Skip to comments.Born–Oppenheimer and Fixed-point Models for Second-order Phonon Exchange in a Metal
Posted on 02/24/2014 9:28:19 PM PST by Kevmo
BornOppenheimer and Fixed-point Models for Second-order Phonon Exchange in a Metal
Peter L. Hagelstein ∗
Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Irfan U. Chaudhary
Department of Computer Science and Engineering, University of Engineering and Technology. Lahore, Pakistan
We have been interested in the development of a model for anomalies in condensed matter nuclear science, and over the past few years we have developed new models that describe coherent phonon exchange between a highly-excited vibrational mode and nuclei under conditions of fractionation. When we modeled collimated X-ray emission in the Karabut experiment, we found that the conditions required by the model did not match the conditions of the experiment. One possible reason for this might be the neglect of phonon fluctuations due to coupling with conduction electrons.
We would like to add a description of this effect to our phononnuclear model; however, models normally used for electronphonon interactions in metals are based on the Bloch picture, and we were concerned that it may not be well suited to the problem. This has motivated us to develop a new model for phonon fluctuations in a metal that is based on the BornOppenheimer picture, within the context of a BrillouinWigner formulation. The BornOppenheimer results are complicated, so we have reduced them in a simpler fixed-point picture (which is based on a Taylor series expansion of the BornOppenheimer approximation around fixed nuclear equilibrium points).
In order to verify the resulting formalism, we constructed a simplified model for the monatomic crystal phonon dispersion relation, which is well known in the Bloch picture literature. From this model we are able to extract the longitudinal dielectric constant. We find that the fixed-point dielectric constant at second order is more accurate than the Bloch picture equivalent, and that it includes dynamic corrections that match the result from field theory up to O(ω 2 ) .
This model is used in a subsequent paper for the development of phonon fluctuation models, where it is found that the Bloch picture is appropriate when the metal sample is micron scale or larger, and that the BornOppenheimer picture is appropriate for nano-scale samples.
Summary and Conclusions
In earlier work we have developed a model that describes coherent energy exchange under conditions of fractionation between nuclei and a highly excited phonon mode. To compare with experiment, we begin with the basic theory described in , we make use of the interpretation (based on coherent energy exchange between acoustic vibrations and excitation of the lowest nuclear level in 201 Hg) described in , and a specific model consistent with this interpretation. What we found was a substantial disagreement between the resulting model and experimental observations.
The resulting disagreement could be due to a problem with the underlying theory, issues with our proposed interpre- tation, or errors in the model and/or model parameters. We were motivated in this work by a concern that the problem might be in the basic theory; in particular we had neglected phonon fluctuations due to coupling with conduction electrons. Our interest in modeling the effect ultimately resulted in this study. The problem that we encountered is that electronphonon interactions in metals is usually formulated in the Bloch picture, but there are differences between how phonon exchange works in the Bloch picture and in the BornOppenheimer picture. We are interested in mod- els that involve off-resonant interactions, and the equivalence of the two pictures has been argued for on-resonance; consequently, we are interested in phonon exchange in a BornOppenheimer picture to describe phonon fluctuations.
It seemed ultimately to be simplest just to start from scratch, and follow the development of the BornOppenheimer approximation in a BrillouinWigner formulation that is well matched to other models we have been constructing. The BrillouinWigner formalism is suited to taking into account the strong first-order interaction, and otherwise separating the phonon and electron degrees of freedom. In the end we have a model that describes the second-order coupling of equivalent dressed phonons (in the BrillouinWigner sense) which gives rise to the fluctuations of interest in the phononnuclear model.
However, in the process we have covered a lot of developmental ground, so there is reason to be concerned as to whether the fixed-point model we are working with is free of errors. In order to test this, we decided to develop relations that describe the phonon dispersion relation for a monatomic metal crystal, which is probably the best known relevant problem from Bloch picture models in the literature. The longitudinal dielectric constant consistent with this model results in the same static model as is obtained from the Bloch picture, and gives results up to second order that are in agreement with literature results from field theory. This provides confidence in the preceding development. We have made use of simple Coulomb potentials for the electron-ion interaction, which is appropriate for long wavelength vibrations. For computations involving shorter wavelength phonons we would need to make use of better electron-ion potentials. This is discussed extensively in the literature, and the modification of the formulas for this case is straightforward. The reduction of the many-electron matrix elements into simpler models is also straightforward, and will have to be addressed in using these results for detailed calculations.
