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Background On These Simulations
The simulations shown here involve physical aspects of the classical hydrogen atom, as described in a series of articles by Dan Cole and Yi Zou. Why the interest in this system? After all, hydrogen is the simplest of the atoms, and we are describing it here by classical physics, as opposed to quantum physics. Indeed, at first glance this does seem bizarre!
However, there are very good reasons, including engineering/technology interests, a fundamental physical perspective, as well as the interesting mathematical nonlinear dynamic aspects, as to why these simulations should prove to be quite helpful and may well serve as a basic foundation for continued investigations of this apparently simple, but beguiling complex and fascinating system.
Studying the hydrogen atom enables us to gain insight into Rydberg atom dynamics. A Rydberg atom is any neutral atom, whether helium, carbon, or even lead, but with one electron in a very highly excited state, so that it's average radial position is far removed from the core of inner electrons. For such an excited electron, the inner core of electrons plus the nucleus will have a net charge of +e, the same charge as exists in the nucleus of the hydrogen atom. Hence, at first approximation, the Rydberg atom behaves very much like the simple hydrogen atom. Since any single atom can be excited into a Rydberg atom situation, then this makes the study of a hydrogen atom somewhat broader than one might initially expect.
Technologically, there are many instances where the Rydberg atom is encountered in applied physics and engineering situations. For example, often technologists want to provide a very pure source of atoms that are singly ionized, so that they have a net charge of +e, such as for ion implantation. Studying the dynamics and control of the Rydberg atom should help provide methods for "purifying" such ion sources. Also, the control of ion behavior and movement in a plasma is essential for precise "plasma etching" techniques in micro and nano electronics. Again, the Rydberg atom serves as a fine line between the pure singly charged ion source and the nonionized atom. Finally, there is the exciting possibility of being able to "read and write" information to a single Rydberg atom by controlling the state of the outer electron. If this can be done in technically feasible ways, then the possibility arises for incredibly dense medium memory sources, with each atom potentially providing a vehicle for memory storage. Such technology advances are undoubtedly years away from practical implementations, but, one needs to start somewhere, and it appears there are good reasons for expecting this may well become achievable. We believe that the simulations provided here, and yet more to be developed, should help both ourselves, as well as other technologists, in designing such systems. As with other simulations reported on this present web site, our goal here is to provide simulation tools that help guide exciting technological directions to enable realizable products in commercial and industrial settings.
As for the deeper physics reason for being interested in the present simulations, there are really two levels here. First, the more immediate and practical one is that the excited electron in a Rydberg atom behaves almost classically. It's "orbit" is large, nearly making it treatable by classical dynamics. However, the key word here is "nearly", since even with the large orbit, the system still has a wealth of subtle quantum mechanical behaviors. Consequently, some researchers have developed "semi-classical" methods for describing this "nearly classical" system. At one level, our present work can be viewed in this light. As for an incentive here, the following quote by Uzer et. al in Ref. [1] provides a concise summary: "Classical and semiclassical methods are unrivaled in providing an intuitive and computationally tractable approach to the study of atomic, molecular, and nuclear dynamics. An important advantage of such methods is their ability to uncover in a single picture underlying structures that may be hard to extract from the profusion of data supplied by detailed quantum calculations."
We believe that our simulations, with the portion of the classical electromagnetic zero-point spectrum included that is most relevant for the dynamics of the excited electron, will provide a very fast (computationally), yet, fairly complete physical description of the behavior of the Rydberg atom for many technological purposes (aside from the second level concern of the complex behavior of the inner core of electrons and nucleus).
Moreover, there exists the very real possibility that including the full classical dynamics of the electron movement, plus the interaction of what is called classical electromagnetic zero-point radiation, at absolute temperature T=0, or, more appropriately, including whatever radiation exists at the approximate temperature one is performing experiments, may well provide nearly all of the quantum mechanical behavior in atomic physics. The basic ideas of this theory were advanced most significantly by Timothy Boyer and Trevor Marshall in the 1960s in Refs. [2]-[6], and then continued by them and other researchers in subsequent years (see Refs. [7]-[10] for various reviews of this body of work). Although this classical physical theory of nature, that came to be called stochastic electrodynamics (SED), seemed initially quite exciting and promising, by the late 1970s and early 1980s, it looked like SED would ultimately fail in the ambitious goal to form a basis for the quantum mechanical behavior of atomic physical systems (see the discussion, for example, in the introductory section of Ref. [10]).
Recently, however, the work by Cole and Zou in (provide hyperlink of our publications) has helped to revitalize the possibility that SED can be pushed much farther than this previous work of the late 1970s and early 1980s suggested. Although much remains to be done to explore the full ramifications and extensions, nevertheless, (provide hyperlink to the preprint of the ground state paper), by using detailed simulation methods, Cole and Zou showed that the ground state probability distribution function of hydrogen, as predicted by QM, does indeed appear to fall out of SED. Hence, possibly, just possibly, the difficult nonlinear dynamics of this surprisingly simple yet complex system of a classical hydrogen atom interacting with the wide frequency spectrum of classical electromagnetic zero-point radiation, has been the main stumbling block for uncovering the full implications of the SED theory. The present direct numerical approaches have side-stepped many of the difficulties of more conventional analytical attacks, and may help to provide future aids in advancing this work yet further.
What other quantum mechanical (QM) aspects will or will not be similarly predicted? Work by ourselves and other colleagues is presently aimed at uncovering the answers to these questions. In the meantime, we also expect that the present simulation methods, coupled with a portion of the zero-point spectrum, should provide a very useful simulation tool for investigating possible technology directions of Rydberg atomic applications.