R. G. Nazmitdinov

TWO-ELECTRON QUANTUM DOT IN A MAGNETIC FIELD: ANALYTICAL RESULTS

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 cases. Exact conditions for phase transitions due to the electron-electron interaction in a quantum dot as a function of the dot size and magnetic field are calculated.

Chaos in axially symmetric potentials with octupole deformation.

Classical and quantum mechanical results are reported for the single particle motion in a harmonic oscillator potential which is characterized by a quadrupole deformation and an additional octupole deformation. The chaotic character of the motion is strongly dependent on the quadrupole deformation in that for a prolate deformation virtually no chaos is discernible while for the oblate case the motion shows strong chaos when the octupole term is turned on.

Roto-vibrational spectrum and Wigner crystallization in two-electron parabolic quantum dots

We provide a quantitative determination of the crystallization onset for two electrons in a parabolic two-dimensional confinement. This system is shown to be well described by a rotovibrational model, Wigner crystallization occurring when the rotational motion gets decoupled from the vibrational one. The Wigner molecule thus formed is characterized by its moment of inertia and by the corresponding sequence of rotational excited states. The role of a vertical magnetic field is also considered. Additional support to the analysis is given by the Hartree-Fock phase diagram for the ground state and by the random-phase approximation for the moment of inertia and vibron excitations.

Conformal Hamiltonian dynamics of general relativity

The General Relativity formulated with the aid of the spin connection coefficients is considered in the finite space geometry of similarity with the Dirac scalar dilaton. We show that the redshift evolution of the General Relativity describes the vacuum creation of the matter in the empty Universe at the electroweak epoch and the dilaton vacuum energy plays a role of the dark energy.

The microscopic description of the isovector dipole excitations at high spins

Abstract The strength functions of the γ-spectrum obtained from the decay of fast rotating nuclei by deexcitation of the isovector dipole modes are calculated in a microscopic model.

Finite-thickness effects in ground-state transitions of two-electron quantum dots

Using the exactly solvable excitation spectrum of two-electron quantum dots with parabolic potential, we show that the inclusion of the vertical extension of the quantum dot provides a consistent description of the experimental findings of Nishi et al. [Phys.Rev.B75, 121301(R) (2007)]. We found that the second singlet-triplet transition in the ground state is a vanishing function of the lateral confinement in the three-dimensional case, while it always persists in the two-dimensional case. We show that a slight decrease of the lateral confinement leads to a formation of the Wigner molecule at low magnetic fields.

Symmetry breaking and the random-phase approximation in small quantum dots

The random-phase approximation has been used to compute the properties of parabolic two-dimensional quantum dots beyond the mean-field approximation. Special emphasis is put on the ground state correlation energy, the symmetry restoration, and the role of the spurious modes within the random-phase approximation. A systematics with the Coulombic interaction strength is presented for the 2-electron dot, while for the 6- and 12-electron dots selected cases are discussed. The validity of the random-phase approximation is assessed by comparison with available exact results.

Equilibrium properties of fast-rotating headed nuclei

Abstract We report on calculations of the equilibrium deformation in excited heated rotating nuclei. At A ∼ 150–200 and temperature t > t c ≈ 1.2 MeV the shell effects turn out to be small to compete with the variations of the liquid drop component of the energy. The transition from the shape of a “cool” nucleus to that of a “hot” nucleus takes place at t c and in deformed nuclei resembles a phase transition. The stiffness parameter with respect to shape variations at t c is anomalously low.

Nonaxial octupole deformations in light N = Z nuclei at high spins

High spin states of 32 S and 56 Ni are investigated by means of the cranking HartreeFock method with the Gogny interaction without imposing a restriction on the axial reflection symmetry. It was found that a non-axial octupole deformation of the Y31 type becomes important in the yrast states of 32 S. A similar effect is predicted for the nucleus 56 Ni.

Spin control in semiconductor quantum wires: Rashba and Dresselhaus interaction

Conselleria d’Educaci´o i Cultura, E-07004 Palma de Mallorca, Spain(Dated: November 30, 2008)We show that spin-flip rotation in a semiconductor quantum wire, caused by the Rashba andthe Dresselhaus interactions (both of arbitrary strengths), can be suppressed by dint of an in-planemagnetic field. We found a new type of symmetry, which arises at a particular set of intensity andorientation of the magnetic field and explains this suppression. Based on our findings, we proposea transport experiment to measure the strengths of the Rashba and the Dresselhaus interactions.