Non-linear magneto-transport through small quantum dots at strong intra-dot correlations

Nonlinear transport through a quantum dot is studied in the limit of weak and strong intra-dot Coulomb interaction. For the latter regime the nonequilibrium self-consistent mean field equations for energies and spectral weights of one-electron transitions are formulated. The increase of the bias-voltage window leads to a strong deviation from Gibbs statistics: the populations of states involved into a tunnelling are equalizing in this limit even at low temperature. For a symmetric coupling of a quantum dot to two leads we provide simple analytical relations between heights of the current steps and degeneracy of a spectrum in a two-dimensional parabolic dot in a perpendicular magnetic field in the both regimes.Comment: 40 preprint pages, 6 figure

Klein collimation by rippled graphene superlattice

The hybridization of $\sigma$ and $\pi$ orbitals of carbon atoms in graphene depends on the surface curvature. Considering a single junction between flat and rippled graphene subsystems, it is found an accumulation of charge in the rippled subsystem due to Klein penetration phenomenon that gives rise to n-p junction. Using this fact, we show that the momentum distribution of electrons in ballisitically propagating beam can be selective without a waveguide, or external electric, and/or magnetic fields in graphene strip under experimentally feasible one-dimensional periodic potential. Such a potential is created with the aid of superlattice that consists of periodically repeated graphene pieces withdifferent hybridizations of carbon orbits, produced by variation of the graphene surface curvature. The charge redistribution and selected transmission of electrons, caused by the superlattice, allows to control the electron focusing in the considered system by simply changing the element properties in the superlatticeComment: 17 pages, 7 figure

Analytic solutions to the problem of Coulomb and confining potentials

The oscillator representation method is presented and used to calculate the energy spectra for a superposition of Coulomb and power-law potentials and for Coulomb and Yukawa potentials. The method provides an efficient way to obtain analytic results for arbitrary values of the parameters specifying the above-type potentials. The calculated energies of the ground and excited states of the quantum systems in question are found to comply well with exact results.Comment: 25 pages (Latex

Triplet absorption spectroscopy and electromagnetically induced transparency

Coherence phenomena in four-level atomic system, cyclicly driven by three coherent fields, are investigated thoroughly at zero and weak magnetic fields. Each strongly interacting atomic state is converted to a triplet due to a dynamical Stark effect. Two dark lines with a Fano-like profile are arising in the triplet absorption spectrum with anomalous dispersions. We provide the conditions to control the widths of the transparency windows by means of the relative phase of the driving fields and the intensity of the microwave field, that closes the optical system loop. The effect of the Doppler broadening on results of the triplet absorption spectroscopy is analysed in detail.Comment: 11 pages, 7 figure

Entanglement as an indicator of a geometrical crossover in a two-electron quantum dot in a magnetic field

We found that a downwardly concave entanglement evolution of the ground state of a two-electron axially symmetric quantum dot testifies that a shape transition from a lateral to a vertical localization of two electrons under a perpendicular magnetic field takes place. Although affected, the two-electron probability density does not exhibit any prominent change.Comment: 4 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1112.347

Self-Consistent Harmonic Oscillator Model and Tilted Rotation

The three dimensional harmonic oscillator model including a cranking term is used for an energy variational calculation. Energy minima are found under variation of the three oscillator frequencies determining the shape of the system for given values of the three components of the rotational vector which determines the orientation of the angular momentum in the intrinsic frame. Tilted rotations are established by numerical means for triaxial nuclei. The onset of tilted rotations is related to an instability of the mean field as verified by the random phase approximation. Analytic expressions are derived for the critical rotational frequencies associated with the mean field instability.Comment: 16 pages, 2 figures, extended versio

Magnetic alteration of entanglement in two-electron quantum dots

Quantum entanglement is analyzed thoroughly in the case of the ground and lowest states of two-electron axially symmetric quantum dots under a perpendicular magnetic field. The individual-particle and the center-of-mass representations are used to study the entanglement variation at the transition from interacting to noninteracting particle regimes. The mechanism of symmetry breaking due to the interaction, that results in the states with symmetries related to the later representation only, being entangled even at the vanishing interaction, is discussed. The analytical expression for the entanglement measure based on the linear entropy is derived in the limit of noninteracting electrons. It reproduces remarkably well the numerical results for the lowest states with the magnetic quantum number M>2 in the interacting regime. It is found that the entanglement of the ground state is a discontinuous function of the field strength. A method to estimate the entanglement of the ground state, characterized by the quantum number M, with the aid of the magnetic field dependence of the addition energy is proposed.Comment: 21 pages, 7 figure

Shape transitions in two-body systems: two-electron quantum dots in a magnetic field

We present a thorough analysis of the electron density distribution (shape) of two electrons, confined in the three-dimensional harmonic oscillator potential, as a function of the perpendicular magnetic field.Explicit algebraic expressions are derived in terms of the system's parameters and the magnetic field strength to trace the shape transformations in the ground and low-lying excited states. We found that the interplay of the classical and quantum properties lead to a quantum shape transition from a lateral to a vertical localization of electrons in low-lying excited states at relatively strong Coulomb interaction with alteration of the magnetic field. In contrast, in that regime in the ground states the electrons form always a ring type distribution in the lateral plane. The analytical results demonstrate a good agreement with quantum numerical results near the transition point and at high magnetic field.Comment: 15 pages, 12 figure

Magnetic Field Dependence of Magic Numbers in Small Quantum Dots

It is argued that various kind of shell structure which occurs at specific values of the magnetic field should be observable in small quantum dots in the addition energies and the magnetic susceptibility.Comment: 4 pages (Latex file) including 4 epsi figures. For enquires see e-mail addresses at the end of the pape

Thomson rings in a disk

We discuss the basic principles of a self-organization of a finite number of charged particles interacting via the 1/r Coulomb potential in a disk geometry. Our approach is based on the cyclic symmetry and periodicity of the Coulomb interaction between particles located on several rings. As a result, a system of equations is derived, which allows us readily to determine with a high accuracy the equilibrium configurations of a few hundreds charged particles. For $n\gtrsim 200$ we predict the formation of a hexagonal core and valence circular rings for the centered configurations.Comment: 13 pages, 3 figures, 1 table. Published version with a new figure and extended discussio