Related papers: A Finite Element Configuration Interaction Method …
In these two related parts we present a set of methods, analytical and numerical, which can illuminate the behaviour of quantum system, especially in the complex systems. The key points demonstrating advantages of this approach are: (i)…
Wigner crystallization of electrons in a 2D quantum dots is reported. It proceeds in two stages: I) via radial ordering of electrons on shells and II) freezing of the inter-shell rotation. The phase boundary of the crystal is computed in…
Equilibration of a one-dimensional system of interacting electrons requires processes that change the numbers of left- and right-moving particles. At low temperatures such processes are strongly suppressed, resulting in slow relaxation…
A system of confined charged electrons interacting via the long-range Coulomb force can form a Wigner crystal due to their mutual repulsion. This happens when the potential energy of the system dominates over its kinetic energy, i.e., at…
What are the ground states of an interacting, low-density electron system? In the absence of disorder, it has long been expected that as the electron density is lowered, the exchange energy gained by aligning the electron spins should…
Wigner crystallization can be induced in a quantum dot by increasing the effective electron-electron interaction through a decrease of the electron density or by the application of a strong magnetic field. We show that the ground state in…
We investigate the ground-state properties of a collection of \textit{N} non-interacting electrons in a macroscopic volume $\Omega$ also containing a crystalline array of \textit{N} spheres of radius $r_c$ each taken as largely impenetrable…
When the motion of electrons is restricted to a plane under a perpendicular magnetic field B, a variety of quantum phases emerge at low temperatures whose properties are dictated by the Coulomb interaction and its interplay with disorder.…
In spite of unscreened Coulomb interactions close to charge neutrality, relativistic massless electrons in graphene allegedly behave as noninteracting particles. A clue to this paradox is that both interaction and kinetic energies scale…
Understanding electron localization in molecules and materials plays a central role in electronic structure theory, and will increase in importance with the rise of data-driven approaches. The electron localization function (ELF) is widely…
Analysis of quantum dot structures is a current topic with important applications in solid-state digital logic design, quantum information technology and quantum optics. In this work, we show a variational formulation for the solution of…
We present a new high-performance configuration interaction code optimally designed for the calculation of the lowest energy eigenstates of a few electrons in semiconductor quantum dots (also called artificial atoms) in the strong…
In quantum mechanics, the Wigner function $\rho_W(\textbf{r},\textbf{p})$ serves as a phase-space representation, capturing information about both the position $\textbf{r}$ and momentum $\textbf{p}$ of a quantum system. The Wigner function…
Calculations for two electrons in an elliptic quantum dot, using symmetry breaking at the unrestricted Hartree-Fock level and subsequent restoration of the broken parity via projection techniques, show that the electrons can localize and…
Two electrons move in a quasi one--dimensional wire under the influence of a short--range interaction. We restrict Hilbert space to those states where the two electrons are close to each other. Using supersymmetry, we present a complete…
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…
Classical surfaces in phase space correspond to quantum states in Hilbert space. Subsystems specify factor spaces of the Hilbert space. An entangled state corresponds semiclassically to a surface that cannot be decomposed into a product of…
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…
Energy spectra, spin configurations, and entanglement characteristics of a system of four electrons in lateral double quantum dots are investigated using exact diagonalization (EXD), as a function of interdot separation, applied magnetic…
Coulomb interactions can have a decisive effect on the ground state of electronic systems. The simplest system in which interactions can play an interesting role is that of two electrons on a string. In the presence of strong interactions…