Binding, Stability, and Non-binding of Multi-polaron Systems

@article{Frank2010BindingSA,
title={Binding, Stability, and Non-binding of Multi-polaron Systems},
author={Rupert L. Frank and Elliott H. Lieb and Robert Seiringer and Lawrence E. Thomas},
journal={arXiv: Strongly Correlated Electrons},
year={2010}
}
• Published 5 October 2010
• Physics
• arXiv: Strongly Correlated Electrons
The binding of polarons, or its absence, is an old and subtle topic. After defining the model we state some recent theorems of ours. First, the transition from many-body collapse to the existence of a thermodynamic limit for N polarons occurs precisely at U=2\alpha, where U is the electronic Coulomb repulsion and \alpha is the polaron coupling constant. Second, if U is large enough, there is no multi-polaron binding of any kind. We also discuss the Pekar-Tomasevich approximation to the ground…
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References

SHOWING 1-10 OF 34 REFERENCES

• Physics
Physical review letters
• 2010
Two things are proved rigorously: the transition from many-body collapse to the existence of a thermodynamic limit for N polarons occurs precisely at U=2α, where U is the electronic Coulomb repulsion and α is the polaron coupling constant.
• Physics
• 2010
We resolve several longstanding problems concerning the stability and the absence of multi-particle binding for N≥2 polarons. Fröhlich’s 1937 polaron model describes non-relativistic particles
• Mathematics
• 1995
Abstract: The polaron has been of interest in condensed matter theory and field theory for about half a century, especially the limit of large coupling constant, α. It was not until 1983, however,
• Physics
• 1991
For more than 40 years it was thought that polaron- and exciton-phonon systems exhibited unexpected localization properties. Particular attention was paid to the so-called phonon-induced
• Physics
Physical review. B, Condensed matter
• 1992
A model that combines the averaging of the relative coordinate over the asymptotically best wave function with a path-integral treatment of the center-of-mass motion is introduced, and the stability region for bipolaron formation is increased.
In the strong-coupling limit, the polaron ground state energy has been known to be proportional to α 2 , α being the electron-phonon coupling constant. The coefficient of proportionality is found by
• Physics
Physical review. B, Condensed matter
• 1994
The nonlinear integro-differential equation for the bipolaron wave function is solved numerically, from which estimates are obtained for the main characteristics of the one-dimensional (1D) large bipolaron.
Summary A new variational method is developed to treat the properties of slow electrons in ionic crystals, and similar problems. It is shown that the true energy of the ground state is always lower
• Physics
• 1952
A variational technique is developed to investigate the low-lying energy levels of a conduction electron in a polar crystal. Because of the strong interaction between the electron and the
• Physics
Physical review. B, Condensed matter
• 1991
The single-polaron--bipolaron transition behaves much like a first-order phase transition and might be of relevance for the bipolaron model of high-{ital T}{sub {ital c}} superconductivity.