Variational Monte Carlo for Interacting Electrons in Quantum Dots

We use a variational Monte Carlo algorithm to solve the electronic structure of two-dimensional semiconductor quantum dots in external magnetic field. We present accurate many-body wave functions for the system in various magnetic field regimes. We show the importance of symmetry, and demonstrate how it can be used to simplify the variational wave functions. We present in detail the algorithm for efficient wave function optimization. We also present a Monte Carlo -based diagonalization technique to solve the quantum dot problem in the strong magnetic field limit where the system is of a multiconfiguration nature.Comment: 34 pages, proceedings of the 1st International Meeting on Advances in Computational Many-Body Physics, to appear in Journal of Low Temperature Physics (vol. 140, nos. 3/4

On the stability of non-isothermal Bonnor-Ebert spheres. II. The effect of gas temperature on the stability

Aims. We investigate the stability of non-isothermal Bonnor-Ebert spheres with a model that includes a self-consistent calculation of the gas temperature. This way we can discard the assumption of equality between the dust and gas temperatures, and study the stability as the gas temperature changes with chemical evolution of the gas. Methods. We use a gas-grain chemical model including a time-dependent treatment of depletion onto grain surfaces, which strongly influences the gas temperature as the main coolant, CO, depletes from the gas. Dust and gas temperatures are solved with radiative transfer. For comparison with previous work, we assume that the cores are deeply embedded in a larger external structure, corresponding to visual extinction $A_{\rm V}^{\rm ext}=10$ mag. Results. We find that the critical non-dimensional radius $\xi_1$ derived here is similar to our previous work where we assumed $T_{\rm dust}=T_{\rm gas}$; the $\xi_1$ values lie below the isothermal critical value $\xi_0\sim6.45$, but the difference is less than 10%. Chemical evolution does not affect notably the stability condition of low-mass cores (<0.75 $M_\odot$). For higher masses the decrease of cooling owing to CO depletion causes substantial temporal changes in the temperature and density profiles of the cores. In the mass range 1-2 $M_\odot$ , $\xi_1$ decreases with chemical evolution, whereas above 3 $M_\odot$ , $\xi_1$ instead increases. We also find that decreasing $A_{\rm V}^{\rm ext}$ increases the gas temperature especially when the gas is chemically old, causing $\xi_1$ to increase with respect to models with higher $A_{\rm V}^{\rm ext}$. The derived $\xi_1$ values are close to $\xi_0$. The density contrast between the core center and edge varies between 8 to 16 depending on core mass and the chemical age of the gas, compared to the constant value $\sim$ 14.1 for the isothermal BES.Comment: 7 pages, 5 figures; accepted for publication in A&A; abstract (heavily) abridged for arXi

Charge dynamics in two-electron quantum dots

We investigate charge dynamics in a two-electron double quantum dot. The quantum dot is manipulated by using a time-dependent external voltage that induces charge oscillations between the dots. We study the dependence of the charge dynamics on the external magnetic field and on the periodicity of the external potential. We find that for suitable parameter values, it is possible to induce both one-electron and two-electron oscillations between the dots.Comment: 4 pages, 7 figures, proceedings of the Quantum Dot 2010 conferenc

Exchange-correlation potentials for inhomogeneous electron systems in two dimensions from exact diagonalization: comparison with the local-spin-density approximation

We consider electronic exchange and correlation effects in density-functional calculations of two-dimensional systems. Starting from wave function calculations of total energies and electron densities of inhomogeneous model systems, we derive corresponding exchange-correlation potentials and energies. We compare these with predictions of the local-spin-density approximation and discuss its accuracy. Our data will be useful as reference data in testing, comparing and parametrizing exchange and correlation functionals for two-dimensional electronic systems.Comment: Submitted to Physical Review B on January 3, 2012. Second revised version submitted on April 13, 201

Lattice density-functional theory on graphene

A density-functional approach on the hexagonal graphene lattice is developed using an exact numerical solution to the Hubbard model as the reference system. Both nearest-neighbour and up to third nearest-neighbour hoppings are considered and exchange-correlation potentials within the local density approximation are parameterized for both variants. The method is used to calculate the ground-state energy and density of graphene flakes and infinite graphene sheet. The results are found to agree with exact diagonalization for small systems, also if local impurities are present. In addition, correct ground-state spin is found in the case of large triangular and bowtie flakes out of the scope of exact diagonalization methods.Peer reviewe