Jacek Matulewski

An object-oriented implementation of a solver of the time-dependent Schrödinger equation using the CUDA technology

Abstract We present a set of C++ classes which allow one to use the graphics card processorʼs cores for quantum ab initio simulations, i.e. a direct solving of the time-dependent Schrodinger equation, gaining the benefits from the parallel architecture of the graphical processor units. We use the Chebyshev polynomial and FFT algorithm. The solution is based on NVIDIA CUDA technology. The speed-up factor in the test runs of our classes performed using the graphics card processor can even be of order of 300 in comparison with the test runs using only the single core of CPU. Not only the Schrodinger equation can be integrated using the presented solver. With only small changes it can be used for solving the nonlinear Gross–Pitaevskii equation of BECʼs dynamics, the heat equation, the diffusion equation or other parabolic partial differential equations of second order. 1 Program summary Program title: QnDynCUDA Catalogue identifier: AELE_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AELE_v1_0.html Program obtainable from: CPC Program Library, Queenʼs University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 101 359 No. of bytes in distributed program, including test data, etc.: 3 165 228 Distribution format: tar.gz Programming language: C++, C for CUDA Computer: Graphics card with CUDA technology recommended Operating system: No limits (tested on 32-bit and 64-bit Windows and 64-bit Linux) Has the code been vectorized or parallelized?: Yes, number of processors used – one CPU core and all CUDA cores of the selected processor of graphics card RAM: Dependent on userʼs parameters, typically between several tens of megabytes and several gigabytes (this concerns also the graphics cardʼs memory) Supplementary material: Test input and output files (approx. 3.4 Gigabytes) are available Classification: 2.7, 6.5 Nature of problem: Solving the time-dependent Schrodinger equation. Solution method: FFT and Chebyshev polynomial algorithm, CUDA technology. Running time: Every test example included in the distribution package takes approximately an hour or so if the GPU is engaged and a day or so if only CPU is used.

Effects of dynamic disorder on the charge transport via DNA molecules

Electron hopping transport along the DNA chain is studied theoretically by a straightforward numerical solution of the time-dependent Schrödinger equation. Results are given for the hole transition rates between two guanine bases bridged by sequences of the adenine-thymine bases with various lengths. Two models are considered: (i) with time-independent chain structure and (ii) with positions of bases on the bridge oscillating with time. It is shown that only the latter model is consistent with experimental data. The problem of the incoherence in the hopping transport mechanism is discussed.

An object-oriented C++ implementation of Davidson method for finding a few selected extreme eigenpairs of a large, sparse, real, symmetric matrix☆

Abstract A C++ class named Davidson is presented for determining a few eigenpairs with lowest or alternatively highest values of a large, real, symmetric matrix. The algorithm described by Stathopoulos and Fischer is used. The exception mechanism is involved to report the errors. The class is written in ANSI C++, so it is fully portable. In addition a console program as well as a program with graphical user interface for Microsoft Windows is attached, which allow one to calculate the lowest eigenstates of time-independent Schrodinger equation for a given binding potential in one, two or three spatial dimensions. The package contains the classes providing often used potential functions (model atom potential, Coulomb potential, square well potential and Kramers–Henneberger well potential) as well as a possibility to use any potential stored in a file (then any dimensionality of the problem is allowed). The described code is the subject of M.Sc. thesis of T.D. prepared under the supervision of J.M. Program summary Program title: Davidson Catalogue identifier: ADZM_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADZM_v1_0.html Program obtainable from: CPC Program Library, Queens University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 3 037 055 No. of bytes in distributed program, including test data, etc.: 20 002 609 Distribution format: tar.gz Programming language: C++ Computer: All Operating system: Any RAM: Users parameters dependent Word size: 32 and 64 bits Supplementary material: Test results for the 2D and 3D cases is available Classification: 4, 4.8 Nature of problem: Finding a few extreme eigenpairs of a real, symmetric, sparse matrix. Examples in quantum optics (interaction of matter with a laser field). Solution method: Davidson algorithm Running time: The test example included in the distribution package (1D matrix) takes approximately 30 minutes to run. 2D matrix calculations can take hours and 3D, days, to run.

Dynamics of strong-field photoionization in two dimensions for short-range binding potentials

Photodetachment in ultrastrong laser field in two spatial dimensions is investigated numerically. The problem of an adiabatic stabilization is discussed, in particular it is shown that a quick drift in the direction of the electric field and a magnetic drift cannot be avoided simultaneously. A qualitative behavior of the packet for a short-range binding potential is contrasted with that for a soft-core potential, in particular dynamical effects due to a rescattering of the fragments separated from the main packet are demonstrated.

GCAF: narzędzie do tworzenia interaktywnych eksperymentów wykorzystujących okulograf i jego użycie w badaniach nabywania mowy przez niemowlęta

GCAF: the environment for designing fully interactive experiments involving eye tracking devices and its use for studying of speech acquisition by infants The aim of this paper is to present our computer software, the GCAF framework, which allow one to design and run applications using the eye trackers, among others the cognitive experiments for infants. In comparison to other tools for creating the experiments, the full interaction with user is possible. User can choose the object on screen activated by its gaze, which is most interesting for him, and therefore control the program activity. This framework and the domain language GIML were already used for designing of several experiments involving infants in Neurocognitive Laboratory located at the Interdisciplinary Centre for Modern Technologies in Nicolaus Copernicus University. One of its main objectives is to investigate the loss of the ability to differentiate speech sounds in native language before the end of the first year of life. In this project, we intend to design and verify the effectiveness of the interactive training, the aim of which is to influence this phenomenon.

Three-dimensional numerical simulations in attosecond physics regime using the CUDA technology: the stabilization phenomenon

The dynamics of an ionization and a recombination in an ultrastrong laser field is studied by ab initio numerical simulations performed for a realistic atomic system in the regime of attosecond laser pulse duration. In particular the stabilization phenomenon is studied, the presence of which is confirmed in 3D. We first describe the method of integrating the Schrödinger equation (in general parabolic equations) which we adopt, taking advantage of the axial symmetry of the studied system and uses the FFT and Chebyshev polynomials (FCP) method. Further we present its implementation based on the CUDA technology to benefit from the power of graphics cards.

CONTROL OF A TWO-COLOUR PHOTOIONIZATION THROUGH A TIME DELAY BETWEEN TWO COMPONENTS OF THE LASER PULSE

Abstract The possibility is demonstrated of controlling two-colour resonant photoionization of multilevel atomic systems by changing the time delay between the components of the pulse corresponding to particular resonant transitions. Theoretical results for the atomic hydrogen ionized by a pulse, which includes a component with a fundamental frequency delayed with respect to its second harmonic, are presented. Both the intuitive and counterintuitive order of the pulses are considered.