Related papers: The Polaron at Strong Coupling
We consider the Fr\"ohlich model of a polaron, and show that its effective mass diverges in the strong coupling limit.
We study the Fr\"ohlich polaron model in $\mathbb{R}^3$, and establish the subleading term in the strong coupling asymptotics of its ground state energy, corresponding to the quantum corrections to the classical energy determined by the…
We investigate the Fr\"ohlich polaron model on a three-dimensional torus, and give a proof of the second-order quantum corrections to its ground-state energy in the strong-coupling limit. Compared to previous work in the confined case, the…
We consider the Fr\"ohlich polaron model in the strong coupling limit. It is well known that to leading order the ground state energy is given by the (classical) Pekar energy. In this work, we establish the subleading correction, describing…
We study the Fr\"ohlich polaron model in $\mathbb{R}^3$, and prove a lower bound on its ground state energy as a function of the total momentum. The bound is asymptotically sharp at large coupling. In combination with a corresponding upper…
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…
We study the Fr\"ohlich polaron in the regime of strong coupling and prove the asymptotically sharp lower bound on the effective mass $m_{\mathrm{eff}}(\alpha)\geq \alpha^4 m_{\mathrm{LP}}-C\alpha^{4-\epsilon}$, where $m_{\mathrm{LP}}$ is…
The polaron model of H. Fr\"ohlich describes an electron coupled to the quantized longitudinal optical modes of a polar crystal. In the strong-coupling limit one expects that the phonon modes may be treated classically, which leads to a…
We study the qualitative behaviour of the energy-momentum relation of the Fr\"ohlich polaron at fixed coupling strength. Among other properties, we show that it is non-decreasing and that the correction to the quasi-particle energy is…
This paper is concerned with Fr\"ohlich polarons subject to external electromagnetic fields in the limit of large electron-phonon coupling. To leading order in the coupling constant, $\sqrt\alpha$, the ground state energy is shown to be…
The bipolaron are two electrons coupled to the elastic deformations of an ionic crystal. We study this system in the Fr\"{o}hlich approximation. If the Coulomb repulsion dominates, the lowest energy states are two well separated polarons.…
We consider the Fr\"ohlich $N$-polaron Hamiltonian in the strong coupling limit and bound the ground state energy from below. In particular, our lower bound confirms that the ground state energy of the Fr\"ohlich polaron and the ground…
A detailed consideration is given to the translation-invariant theory of Tulub polaron constructed without the use of Pekar ansatz. A fundamental result of the theory is that the value of the polaron energy is lower than that obtained on…
The solution for the large-radius Fr\"{o}hlich polaron in the Schr\"{o}dinger representation of the quantum theory is constructed in the entire range of variation of the coupling constant. The energy and the effective mass of the polaron…
The path measure corresponding to the Fr\"ohlich Polaron appearing in quantum statistical mechanics is defined as the tilted measure $$ \widehat{\mathbb P}_{\varepsilon,T}=…
Properties of the energy-momentum relation for the Fr\"ohlich polaron are of continuing interest, especially for large values of the coupling constant. By combining spectral theory with the available results on the central limit theorem for…
We consider the one-dimensional Froehlich polaron localized in a symmetric decreasing electric potential. It is known that the non-linear Pekar functional corresponding to our model admits a unique minimizer. In the strong-coupling limit,…
Fr\"{o}hlich's polaron Hamiltonian describes an electron coupled to the quantized phonon field of an ionic crystal. We show that in the strong coupling limit the dynamics of the polaron is approximated by an effective non-linear partial…
Starting from recent advances in the first-principles modeling of polarons, variational polaron equations in the strong-coupling adiabatic approximation are formulated in Bloch space. In this framework, polaron formation energy as well as…
We prove that there is a constant $\overline C\in (0,\infty)$ such that the effective mass $m(\alpha)$ of the Fr\"ohlich Polaron satisfies $m(\alpha) \geq \overline C \alpha^4$, which is sharp according to a long-standing prediction of…