Related papers: Two electrons in a two dimensional random potentia…
It is shown that the Coulomb correlation problem for a system of two electrons (two charged particles) in an external oscillator potential possesses a hidden $sl_2$-algebraic structure being one of recently-discovered quasi-exactly-solvable…
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…
Recent work on the temperature-driven delocalization in the quantum Hall regime is reviewed, with emphasis on the role of electron-electron interactions and the correlation properties of disorder. We have stressed (i) the crucial role of…
Two interacting electrons in a harmonic oscillator potential under the influence of a perpendicular homogeneous magnetic field are considered. Analytic expressions are obtained for the energy spectrum of the two- and three-dimensional…
Recent experimental progress in development of on-demand sources of electrons propagating along depleted quantum Hall edge channels has enabled creation and characterization of sufficiently compact single- and two-electron distributions…
Crystallization of a classical two-dimensional one-component plasma (electrons interacting with the Coulomb repulsion in a uniform neutralizing positive background) is investigated with a molecular dynamics simulation. The positional and…
Low-lying energy levels of two interacting electrons confined in a two-dimensional parabolic quantum dot in the presence of an external magnetic field have been revised within the frame of a novel model. The present formalism, which gives…
We obtain by invariance arguments the relativistic and non-relativistic invariant dynamical equations of a classical model of a spinning electron. We apply the formalism to a particular classical model which satisfies Dirac's equation when…
We use a nonlinear Schroedinger-Poisson equation to describe two interacting electrons with opposite spins confined in a parabolic potential, a quantum dot. We propose an effective form of the Poisson equation taking into account the…
We calculate in a linear response the admittance of a quantum dot out of equilibrium. The interaction between two electrons with opposite spins simultaneously residing on the resonant level is modeled by an Anderson Hamiltonian. The…
Separate spin evolution quantum hydrodynamics is generalized to include the Coulomb exchange interaction. The Coulomb exchange interaction is considered as the interaction between the spin-down electrons being in the quantum states occupied…
We study a two-dimensional system of two Coulombically interacting electrons in an external harmonic confining potential. More precisely, we present calculations for the singlet ground-state of the system. We explain the nature of the…
We study the spectral statistics of interacting spinless fermions in a two-dimensional disordered lattice. Within a full quantum treatment for small few-particle-systems, we compute the low-energy many-body states numerically. While at weak…
The unique property of Coulomb interaction in strict one-dimensional (1D) system is revealed that the Coulomb repulsion energy of paired electrons is divergent. As consequences, electrons in 1D system can not doubly occupy the same spatial…
Spatial localization of the electrons of an atom or molecule is studied in models of non-relativistic matter coupled to quantized radiation. We give two definitions of the ionization threshold. One in terms of spectral data of cluster…
The analysis of correlation energy of the simplest first approximation of a variational method for the intrashell states of two-electron atoms is the purpose of the present work. This method allows to divide energy of atom on Coulomb and…
The magnetic character of the ground-state of two electrons on a double quantum dot, connected in series to left and right single-channel leads, is considered. By solving exactly for the spectrum of the two interacting electrons, it is…
Effects of randomness have supplied fundamental problems in condensed matter physics and localization due to interference of quantum mechanical electrons are well studied as the Anderson localization. Although we have well established…
We consider the combined influence of disorder, electron-electron interactions and quantum hopping on the properties of electronic systems in a localized phase, approaching an insulator-metal transition. The generic models in this regime…
We consider two particles with a local interaction $U$ in a random potential at a scale $L_1$ (the one particle localization length). A simplified description is provided by a Gaussian matrix ensemble with a preferential basis. We define…