Related references
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Article
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Summary: In this study, we investigate the characteristics of a class of polaron-type Hamiltonians under the strong-coupling limit. The results show that the ground state energy of the system is bounded by the total momentum, in agreement with the semiclassical approximation. Additionally, we demonstrate that the effective mass diverges in the strong coupling limit for all models in all spatial dimensions. Moreover, for certain models with a phonon dispersion relation that grows at least linearly with momentum, we obtain an asymptotic formula for the effective mass quotient, which agrees with the semiclassical Landau-Pekar formula and provides a rigorous confirmation of its validity.
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Summary: The application of the Feynman-Kac formula to Polaron models of quantum theory leads to the path measure of Brownian motion perturbed by a translation-invariant pair potential. This study addresses the validity of a central limit theorem in infinite volume and shows the existence of relevant infinite volume limits. The results apply to the Frohlich Polaron for all coupling constants.
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Summary: In this work, the subleading correction of the ground state energy in the Frohlich polaron model in the strong coupling limit was established, taking into account quantum fluctuations around the classical limit. The study focused on a confined polaron model, where both the electron and the polarization field are restricted to a finite volume set with a linear size determined by the natural length scale of the Pekar problem.
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Summary: The study investigates the Frohlich polaron model on a three-dimensional torus, providing a proof of the second-order quantum corrections to its ground-state energy in the strong-coupling limit. The presence of translational symmetry (and its breakdown in the Pekar approximation) makes the analysis significantly more challenging than in previous studies in confined cases.
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Article
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David Mitrouskas
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