Related papers: Wigner crystallization in the quantum 1D jellium a…
The uniform electron gas or UEG (also known as jellium) is one of the most fundamental models in condensed-matter physics and the cornerstone of the most popular approximation --- the local-density approximation --- within…
A Wigner crystal, a regular electron lattice arising from strong correlation effects, is one of the earliest predicted collective electronic states. This many-body state exhibits quantum and classical phase transitions and has been proposed…
It is an old idea of ours (H. B. "Nielsen Dual Models" section 6 "Catastrophe Theory Program" Scottish University Summer school 1976) that a most general material with only translation symmetry, but otherwise no symmetries should…
A floating Wigner crystal differs from the standard one by a spatial averaging over positions of the Wigner-crystal lattice. It has the same internal structure as the fixed crystal, but contrary to it, takes into account rotational and/or…
We consider a two-dimensional electron or hole system at zero temperature and low carrier densities, where the long-range Coulomb interactions dominate over the kinetic energy. In this limit the clean system will form a Wigner crystal.…
The behavior of two-dimensional electron gas (2DEG) in extreme coupling limits are reasonably well-understood, but our understanding of intermediate region remains limited. Strongly interacting electrons crystalize into a solid phase known…
Wigner crystallization in mesoscopic quantum dots containing only few ($N < 50$) electrons exhibits a number of interesting peculiarities: (i) there exist two distinct crystal phases, and (ii) the phase boundary sensitively depends on the…
In the preceding paper, the structure and thermodynamics of a given quantum system was represented by a corresponding classical system having an effective temperature, local chemical potential, and pair potential. Here, that formal…
In quantum theory, symmetry has to be defined necessarily in terms of the family of unit rays, the state space. The theorem of Wigner asserts that a symmetry so defined at the level of rays can always be lifted into a linear unitary or an…
Eugene Wigner predicted long ago that when the Coulomb interactions between electrons become much stronger than their kinetic energy, electrons crystallize into a closely packed lattice. A variety of two-dimensional systems have shown…
We study scattering of charge and spin excitations in a system of interacting electrons in one dimension. At low densities electrons form a one-dimensional Wigner crystal. To first approximation the charge excitations are the phonons in the…
The effect of dimensionality on materials properties has become strikingly evident with the recent discovery of graphene. Charge ordering phenomena can be induced in one dimension by periodic distortions of a material's crystal structure,…
We consider the Thomas--Fermi--Dirac--von~Weizs{\"a}cker model for a system composed of infinitely many nuclei placed on a periodic lattice and electrons with a periodic density. We prove that if the Dirac constant is small enough, the…
We study the quantum phase transition of interacting electrons in quantum wires from a one-dimensional (1D) linear configuration to a quasi-1D zigzag arrangement using quantum Monte Carlo methods. As the density increases from its lowest…
One-dimensional systems, such as nanowires or electrons moving along strong magnetic field lines, have peculiar thermalization physics. The binary collision of point-like particles, typically the dominant process for reaching thermal…
A tight binding model of electrons interacting via bare Coulomb repulsion is numerically investigated by use of the Density Matrix Renormalization Group method which we prove applicable also to very long range potentials. From the analysis…
A quantum system at equilibrium is represented by a corresponding classical system, chosen to reproduce thermodynamic and structural properties. The motivation is to allow application of classical strong coupling theories and molecular…
We introduce a new approach for the correlation energy of one- and two-valley two-dimensional electron gas (2DEG) systems. Our approach is based on a random phase approximation at high densities and a classical approach at low densities,…
Building on insights about the classical pathways to double ionization in strong laser fields we here propose a 1+1-dimensional model that captures essentials of the 3-d potential landscape and allows efficient studies of the process in…
The quantum-classical crossover from the Fermi liquid towards the Wigner solid is numerically revisited, considering small square lattice models where electrons interact via a Coulomb $U/r$ potential. The studies of models without disorder…