Perttu Luukko

Introducing libeemd: a program package for performing the ensemble empirical mode decomposition

The ensemble empirical mode decomposition (EEMD) and its complete variant (CEEMDAN) are adaptive, noise-assisted data analysis methods that improve on the ordinary empirical mode decomposition (EMD). All these methods decompose possibly nonlinear and/or nonstationary time series data into a finite amount of components separated by instantaneous frequencies. This decomposition provides a powerful method to look into the different processes behind a given time series data, and provides a way to separate short time-scale events from a general trend. We present a free software implementation of EMD, EEMD and CEEMDAN and give an overview of the EMD methodology and the algorithms used in the decomposition. We release our implementation, libeemd, with the aim of providing a user-friendly, fast, stable, well-documented and easily extensible EEMD library for anyone interested in using (E)EMD in the analysis of time series data. While written in C for numerical efficiency, our implementation includes interfaces to the Python and R languages, and interfaces to other languages are straightforward.

Electronic structures in single self-assembled InAs quantum dashes detected by nanogap metal electrodes

We have investigated electronic structures in single self-assembled InAs quantum dashes (QDHs) coupled to metal nanogap electrodes. The fabricated QDH samples operate as single electron transistors, exhibiting high differential conductances as well as small charging/orbital quantization energies for large electron numbers. In the few electron regimes, the conductance and addition energies strongly depend on the number of the electrons. Calculation of electronic properties by spin-density-functional theory reveals that electron transport is affected by a drastic change in the electronic orbital shape. These transport properties are intrinsic to InAs QDH structures with a highly anisotropic wire-like shape.

Polyatomic Trilobite Rydberg Molecules in a Dense Random Gas

Trilobites are exotic giant dimers with enormous dipole moments. They consist of a Rydberg atom and a distant ground-state atom bound together by short-range electron-neutral attraction. We show that highly polar, polyatomic trilobite states unexpectedly persist and thrive in a dense ultracold gas of randomly positioned atoms. This is caused by perturbation-induced quantum scarring and the localization of electron density on randomly occurring atom clusters. At certain densities these states also mix with an s state, overcoming selection rules that hinder the photoassociation of ordinary trilobites.

Electron magneto-tunneling through single self-assembled InAs quantum dashes

We have investigated electron magneto-tunneling through single self-assembled InAs quantum dashes (QDHs) coupled to metal nanogap electrodes. The samples operate as single electron transistors and exhibit clear shell structures, reflecting the anisotropic shape of the QDHs. In high magnetic fields, the samples exhibit strongly orbital-dependent large diamagnetic shifts and large electron g-factors in the range |g| ~ 3–11. The strong level-to-level fluctuation of the g-factors implies the presence of strong spin–orbit interaction in this system. These properties suggest that InAs QDHs are promising for the manipulation of single-electron orbital/spin states by external electric/magnetic fields.

Bill2d — A software package for classical two-dimensional Hamiltonian systems☆

Abstract We present Bill2d , a modern and efficient C++ package for classical simulations of two-dimensional Hamiltonian systems. Bill2d can be used for various billiard and diffusion problems with one or more charged particles with interactions, different external potentials, an external magnetic field, periodic and open boundaries, etc. The software package can also calculate many key quantities in complex systems such as Poincare sections, survival probabilities, and diffusion coefficients. While aiming at a large class of applicable systems, the code also strives for ease-of-use, efficiency, and modularity for the implementation of additional features. The package comes along with a user guide, a developer’s manual, and a documentation of the application program interface (API). Program summary Program title: Bill2d Catalogue identifier: AEYL_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEYL_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 No. of lines in distributed program, including test data, etc.: 37098 No. of bytes in distributed program, including test data, etc.: 1155037 Distribution format: tar.gz Programming language: C++(14). Computer: Tested on x86 and x86 64 architectures. Operating systems: Tested on Linux, and OS X versions 10.9–10.11. Has the code been vectorized or parallelized?: Shared memory parallelization when simulating ensembles of systems. Vectorization of operations with R 2 vectors. RAM: Simulation dependent: kilobytes to gigabytes Classification: 4.3, 7.8, 7.9, 7.10, 16.9. External routines: Boost, CMake, GSL, HDF5; and optionally Google-Mock, GoogleTest, and Doxygen Nature of problem: Numerical propagation of classical two-dimensional single and many-body systems, possibly in a magnetic field, and calculation of relevant quantities such as Poincare sections, survival probabilities, diffusion co-efficients, etc. Solution method: Symplectic numerical integration of Hamilton’s equations of motion in Cartesian coordinates, or solution of Newton’s equations of motion if in a magnetic field. The program implements several well-established algorithms. Restrictions: Pointlike particles with equal masses and charges, although the latter restrictions are easy to lift. Unusual features: Program is efficient, extremely modular and easy to extend, and allows arbitrary particle–particle interactions. Additional comments: The source code is also available at https://bitbucket.org/solanpaa/bill2d . See README for locations of user guide, developer manual, and API docs. Running time: From milliseconds to days, depends on type of simulation.

