We study a class of polaron-type Hamiltonians with sufficiently regular form factor in the interaction term. We investigate the strong-coupling limit of the model, and prove suitable bounds on the ground state energy as a function of the total momentum of the system. These bounds agree with the semiclassical approximation to leading order. The latter corresponds here to the situation when the particle undergoes harmonic motion in a potential well whose frequency is determined by the corresponding Pekar functional. We show that for all such models the effective mass diverges in the strong coupling limit, in all spatial dimensions. Moreover, for the case when the phonon dispersion relation grows at least linearly with momentum, the bounds result in an asymptotic formula for the effective mass quotient, a quantity generalizing the usual notion of the effective mass. This asymptotic form agrees with the semiclassical Landau–Pekar formula and can be regarded as the first rigorous confirmation, in a slightly weaker sense than usually considered, of the validity of the semiclassical formula for the effective mass.
Journal of Statistical Physics
Financial support through the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme Grant Agreement No. 694227 (R.S.) and the Maria Skłodowska-Curie Grant Agreement No. 665386 (K.M.) is gratefully acknowledged. Open access funding provided by Institute of Science and Technology (IST Austria).
Mysliwy K, Seiringer R. Polaron models with regular interactions at strong coupling. Journal of Statistical Physics. 2022;186(1). doi:10.1007/s10955-021-02851-w
Mysliwy, K., & Seiringer, R. (2022). Polaron models with regular interactions at strong coupling. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-021-02851-w
Mysliwy, Krzysztof, and Robert Seiringer. “Polaron Models with Regular Interactions at Strong Coupling.” Journal of Statistical Physics. Springer Nature, 2022. https://doi.org/10.1007/s10955-021-02851-w.
K. Mysliwy and R. Seiringer, “Polaron models with regular interactions at strong coupling,” Journal of Statistical Physics, vol. 186, no. 1. Springer Nature, 2022.
Mysliwy K, Seiringer R. 2022. Polaron models with regular interactions at strong coupling. Journal of Statistical Physics. 186(1), 5.
Mysliwy, Krzysztof, and Robert Seiringer. “Polaron Models with Regular Interactions at Strong Coupling.” Journal of Statistical Physics, vol. 186, no. 1, 5, Springer Nature, 2022, doi:10.1007/s10955-021-02851-w.
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