Related papers: Identification of the Polaron measure in strong co…
The {\it{Polaron measure}} is defined as the transformed path measure $$\widehat{\mathbb P}_{\epsilon,T}= Z_{\epsilon,T}^{-1}\,\, \exp\bigg\{\frac{1}{2}\int_{-T}^T\int_{-T}^T\frac{\epsilon\e^{-\epsilon|t-s|}}{|\omega(t)-\omega(s)|} \,\d s…
We consider the Fr\"ohlich model of the Polaron whose path integral formulation leads to the transformed path measure $$ \widehat{\mathbb P}_{\alpha,T}(\mathrm d\omega)= Z_{\alpha,T}^{-1}\,\,…
We review old and new results on the Fr\"ohlich polaron model. The discussion includes the validity of the (classical) Pekar approximation in the strong coupling limit, quantum corrections to this limit, as well as the divergence of 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 consider mean-field interactions corresponding to Gibbs measures on interacting Brownian paths in three dimensions. The interaction is self-attractive and is given by a singular Coulomb potential. The logarithmic asymptotics of the…
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…
The application of the Feynman-Kac formula to Polaron models of quantum theory leads to the path measure of Brownian motion perturbed by a pair potential that is translation invariant both in space and time. An important problem in this…
The virial theorem for the translation-invariant theory of a polaron [3] is discussed. It is shown that, in [3], Tulub made a nonoptimal choice of variational parameters in the strong-coupling limit, which led to the violation of the virial…
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…
Measurements of the polarization and spin correlation in top quark pairs ($\mathrm{t\bar{t}}$) are presented using events with a single electron or muon and jets in the final state. The measurements are based on proton-proton collision data…
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 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…
The description of an impurity atom in a Bose-Einstein condensate can be cast in the form of Frohlich's polaron Hamiltonian, where the Bogoliubov excitations play the role of the phonons. An expression for the corresponding polaronic…
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 thermal equilibrium of classical pointlike counterions confined between symmetrically charged walls at distance $d$. At very large couplings when the counterion system is in its crystal phase, a harmonic expansion of particle…
It is well known that the Poisson-Boltzmann (PB) equation yields the exact counterion density around charged objects in the weak coupling limit. In this paper we generalize the PB approach to account for coupling of arbitrary strength by…
We investigate the emergence of temperature $T$ in the system-plus-reservoir paradigm starting from the fundamental microcanonical scenario at total fixed energy $E$ where, contrary to the canonical approach, $T=T(E)$ is not a control…
Determining the statistics of work done on a quantum system while strongly coupled to a reservoir is a formidable task, requiring the calculation of the full eigenspectrum of the combined system and reservoir. Here we show that this issue…
We consider the Fr\"ohlich Hamiltonian with large coupling constant $\alpha$. For initial data of Pekar product form with coherent phonon field and with the electron minimizing the corresponding energy, we provide a norm approximation of…