Coulomb-interacting billiards in circular cavities

We apply a molecular dynamics scheme to analyze classically chaotic properties of a two-dimensional circular billiard system containing two Coulomb-interacting electrons. As such, the system resembles a prototype model for a semiconductor quantum dot. The interaction strength is varied from the noninteracting limit with zero potential energy up to the strongly interacting regime where the relative kinetic energy approaches zero. At weak interactions the bouncing maps show jumps between quasi-regular orbits. In the strong-interaction limit we find an analytic expression for the bouncing map. Its validity in the general case is assessed by comparison with our numerical data. To obtain a more quantitative view on the dynamics as the interaction strength is varied, we compute and analyze the escape rates of the system. Apart from very weak or strong interactions, the escape rates show consistently exponential behavior, thus suggesting strongly chaotic dynamics and a phase space without significant sticky regions within the considered time scales.We apply a molecular dynamics scheme to analyze classically chaotic properties of a two-dimensional circular billiard system containing two Coulombinteracting electrons. As such, the system resembles a prototype model for a semiconductor quantum dot. The interaction strength is varied from the noninteracting limit with zero potential energy up to the strongly interacting regime where the relative kinetic energy approaches zero. At weak interactions the bouncing maps show jumps between quasi-regular orbits. In the strong-interaction limit we find an analytic expression for the bouncing map. Its validity in the general case is assessed by comparison with our numerical data. To obtain a more quantitative view on the dynamics as the interaction strength is varied, we compute and analyze the escape rates of the system. Apart from very weak or strong interactions, the escape rates show consistently exponential behavior, thus suggesting strongly chaotic dynamics and a phase space without significant sticky regions within the considered time scales. PACS numbers: 05.45.Pq, 82.40.Bj, 73.21.La Chaotic properties of Coulomb-interacting circular billiards 2

Many-particle dynamics and intershell effects in Wigner molecules.

We apply classical molecular dynamics within the velocity Verlet algorithm to examine the formation dynamics of Wigner crystals in two-dimensional harmonic oscillators. Using a large ensemble of initial conditions as well as different freezing mechanisms, we obtain reliable information on the energies and probabilities of stable and metastable configurations, their formation dynamics, and their stability. Wigner-crystal configurations of up to 30 particles are presented and the dynamics of transition processes, e.g., intershell effects, are analyzed.

Controllable quantum scars in semiconductor quantum dots

Quantum scars are enhancements of quantum probability density along classical periodic orbits. We study the recently discovered phenomenon of strong, perturbation-induced quantum scarring in the two-dimensional harmonic oscillator exposed to a homogeneous magnetic field. We demonstrate that both the geometry and the orientation of the scars are fully controllable with a magnetic field and a focused perturbative potential, respectively. These properties may open a path into an experimental scheme to manipulate electric currents in nanostructures fabricated in a two-dimensional electron gas.

Corrigendum to “Imaginary time propagation code for large-scale two-dimensional eigenvalue problems in magnetic fields” [Comput. Phys. Comm. 184(3) (2013) 769–776]

Our original publication [1] contains an error in the terminology regarding different orthonormalization algorithms. Section 2.2 of the original publication describes the orthonormalization algorithmwehave used,which is the subspace orthonormalization algorithm (SO). This algorithm has also been used in previous imaginary time propagation implementations, and shown to cause faster convergence compared to a traditional Gram–Schmidt process [2,3]. In Section 2.2 it is erroneously claimed that SO is the same as the symmetric Löwdin orthonormalization algorithm (LO) [4,5]. The two algorithms are similar, but not the same. Their difference is most clearly presented in a matrix form. Let the columns of a matrix V represent the vectors to be orthonormalized. The overlap matrixM = V V is Hermitian, with a spectral decompositionM = UDU. LO produces the orthonormalized vectors as the columns of the matrix