Translation invariant theory of polaron (bipolaron) and the problem of quantizing near the classical solution
- PDF / 198,987 Bytes
- 5 Pages / 612 x 792 pts (letter) Page_size
- 50 Downloads / 153 Views
MOLECULES, OPTICS
Translation Invariant Theory of Polaron (Bipolaron) and the Problem of Quantizing Near the Classical Solution V. D. Lakhno Institute of Mathematical Problems of Biology, Russian Academy of Sciences, Pushchino, Moscow Region, 142290 Russia email: [email protected] Received November 12, 2012
Abstract—A physical interpretation of translationinvariant polarons and bipolarons is presented, some results of their existence are discussed. Consideration is given to the problem of quantization in the vicinity of the classical solution in the quantum field theory. The lowest variational estimate is obtained for the bipo laron energy E(η) with E(0) = –0.440636α2, where α is a constant of electron–phonon coupling, η is a parameter of ion binding. DOI: 10.1134/S1063776113060083 1
1. INTRODUCTION
The quantum field theory is based on the idea that there exist classical solutions in the vicinity of which quantization of fields is realized [1]. Such classical solutions can be ordinary plane waves, solitons, kinks, etc. In particular, quantum field theories of a particle interacting with a field proceed from the assumption of the existence of a semiclassical solution (i.e. when a quantum particle moves in a classical field) to which the solution of the quantum field problem must con ∞. In the vicinity of such a verge in the limit of α solution one can quantize the field and search for the solutions of the quantum field problem thus emerged. In paper [2] we, using the quantum field theory of a strong coupling polaron as an example, demon strated that, this is not always true and one cannot pass on to the semiclassical description in the case of the limiting transition. This result has a lot of conse quences, the most important of which are discussed in this paper. 2. INTERPRETATION AND PHYSICAL PROPERTIES OF TRANSLATIONINVARIANT POLARONS The polaron quantum field translationinvariant theory was constructed in [3]. According to this work, the ground state of a translationinvariant polaron is a delocalized state of the electron–phonon system: the probabilities of electron’s occurrence at any point of the space are similar. Both the electron density and the amplitudes of phonon modes (renormalized by an interaction with the electron) are delocalized. The concept of a polaron potential well (formed by local phonons [4]) in which the electron is localized, i.e. the 1 The article was translated by the authors.
selftrapped state is lacking. Accordingly, the induced polarization charge of the translationinvariant polaron is equal to zero. Polaron’s lacking a localized “phonon environment” suggests that its effective mass is not very much different from that of an electron. The ground state energy of the translationinvariant polaron is lower than that of Pekar polaron and is E0 = –0.1257520α2, [2] (for Pekar polaron E0 = ⎯0.10851128α2, [5]). Thus, for P = 0, where P is the total momentum of the polaron there is an energy gap between the transla tioninvariant polaron state and the Pekar one (i.e. the state with
Data Loading...
