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APPROACH TO THE POLARON AND RELATED SYSTEMS

Janusz Adamowski, B. Gerlach, Hajo Leschke

Published Jan 1, 1984• 0 citations
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BINDING, STABILITY, AND NON-BINDING OF MULTI-POLARON SYSTEMS

Rupert L. Frank, Élliott H. Lieb, Robert Seiringer +1 more

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=2α, where U is the electronic Coulomb repulsion and αis 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 state energy, which is valid for large α. Finally, we derive exact results, not reported before, about the one-dimensional toy model introduced by E. P. Gross.

arXiv:1010.0737•Mathematical Results in Quantum Mechanics (QMath)•May 1, 2011•5 citations
At first glance it is surprising that there are papers describing experiments fitting to the quantum Zeno effect and on the other hand there are very similar experiments which seem to contradict to the quantum Zeno effect.Now the quantum Zeno effect should be related to a suppression of the time evolution in case of an "almost continuous measurement".What does that mean?In this paper we discuss two possibilities to give a precise notion of such a suppression.That completes the considerations of the quantum Zeno scheme in our previous paper (K.-H.Fichtner and K. Inoue, 2013).
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=2α, where U is the electronic Coulomb repulsion and αis 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 state energy, which is valid for large α. Finally, we derive exact results, not reported before, about the one-dimensional toy model introduced by E. P. Gross.