Related papers: Stability and Absence of Binding for Multi-Polaron…
The binding of polarons, or its absence, is an old and subtle topic. After defining the model we state some recent theorems of ours. First, the transition from many-body collapse to the existence of a thermodynamic limit for N polarons…
The binding of polarons, or its absence, is an old and subtle topic. Here we prove two things rigorously. First, the transition from many-body collapse to the existence of a thermodynamic limit for N polarons occurs precisely at U=2\alpha,…
We summarize our recent results on the ground state energy of multi-polaron systems. In particular, we discuss stability and existence of the thermodynamic limit, and we discuss the absence of binding in the case of large Coulomb repulsion…
For systems of $N$ charged fermions (e.g. electrons) interacting with longitudinal optical quantized lattice vibrations of a polar crystal we derive upper and lower bounds on the minimal energy within the model of H. Fr\"ohlich. The only…
In this paper estimates on the ground state energy of Fr\"ohlich $N$-polarons in electromagnetic fields in the strong coupling limit, $\alpha\to\infty$, are derived. It is shown that the ground state energy is given by $\alpha^2$ multiplied…
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 a multi-polaron model obtained by coupling the many-body Schr\"odinger equation for N interacting electrons with the energy functional of a mean-field crystal with a localized defect, obtaining a highly non linear many-body…
The last unsolved problem about the many-polaron system, in the Pekar-Tomasevich approximation, is the case of bosons with the electron-electron Coulomb repulsion of strength exactly 1 (the 'neutral case'). We prove that the ground state…
If the polaron coupling constant $\alpha$ is large enough, bipolarons or multi-polarons will form. When passing through the critical $\alpha_c$ from above, does the radius of the system simply get arbitrarily large or does it reach a…
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…
In the context of the massless Nelson model, we prove that two non-relativistic nucleons interacting with a massless meson field do not bind when a sufficiently strong Coulomb repulsion between the nucleons is added to the Hamiltonian. The…
The binding of a system of $N$ polarons subject to a constant magnetic field of strength $B$ is investigated within the Pekar-Tomasevich approximation. In this approximation the energy of $N$ polarons is described in terms of a…
We show how the stability conditions for a system of interacting fermions that conventionally involve variations of thermodynamic potentials can be rewritten in terms of one- and two-particle correlators. We illustrate the applicability of…
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…
We theoretically investigate the polaron physics of an impurity immersed in a two-dimensional Fermi sea, interacting via a p-wave interaction at finite temperature. In the unitary limit with a divergent scattering area, we find a…
We begin to study in this paper orbital and asymptotic stability of standing waves for a model of Schr\"odinger equation with concentrated nonlinearity in dimension three. The nonlinearity is obtained considering a {point} (or contact)…
We study a nonlinear Schr\"{o}dinger-Poisson system which reduces to the nonlinear and nonlocal equation \[- \Delta u+ u + \lambda^2 \left(\frac{1}{\omega|x|^{N-2}}\star \rho u^2\right) \rho(x) u = |u|^{q-1} u \quad x \in \mathbb R^N, \]…
We consider non-relativistic systems in quantum mechanics interacting through the Coulomb potential, and discuss the existence of bound states which are stable against spontaneous dissociation into smaller atoms or ions. We review the…
On the basis of analytic solutions of Schrodinger and Pauli equations for a uniform magnetic field and a single attractive $\delta({\bf r})$-potential the equations for the bound one-active electron states are discussed. It is vary…
It is shown that at least one particle is bound in the $N$-particle semi-relativistic Pauli-Fierz model with negative potential $V(\bx)$. It is assumed that the particles have no spin and obey the Bose or Boltzmann statistics, and the one…