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Many-Body Physics in Real Space

已有 273 次阅读 2019-11-12 13:37 |系统分类:科研笔记

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A two-density model to a general many-body problem: News and novelties


It has long been believed, and in fact this believe can be traced back to the very first articles defining modern theoretical physics in the twentieth century, that atomic physics is inherently random and not amenable to a thorough analysis in terms of cause and effect.

    This article, which is concluding a long standing investigation on this claim, starting in 2010 [1-5], finally establishes that this believe is unfounded. Atomic physics is not inherently random, if the theoretical description remains confined to three dimensional real space, a space one could call physical space.

    In such a theoretical framework all variables of the theoretical framework are physical objects, essentially scalar and vector densities. In this case a theoretical model can be constructed, which is fully causal and deterministic.

    The method is based on three key ideas: 

    Firstly, that events at the atomic scale have to be described by two densities, and not one as in the conventional density functional theory (DFT). With two densities, it becomes immediately understandable, why electrons change their wavelength, as they change their velocity. While quantum mechanics and conventional DFT cannot address this problem, the new framework can, as a shift from one density-mass density-to the second density-spin density-changes the balance between the two densities leading to a change of the wavelength.

    The two densities combined yield the conventional DFT density. Since this is the case, theoretical models based on the two densities can still use current DFT evaluation routines. These evaluation routines, for example in transport models, will probably remain valid until a better method, based on the two densities, has been developed.

    The second new idea is that the Hohenberg-Kohn theorems, which are the basis of DFT, are also valid for a two density model. The proof to this effect is part of the article [5]. This allows to adapt a large part of the existing expertise in DFT to be translated seamlessly into the new model.

    The third new idea is that a many-electron framework based on the two densities and including many-electron wavefunctions is much simpler than the conventional one as effective wavefunctions then only have four instead of 3N independent variables, where N is the number of electrons. This makes simulations of many-electron systems much simpler, potentially allowing for an efficiency gain of six orders of magnitude.

    The new framework has been tested on a set of forty atomic systems and a few multi-atomic systems, as this article reveals, and was found to be as accurate as the best current DFT methods [5].

    In an upcoming article [6] we show that the Kohn-Sham kinetic energy functionals are approximations, and we derive the exact kinetic energy functional for general many-electron systems. It is shown that these kinetic energy functionals also yield the accurate kinetic energy for free electrons, which in conventional DFT cannot be derived from the density.  

    In conclusion, there might be no reason to adhere to the traditional models in quantum mechanics and many-body physics, because they are less transparent, provide less information about a system, are plagued by paradoxes and are, crucially, much less efficient.


References
[1] W. A. Hofer, Unconventional approach to orbital-free density functional theory based on a model of extended electronsFound. Phys. 41, 754 (2011)
[2] W. A. Hofer, Heisenberg, uncertainty, and the scanning tunneling microscopeFront. Phys. 7, 218 (2012)
[3] W. A. Hofer, Solving the Einstein-Podolsky-Rosen puzzle: The origin of non-locality in Aspect-type experimentsFront. Phys. 7, 504 (2012)
[4] T. Pope and W. Hofer, Spin in the extended electron modelFront. Phys. 12, 128503 (2017)
[5] T. Pope and W. Hofer, A two-density approach to the general many-body problem and a proof of principle for small atoms and moleculesFront. Phys.  14, 23604 (2019)
[6] T. Pope and W. Hofer, Exact orbital-free kinetic energy functional of general many-electron systems, Frontiers of Physics (submitted), arxiv: 1907.06433


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作者简介:

Professor Werner Hofer is Professor of Chemical Physics, with expertise in theoretical condensed matter physics, physical chemistry, and electron theory, including fundamental aspects of quantum mechanics. He holds a master's degree in engineering physics from the University of Technology, Vienna, and a PhD in Condensed Matter Theory from the same University. Prof. Hofer is internationally known for his work on the nanoscience of surfaces and interfaces and has worked for nearly twenty years in this field with international collaborators in Canada, the US, China, and Europe. From 1999 to 2002 he was research assistant and research associate at University College London, from 2002 to 2014 he was Lecturer, Reader (2005) and Professor (2006) in the Department of Chemistry at the University of Liverpool. He was awarded a competitive Royal Society University Research Fellowship in 2003, which he held until 2011. From 2007 to 2013 he was an international member of the Canadian Institute for Advanced Research, participating in research on nanoelectronics. Since 2014 he is Professor of Chemical Physics at Newcastle University. His editorial roles include member of the editorial board of Journal of Physics (2005-2008), Editor of the Elsevier journal Surfaces and Interfaces (2016-2017), and Associate Editor-in-Chief of Frontiers of Physics (Higher Education Press and Springer, since 2016). He publishes regularly in high-impact journals like Nature, Nature Chemistry, Nature Nanotechnology, Angewandte Chemie, Reviews of Modern Physics, Physical Review Letters, Nano Letters, and the Journal of the American Chemical Society.



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