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

Covariant Dirac Operators on Quantum Groups

We give a construction of a Dirac operator on a quantum group based on any simple Lie algebra of classical type. The Dirac operator is an element in the vector space U_q(\g) \otimes \mathrm{cl}_q(\g) where the second tensor factor is a $q$-deformation of the classical Clifford algebra. The tensor space U_q(\g) \otimes \mathrm{cl}_q(\g) is given a structure of the adjoint module of the quantum group and the Dirac operator is invariant under this action. The purpose of this approach is to construct equivariant Fredholm modules and $K$-homology cycles. This work generalizes the operator introduced by Bibikov and Kulish in \cite{BK}

Far-infrared spectra of lateral quantum dot molecules

We study effects of electron-electron interactions and confinement potential on the magneto-optical absorption spectrum in the far-infrared range of lateral quantum dot molecules. We calculate far-infrared (FIR) spectra for three different quantum dot molecule confinement potentials. We use accurate exact diagonalization technique for two interacting electrons and calculate dipole-transitions between two-body levels with perturbation theory. We conclude that the two-electron FIR spectra directly reflect the symmetry of the confinement potential and interactions cause only small shifts in the spectra. These predictions could be tested in experiments with nonparabolic quantum dots by changing the number of confined electrons. We also calculate FIR spectra for up to six noninteracting electrons and observe some additional features in the spectrum.Comment: For better quality Figs download manuscript from http://www.fyslab.hut.fi/~mma/FIR/Helle_qdmfir.ps.g

Various spin-polarization states beyond the maximum-density droplet: a quantum Monte Carlo study

Using variational quantum Monte Carlo method, the effect of Landau-level mixing on the lowest-energy--state diagram of small quantum dots is studied in the magnetic field range where the density of magnetic flux quanta just exceeds the density of electrons. An accurate analytical many-body wave function is constructed for various angular momentum and spin states in the lowest Landau level, and Landau-level mixing is then introduced using a Jastrow factor. The effect of higher Landau levels is shown to be significant; the transition lines are shifted considerably towards higher values of magnetic field and certain lowest-energy states vanish altogether.Comment: 4 pages, 2 figures. Submitted to Phys. Rev.

Many-body wave function for a quantum dot in a weak magnetic field

The ground states of parabolically confined electrons in a quantum dot are studied by both direct numerical diagonalization and quantum Monte Carlo (QMC) methods. We present a simple but accurate variational many-body wave function for the dot in the limit of a weak magnetic field. The wave function has the center-of-mass motion restricted to the lowest-energy state and the electron-electron interaction is taken into account by a Jastrow two-body correlation factor. The optimized wave function has an accuracy very close to the state-of-the-art numerical diagonalization calculations. The results and the computational efficiency indicate that the presented wave function combined with the QMC method suits ideally for studies of large quantum dots.Peer reviewe

A new proof for the decidability of D0L ultimate periodicity

We give a new proof for the decidability of the D0L ultimate periodicity problem based on the decidability of p-periodicity of morphic words adapted to the approach of Harju and Linna.Comment: In Proceedings WORDS 2011, arXiv:1108.341

Functional Landscape Connectivity Of Greater Sage Grouse Habitat In A Multiple Use Landscape

Maintaining connectivity of sage-grouse habitat is critical to managing sage-grouse populations in the presence of widespread human disturbance. We used an empirical approach to model connectivity of a landscape based on resource selection of free-ranging GPS-collared greater sage-grouse (Centrocercus urophasianus) in a natural gas field in central Wyoming. We analyzed resource selection during three movement states (encamped, traveling, and relocating) and incorporated turning angle to identify features that functioned as barriers or conduits to movement. To illustrate application of the results we used the resource selection model to create spatially-explicit predictive maps identifying areas that generally provided large amounts of high quality ‘movement habitat.’ We found that both males and females selected for vegetation variables at multiple spatial scales. When traveling or relocating, males and females tended to avoid natural gas and oil wells and associated infrastructure and avoided areas with high topographic roughness within 800m. High topographic roughness was a barrier for traveling males. Relocating females were more likely to travel in a straight direction through areas of high road density and steep slopes. The predictive maps validated well using independent GPS location data. These results provide insight into habitat preferences of sage-grouse and can be used for both general and site-specific guidance on identifying habitats preferred or avoided during moderate and long distance movements of sage-grouse. When combined with critical seasonal use maps, e.g., nesting/brooding habitat and winter range, land managers could delineate areas of high value for connectivity of critical seasonal use areas

Interacting electrons on a quantum ring: exact and variational approach

We study a system of interacting electrons on a one-dimensional quantum ring using exact diagonalization and the variational quantum Monte Carlo method. We examine the accuracy of the Slater-Jastrow -type many-body wave function and compare energies and pair distribution functions obtained from the two approaches. Our results show that this wave function captures most correlation effects. We then study the smooth transition to a regime where the electrons localize in the rotating frame, which for the ultrathin quantum ring system happens at quite high electron density.Comment: 19 pages, 10 figures. Accepted for publication in the New Journal of Physic

Electronic structure of rectangular quantum dots

We study the ground state properties of rectangular quantum dots by using the spin-density-functional theory and quantum Monte Carlo methods. The dot geometry is determined by an infinite hard-wall potential to enable comparison to manufactured, rectangular-shaped quantum dots. We show that the electronic structure is very sensitive to the deformation, and at realistic sizes the non-interacting picture determines the general behavior. However, close to the degenerate points where Hund's rule applies, we find spin-density-wave-like solutions bracketing the partially polarized states. In the quasi-one-dimensional limit we find permanent charge-density waves, and at a sufficiently large deformation or low density, there are strongly localized stable states with a broken spin-symmetry.Comment: 8 pages, 9 figures, submitted to PR

Revisiting the Equivalence Problem for Finite Multitape Automata

The decidability of determining equivalence of deterministic multitape automata (or transducers) was a longstanding open problem until it was resolved by Harju and Karhum\"{a}ki in the early 1990s. Their proof of decidability yields a co_NP upper bound, but apparently not much more is known about the complexity of the problem. In this paper we give an alternative proof of decidability, which follows the basic strategy of Harju and Karhumaki but replaces their use of group theory with results on matrix algebras. From our proof we obtain a simple randomised algorithm for deciding language equivalence of deterministic multitape automata and, more generally, multiplicity equivalence of nondeterministic multitape automata. The algorithm involves only matrix exponentiation and runs in polynomial time for each fixed number of tapes. If the two input automata are inequivalent then the algorithm outputs a word on which they differ