Related papers: Wigner localization in two and three dimensions: a…
It was predicted by Wigner in 1934 that the electron gas will undergo a transition to a crystallized state when its density is very low. Whereas significant progress has been made towards the detection of electronic Wigner states, their…
We give a detailed survey of results obtained in the most recent half decade which led to a deeper understanding of the random displacement model, a model of a random Schr\"odinger operator which describes the quantum mechanics of an…
We present an extensive comparative study of ground-state densities and pair distribution functions for electrons confined in two-dimensional parabolic quantum dots over a broad range of coupling strength and electron number. We first use…
The problem of interacting electrons moving under the influence of a strong magnetic field in two dimensions on a finite disk is reconsidered. First, the results of exact diagonalizations for up to $N=9$ electrons for Coulomb as well as for…
We present a highly flexible computational scheme for studying correlated electrons confined by an arbitrary external potential in two-dimensional semiconductor quantum dots. The method starts by a Lagrange mesh calculation for the…
The spectral properties of up to four interacting electrons confined within a quasi one--dimensional system of finite length are determined by numerical diagonalization including the spin degree of freedom. The ground state energy is…
It is known that a gas of electrons in a uniform neutralizing background can crystallize and form a lattice if the electron density is less than a critical value. This crystallization may have two- or three-dimensional structure. Since the…
We discuss the localization of wavefunctions along planes containing the shortest periodic orbits in a three-dimensional billiard system with axial symmetry. This model mimicks the self-consistent mean field of a heavy nucleus at…
Motivated by recent experiments on radiative recombination of two-dimensional electrons in acceptor doped GaAs-AlGaAs heterojunctions as well as the success of a harmonic solid model in describing tunneling between two-dimensional electron…
It was recently argued that in small quantum dots the electrons could crystallize at much higher densities than in the infinite two-dimensional electron gas. We compare predictions that the onset of spin polarization and the formation of…
We study the propagation of high-frequency electromagnetic waves in randomly heterogeneous bianisotropic media with dissipative properties. For that purpose we consider randomly fluctuating optical responses of such media with correlation…
We propose a simple and efficient real-space approach for the calculation of the ground-state energies of Wigner crystals in 1, 2, and 3 dimensions. To be precise, we calculate the first two terms in the asymptotic expansion of the total…
Few-electron systems confined in two-dimensional parabolic quantum dots at high magnetic fields are studied by the Hartree-Fock (HF) and exact diagonalization methods. A generalized multicenter Gaussian basis is proposed in the HF method. A…
We formulate a three-dimensional semi-classical model to address triple and double ionization in three-electron atoms driven by intense infrared laser pulses. During time propagation, our model fully accounts for the Coulomb singularities,…
A new variational basis with well-behaved local approximation properties and multiple output is proposed for Coulomb systems. The trial function has proper behaviour at all Coulomb centres. Nonlinear asymptotic parameters are introduced…
We show that the exact wave function for two electrons, interacting through a Coulomb potential but constrained to remain on the surface of a $\mathcal{D}$-sphere ($\mathcal{D} \ge 1$), is a polynomial in the interelectronic distance $u$…
We introduce a new paradigm for finite and infinite strict-one-dimensional uniform electron gases. In this model, $n$ electrons are confined to a ring and interact via a bare Coulomb operator. In the high-density limit (small-$r_s$, where…
We discuss the construction of low-energy tight-binding Hamiltonians for condensed matter systems with a strong coupling to the quantum electromagnetic field. Such Hamiltonians can be obtained by projecting the continuum theory on a given…
This work explores the intersection of quantum mechanics and curved spacetime by employing the Wigner formalism to investigate quantum systems in the vicinity of black holes. Specifically, we study the quantum dynamics of a probe particle…
The realization of mixtures of excitons and charge carriers in van-der-Waals materials presents a new frontier for the study of the many-body physics of strongly interacting Bose-Fermi mixtures. In order to derive an effective low-energy…