ALTDSE: An Arnoldi–Lanczos program to solve the time-dependent Schrödinger equation

We describe a general ab initio and non-perturbative method to solve the time-dependent Schrödinger equation (TDSE) for the interaction of a strong attosecond laser pulse with a general atom. While the field-free Hamiltonian and the dipole matrices may be generated using an arbitrary primitive basis, they are assumed to have been transformed to the eigenbasis of the problem before the solution of the TDSE is propagated in time using the Arnoldi–Lanczos method. Probabilities for survival of the ground state, excitation, and single ionization can be extracted from the propagated wavefunction.

Program summary

Program title: ALTDSECatalogue identifier: AEDM_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDM_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 2154No. of bytes in distributed program, including test data, etc.: 30 827Distribution format: tar.gzProgramming language: Fortran 95. [A Fortran 2003 call to “flush” is used to simplify monitoring the output file during execution. If this function is not available, these statements should be commented out.].Computer: Shared-memory machinesOperating system: Linux, OpenMPHas the code been vectorized or parallelized?: YesRAM: Several Gb, depending on matrix size and number of processorsSupplementary material: To facilitate the execution of the program, Hamiltonian field-free and dipole matrix files are provided.Classification: 2.5External routines: LAPACK, BLASNature of problem: We describe a computer program for a general ab initio and non-perturbative method to solve the time-dependent Schrödinger equation (TDSE) for the interaction of a strong attosecond laser pulse with a general atom [1,2]. The probabilities for survival of the initial state, excitation of discrete states, and single ionization due to multi-photon processes can be obtained.Solution method: The solution of the TDSE is propagated in time using the Arnoldi–Lanczos method. The field-free Hamiltonian and the dipole matrices, originally generated in an arbitrary basis (e.g., the flexible B-spline R-matrix (BSR) method with non-orthogonal orbitals [3]), must be provided in the eigenbasis of the problem as input.Restrictions: The present program is restricted to a ¹S^e initial state and linearly polarized light. This is the most common situation experimentally, but a generalization is straightforward.Running time: Several hours, depending on the number of threads used.References: [1] X. Guan, O. Zatsarinny, K. Bartschat, B.I. Schneider, J. Feist, C.J. Noble, Phys. Rev. A 76 (2007) 053411. [2] X. Guan, C.J. Noble, O. Zatsarinny, K. Bartschat, B.I. Schneider, Phys. Rev. A 78 (2008) 053402. [3] O. Zatsarinny, Comput. Phys. Comm. 174 (2006) 273.     

Factors Determining the Relevance of Creating a Research Infrastructure for Synthesizing New Materials in Implementing the Priorities of Scientific and Technological Development of Russia

Russian Microelectronics - In the modern world, knowledge and advanced technologies determine the effectiveness of the economy, and they can radically improve the quality of life of people,...     

BSR: B-spline atomic R-matrix codes

BSR is a general program to calculate atomic continuum processes using the B-spline R-matrix method, including electron-atom and electron-ion scattering, and radiative processes such as bound-bound transitions, photoionization and polarizabilities. The calculations can be performed in LS-coupling or in an intermediate-coupling scheme by including terms of the Breit-Pauli Hamiltonian.

New version program summary

Title of program: BSRCatalogue identifier: ADWYProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWYProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandComputers on which the program has been tested: Microway Beowulf cluster; Compaq Beowulf cluster; DEC Alpha workstation; DELL PCOperating systems under which the new version has been tested: UNIX, Windows XPProgramming language used: FORTRAN 95Memory required to execute with typical data: Typically 256-512 Mwords. Since all the principal dimensions are allocatable, the available memory defines the maximum complexity of the problemNo. of bits in a word: 8No. of processors used: 1Has the code been vectorized or parallelized?: noNo. of lines in distributed program, including test data, etc.: 69 943No. of bytes in distributed program, including test data, etc.: 746 450Peripherals used: scratch disk store; permanent disk storeDistribution format: tar.gzNature of physical problem: This program uses the R-matrix method to calculate electron-atom and electron-ion collision processes, with options to calculate radiative data, photoionization, etc. The calculations can be performed in LS-coupling or in an intermediate-coupling scheme, with options to include Breit-Pauli terms in the Hamiltonian.Method of solution: The R-matrix method is used [P.G. Burke, K.A. Berrington, Atomic and Molecular Processes: An R-Matrix Approach, IOP Publishing, Bristol, 1993; P.G. Burke, W.D. Robb, Adv. At. Mol. Phys. 11 (1975) 143; K.A. Berrington, W.B. Eissner, P.H. Norrington, Comput. Phys. Comm. 92 (1995) 290].     

A B-spline Galerkin method for the Dirac equation

The B-spline Galerkin method is first investigated for the simple eigenvalue problem, y^″=−λ²y, that can also be written as a pair of first-order equations y^′=λz, z^′=−λy. Expanding both y(r) and z(r) in the Bk basis results in many spurious solutions such as those observed for the Dirac equation. However, when y(r) is expanded in the Bk basis and z(r) in the dBk/dr basis, solutions of the well-behaved second-order differential equation are obtained. From this analysis, we propose a stable method (Bk,Bk±1) basis for the Dirac equation and evaluate its accuracy by comparing the computed and exact R-matrix for a wide range of nuclear charges Z and angular quantum numbers κ. When splines of the same order are used, many spurious solutions are found whereas none are found for splines of different order. Excellent agreement is obtained for the R-matrix and energies for bound states for low values of Z. For high Z, accuracy requires the use of a grid with many points near the nucleus. We demonstrate the accuracy of the bound-state wavefunctions by comparing integrals arising in hyperfine interaction matrix elements with exact analytic expressions. We also show that the Thomas-Reiche-Kuhn sum rule is not a good measure of the quality of the solutions obtained by the B-spline Galerkin method whereas the R-matrix is very sensitive to the appearance of pseudo-states.     

Scientific Services Consolidation Methods

Russian Microelectronics - The article discusses methods of consolidating scientific services of a digital platform for integrating a set of scientific services for various fields of science for...