Browsing by Author "Wellig, David"

Now showing 1 - 1 of 1

Open Access
On polarons and multipolarons in electromagnetic fields
(2013) Wellig, David; Griesemer, Marcel (Prof. Dr.)
This dissertation is concerned with a system of so-called large polarons in electromagnetic fields. We are especially interested in the ground state energy in the case of strong interactions between electrons and phonons, the strength of which is described by a coupling constant, and in the existence of bound states of several polarons. For the description of the polarons we use the model of H. Fröhlich, as well as the approximative models of Pekar, and Pekar and Tomasevich. The conjecture, that the ground state energies of these models asymptotically coincide in the leading order of the coupling constant, was the starting point of this work. We prove this conjecture for a large class of external electromagnetic fields. A suitable scaling of the fields makes sure, that they already play a non-trivial role in the leading order. The asymptotic coincidence of the ground state energies allows us to trace back the question of binding of Fröhlich polarons in the case of large couplings to the corresponding question in the model of Pekar and Tomasevich. The transcription of this dissertation is divided into four chapters, of which the introduction is the first one. The Chapters 2, 3 and 4 constitute three independent publications. The Chapter 2 is dedicated to the Pekar functional with electromagnetic fields. We proof the existence of a minimizer in the case of a constant magnetic field and a vanishing electric field. The minimizer exists as well, if this field configuration is locally perturbed such that the minimal energy is lowered. From the existence of the minimizer of the Pekar functional we derive binding of two polarons in the model of Pekar and Tomasevich. In Chapter 3, we compare the ground state energy of the 1-particle Fröhlich model in the limit of strong couplings with the minimum of the corresponding Pekar functional. We prove the above mentioned conjecture in the case of a single polaron. This result, in connection with the results of Chapter 2, allows us to prove binding of two Fröhlich polarons in strong electromagnetic fields. In Chapter 4 the analysis of the previous chapter is extended to N-polaron systems. To do so, an estimate of the interaction energy of spatially divided clusters of polarons in electromagnetic fields is derived. This allows us to proof the asymptotic exactness of the minimal energy of the Pekar-Tomasevich functional for strong couplings, whereas, as in Chapter 3, the external fields are suitably rescaled. As an application binding for N polarons in constant strong magnetic fields is proved.