A reviewer noted that this paper seems to lack a major punchline. In response it seems useful to spell out the major punchlines for this paper, and for what we found subsequently when we made use of it. The first is that there does not exist in the literature a systematic treatment of BornOppenheimer and related approximations adapted for the case of a metal, which in our view is suitable for the development of a fluctuation model; the biggest contribution of this paper then is to provide a useful foundation in a relevant language. Another significant result is the clarification of how the longitudinal dielectric constant of a metal comes about in the lowest orders of perturbation theory in a BornOppenheimer approximation. Although it is mentioned in a few works that such a result was known previously, we have not found a clear discussion of it. Another important result which we found when we used the model described here to develop a fluctuation model is that the results from the BornOppenheimer picture are very different from what we get with a Bloch picture model.
In the literature the two pictures are largely viewed as equivalent in connection with describing phonon exchange in metals; while perhaps true for screening and for lowest-order phonon exchange, this is certainly not the case for phonon fluctuations. And finally, we will discuss in a following publication that a fluctuation model based on the BornOppenheimer picture is inappropriate above a certain size scale, so that a fluctuation model based on the Bloch picture must be used. On the other hand, fluctuations for a nano-scale metal sample should be treated using a BornOppenheimer model.
The Cold Fusion/LENR Ping List
Best book to get started on this subject:
Why Cold Fusion Research Prevailed
Much ado about nothing ?
Bevis: “Uh, heh heh . . . he said, ‘a highly-excited vibrational mode . . .’ heh, heh.”
Butthead: “Yeah, and ‘coupling of equivalent dressed phonons!’ “
Beavis: “Yeah . . . heh heh . . . “
I believe that the corrections match the result from field theory up ONLY up to to O(ω 1 ).
Hey, just kidding. I have some scientific background, and the whole post looks like gibberish to me. I suppose that's because I went to a state university and not a private school.
Asked & answered
A phonon is a vibration in a crystal. A sound, if you wish; that is also true. It is defined in classical mechanics and in quantum mechanics.
This paper does not have a punchline, as the reviewer said. This is probably true, though it does have several specific outputs:
1) The first is that the current science have not created a sufficiently correct model of phonons in metal. The authors began that work.
2) The authors spell out a specific behavior of metals that is pretty complex to explain. The authors acknowledge that this behavior was known before, but not widely known.
3) The authors say that their model differs from the model that is in prevailing use today.
If I were to take the scientific significance of this paper down to the level of a woodworker, they are saying that when you put a specific varnish onto a specific wood in just the right way, the wood may shine slightly differently from what you'd expect. It's a good thing to know, but it's a highly specialized bit of information, and it is of use only to highly skilled woodworkers. For everyone else it's just a bunch of strange words.
The reason why phonons are important is that they are postulated to be the absorption path for gamma rays or other high energy products of fusion. So, these guys are looking into the right way to model it. For larger systems, the Bosch model works, and for smaller systems (like LENR), the Born-Oppenheimer model works better. In the paper, they went through the math for why that is the case.
The Extended Lochon Theory proposes that Phonons are important in the IniTIATion of Cold Fusion, not just the absorption of its products.
Extended Lochon Theory
Model proposed by KP Sinha and Andrew Meulenberg. Postulates that fusion can occur between hydrogen or deuterium within solid state lattice systems that contain linear defects. Linear defects are degraded surface phenomena caused by heavy loading processes where mobile protons/deuterons are then able to congregate. These interstitial surface anomalies are sometimes referred to as a sub-lattice in ELT and have recently been correlated with Storms’ Nano-crack NAE by Meulenberg himself at ICCF-18.
Longitudinal phonon modes originating from these localized interstitial arrays (Linear NAE plus Ions) A) facilitate the creation of lochons (local charged boson electron pairs) and B) polarize ion pairs within the defects. Lochons will merge with H or D to form H- and D- ions respectively. They also provide strong screening effects between H+/H- and D+/D- nuclei. Lochon assisted screening in conjunction with subsequent deepening of the coulomb potential-well facilitates the initiation of low-level, tunneling-assisted fusion processes.
Absence of radiation is accounted for by two mechanisms. Firstly, gradual dissipation and exchange of thermal energy occurs between ion chains and the lattice before H+H-/D+D- fusion takes place. Secondly, H+H-/D+D- that are deeply bound with lochons do not occupy an excited state above the fragmentation level which prevents gamma transitions after fusion.
Much ado about nothing ?
With Crazy K, it’s all about the quantity of cold fusion spam, not the quality of science.
With moonboy, it’s all about acting like a seagull. That’s utterly rich, for HIM to comment on the “quality of science”. This is a pure science thread, all about theory, and his contribution is??? to add invective, not address ANYTHING about the ACTUAL science being discussed, and engage in vigilante censorship.
Without the quantity, it is hard for me to have enough knowledge to be able to understand when I find quality.
In this case, even though they failed to produce their desired results, they did learn ways not to do it, and adapted their model for another try.
Edison didn't invent the light bulb on the first try.