相关论文: Nonexistence in Thomas-Fermi-Dirac-von Weizs\"acke…

We demonstrate that electrons in quantum dots defined by electrostatic gates in semiconductor nanotubes freeze orderly in space realizing a `Wigner molecule'. Our exact diagonalisation calculations uncover the features of the electron…

We consider bosonic Coulomb systems with $N$-particles and $K$ static nuclei. Let $E_N^Z$ denote the ground state energy of a bosonic molecule of the total nuclear charge $Z$. We prove that the system has no normalizable ground state when…

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…

We study minimizers of non-autonomous energies with minimal growth and coercivity assumptions on the energy. We show that the minimizer is nevertheless the solution of the relevant Euler--Lagrange equation or inequality. The main tool is an…

Recently, we have proposed the existence of a universal relation between the maximal electric charge and total mass of any weakly self-gravitating object: $Z\leq Z^*={\alpha}^{-1/3}A^{2/3}$, where $Z$ is the number of protons, $A$ is the…

We reconsider the geometrically nonlinear Cosserat model for a uniformly convex elastic energy and write the equilibrium problem as a minimization problem. Applying the direct methods of the calculus of variations we show the existence of…

We derive the free energy for fermions and bosons from fragmentation data. Inspired by the symmetry and pairing energy of the Weizsacker mass formula we obtain the free energy of fermions (nucleons) and bosons (alphas and deuterons) using…

We consider the following time-independent nonlinear $L^2$-critical Schr\"{o}dinger equation \[ -\Delta u(x)+V(x)u(x)-a|x|^{-b}|u|^{1+\frac{4-2b}{N}}=\mu u(x)\,\ \hbox{in}\,\ \mathbb{R}^N, \] where $\mu\in\mathbb{R}$, $a>0$, $N\geq 1$,…

Using the Wentzel-Kramers-Brillouin method, we derive a modified form of the Thomas-Fermi approximation to electron density. This new result enables us to calculate the details of the self-consistent ion cores, as well as the ionization…

We study the self-interaction effects for the Dirac particle moving in an external field created by static charges in (1+1)-dimensions. Assuming that the total electric charge of the system vanishes, we show that the asymptotically linearly…

This paper investigates the existence and qualitative properties of minimizers for a class of nonlocal micromagnetic energy functionals defined on bounded domains. The considered energy functional consists of a symmetric exchange…

We study isomerizations in quantum mechanics. We consider a neutral molecule composed of N quantum electrons and M classical nuclei and assume that the first eigenvalue of the corresponding N-particle Schr\"odinger operator possesses two…

In this paper, we show the existence and non-existence of minimizers of the following minimization problems which include an open problem mentioned by Horiuchi and Kumlin in 2012: \begin{align*} G_a := \inf_{u \in W_0^{1,N}(\Omega )…

In the context of an idealized model describing an atom coupled to black-body radiation at a sufficiently high positive temperature, we show that the atom will end up being ionized in the limit of large times. Mathematically, this is…

The crystallization of electrons in quasi low-dimensional solids is studied in a model which retains the full three-dimensional nature of the Coulomb interactions. We show that restricting the electron motion to layers (or chains) gives…

Dirac in 1931 gave a beautiful argument for the quantization of electric charge, which required only the existence in the universe of one magnetic monopole, because gauge invariance of the interaction between the pole and any charge could…

In a previous paper (http://www.phys.uri.edu/people/nightingale/publications.html, chem-ph/9406003) we developed a form of variational trial wave function and applied it to van der Waals clusters: five or less atoms of Ar and Ne modeled by…

We consider a stationary drift-diffusion system with ionic charge carriers and external generation of electron and hole charge carriers. This system arises, among other applications, in the context of semiconductor modeling for perovskite…

This doctoral thesis is devoted to the analysis of some minimization problems that involve nonlocal functionals. We are mainly concerned with the $s$-fractional perimeter and its minimizers, the $s$-minimal sets. We investigate the behavior…

The theory of point-particles in classical electrodynamics has a well-known problem of infinite self-energy, and the same is true of quantum electrodynamics. Instead of concluding that there is no such thing as a true point-particle, it is…