Rigorous Ground State Energy of a Linearized Model of a Polaron in a Magnetic Field

Abstract

An explicit analytical expression is derived for the ground state energy of a linearized polaron model in a constant and uniform magnetic field. I n this model, the validity of the Feynman inequality in a magnetic field is investigated. In a fixed magnetic field, it is shown that even for arbitrarily small electron-phonon coupling, the presence of a magnetic field is prohibitive for the application of the Feynman inequality.Es wird ein expliziter analytischer Ausdruck fur die Grundzustandsenergie eines linearisierten Polaronenmodells in einem konstanten und gleichformigen Magnetfeld abgeleitet. I n diesem Modell wird die Gultigkeit der Feynmanungleichheit in einem Magnetfeld untersucht. Es wird gezeigt, daB insbesonders fur beliebig kleine Elektron-Phonon-Kopplung die Anwesenheit eines Magnetfeldes die Anwendung der Feynman-Ungleichung verbietet.

The Bogolubov representation of the polaron model and its completely integrable RPA-approximation

“…As it is well known, the temperature dependence of the effective polaron mass is of great interest for physical applications, in particular, with its relation to the interpretation of experiments of cyclotronic resonance in polar crystals [4][5][6]. Measurements fulfilled in the crystals CdTe and AgBr in weak magnetic fields at small cyclotronic frequencies demonstrate clearly enough that the corresponding cyclotronic polaron mass grows with temperature at its low values.…”

“…It is interesting to note, that the analytical studies of statistical properties of the model of polaron in all of the works on this problem [1,3,6,13,21], except the works [4,5], were based on the Hamiltonian expression (1). But, as it was pointed out in [1], the statistical properties of the model do not depend on the unitary-equivalent representation choice for operator (1).…”

“…In a series of papers on the polaron theory [1,6] the oscillator approximation of the Hamiltonian (1) was analyzed. This approximation leads to the so-called "linearized" model of the polaron, when only the first member of the expansion exp(i r, f ) 1 + i r, f in (1) was taken into account and the quadratic compensating part K 0 r 2 /2, where…”

“…It can be shown using the standard considerations, devised in [6,20] jointly with the Bogolubov inequality [1], that the corresponding statistical sums for the Hamiltonian operators (7) and (3) in the thermodynamical limit are asymptotically equal as the intensity parameter α → ∞. The analytical details of this analysis will be presented in the Part 2 of this work.…”