tunneling is one of the phenomena displaying the odd nature of Quantum Mechanics. It concerns particles in their wave states, where each observable can be described most acutely by a distribution of probability. This is the main point, that there is no point. Classically, it is assumed that particles that we can observe to be point-like should behave as if under the rules that govern the more massive objects that we have encountered, that is, they should behave deterministically. But due to the nature of Quantum Mechanics, there is a magnitude of size and complexity for which the rules seem to change. Image:

Quantum Mechanics: Introduction to the Concept Particles that we had assumed to be definite in their properties, (position, energy, time, momentum…) can only be described as distributions of probability. These distributions have another limitation. Due to our methods of detection, we are restricted to never knowing two properties of a particle simultaneously. We can never understand fully (with our current knowledge) what the particle/ distribution is doing, nor predict what it will do. This is the reason why we do not yet know what to call these objects. Waves or particles. Quantum mechanics emphasizes the “wave-nature”, because it is through wave mechanics that we can describe these probability distributions and how they could be an adequate description of the particle, though an unintuitive one. A few wave distributions of a hydrogen atom, describing varying positions (or potential positions) of the electron. Image:

Heisenberg’s Uncertainty Principle The inability to know certain multiple properties of an object at the same time is due to the uncertainty principle. This principle is the concept behind quantum tunneling. It is due to this lack of knowledge about the particle that we call the action of tunneling an odd phenomena. Indeed, it makes describing the rules and properties of nature a much more complex activity than once thought. “If the properties of the atom and particle could be known with certainty, then they would decohere and their wave behavior and their ability to interfere would be destroyed”- An interpretation of Quantum Mechanics Equations of the Uncertainty Principle

The Tunneling of a Particle Tunneling refers to the ability of a particle to overcome and cross a potential energy barrier that it would not be able do based on classical understanding. It is only the particle’s wave-nature that allows for this phenomenon. The probability wave describing the particle’s position is an integral that overlaps into the energy barrier, allowing for some finite probability that the particle might actually “tunnel” through. Images: abyss.uoregon.edu/.../ quantum_tunneling.gif

Tunneling in Nature Our sun persists in keeping us warm (and alive) through the process of fusion. Fusion is the creation of larger atomic nuclei/elements from smaller ones. Fusion occurs only at extremely high temperatures, where the Kinetic Energy is high enough to overcome the potential barrier due to the repelling of the nucleons. The only thing is that our sun is not hot enough to produce these high energies. Tunneling is the explanation. Only due to the overlap of the probability waves of the nuclei can they overcome the barrier separating them and fuse. Radioactive decay is another example of how tunneling circumvents the tendencies of nature. Particles such as alpha particles are held in the nucleus by the strong force, which means that they shouldn’t be able to escape. Tunneling again explains how the particles are able to overcome the strongest known force in nature. In the case of the alpha particle for instance, the location of the particle within the nucleus is fairly accurately known, and due to the uncertainty principle, the probability wave for the velocity (and therefore kinetic energy) is greater. The property unable to be defined and the wave description gives it a finite probability to arrive outside of the nucleus.

Technological Applications Once of the most important uses of electron tunneling is the production of current. A new and interesting use is within the new touch screen phones. By applying a force (pressure with the finger), the layers particles of polymer within the screen come closer together. Before they are moved together there is a “large enough” vacuum between the layers and so that the probability of electrons tunneling from one layer to another is very low. By exerting force on the layers, we are able to bring the probability waves of the electrons closer together, increasing the rate of tunneling, enough to produce current on- demand, changing the material from an insulator to a “metal”. The change in tunneling is extreme. For every Angstrom closer (1/10th of a nanometer) the rate of tunneling increases by ten times. And the resistance changes from 10^12 ohms to 1 ohm!

Another strange fact… Fruit flies have been shown to be able to distinguish between a particular molecule (such as acetophenone) and its deuterated version through the process of quantum tunneling via the receptors within the fruit fly’s nose. Within some molecules, deuterium-carbon bond vibrations are similar to the vibrations found in the bonds between carbon and nitrogen, which will result in a similar sent. A majority of fruit flies tend to avoid nitrogen molecules (nitriles), and so too with the deuterated versions of molecules that tend to attract them. Further studies in the nose’s abilities to employ quantum tunneling could lead to artificial noses and more sensitive instruments in the field.

Sources New Ideas in Quantum Tunneling. arxiv/23409/New Ideas in Quantum Tunneling. arxiv/23409/ Explanation of simple concept. um_tunneling.htmlExplanation of simple concept. um_tunneling.html Lecture onQuantumTunneling. ch?v=vMndTqowzqU Molecular vibration-sensing component in Drosophila melanogaster olfaction ). (All researched May 5, 2011)