János Pipek

Budapest University of Technology and Economics, Budapeŝto, Budapest, Hungary

Are you János Pipek?

Claim your profile

Publications (46)88.1 Total impact

  • Source
    Szilvia Nagy, János Pipek
    [Show abstract] [Hide abstract]
    ABSTRACT: In wavelet based electron structure calculations introducing a new, finer resolution level is usually an expensive task, this is why often a two-level approximation is used with very fine starting resolution level. This process results in large matrices to calculate with and a large number of coefficients to be stored. In our previous work we have developed an adaptively refining solution scheme that determines the indices, where refined basis functions are to be included, and later a method for predicting the next, finer resolution coefficients in a very economic way. In the present contribution we would like to determine, whether the method can be applied for predicting not only the first, but also the other, higher resolution level coefficients. Also the energy expectation values of the predicted wave functions are studied, as well as the scaling behaviour of the coefficients in the fine resolution limit.
  • János Pipek, Szilvia Nagy
    [Show abstract] [Hide abstract]
    ABSTRACT: The wave function of a many electron system contains inhomogeneously distributed spatial details, which allows to reduce the number of fine detail wavelets in multiresolution analysis approximations. Finding a method for decimating the unnecessary basis functions plays an essential role in avoiding an exponential increase of computational demand in wavelet-based calculations. We describe an effective prediction algorithm for the next resolution level wavelet coefficients, based on the approximate wave function expanded up to a given level. The prediction results in a reasonable approximation of the wave function and allows to sort out the unnecessary wavelets with a great reliability. © 2012 Wiley Periodicals, Inc.
    Journal of Computational Chemistry 03/2013; 34(6). DOI:10.1002/jcc.23154 · 3.60 Impact Factor
  • A. Feher, S. Nagy, J. Pipek
    [Show abstract] [Hide abstract]
    ABSTRACT: Wavelets provide an effective toolbox for solving differential equations by representing the continuous functions by their wavelet expansion coefficients and the corresponding differential equations by discrete matrix equations. The wavelet basis functions are organized into resolution levels of different frequency terms at different locations, and the main advantage of the wavelet expansion representation is that the resolution level can be different at different locations, if the solution function contains higher frequency terms in one place and restricted to lower frequencies at other places. Wavelet based differential equation solving methods can be adaptive, it is possible to refine the solution locally, if the precision is not sufficient at some regions. In the present work a simple method for estimating the next resolution level wavelet coefficients is presented. Predicting the approximate value of these coefficients makes it possible to select the minimal set of wavelet basis functions for the next resolution level solution in a computationally economic way, or in the last resolution levels it can substitute the next level solution of the matrix equation.
    Antennas and Propagation (MECAP), 2012 Middle East Conference on; 01/2012
  • Szilvia Nagy, János Pipek
    [Show abstract] [Hide abstract]
    ABSTRACT: The possibilities for reducing the necessary computation power in wavelet-based electronic structure calculations are studied. The expansion of the expectation values of energy operators, the integrals of basis functions are mostly system-independent, consequently it is not necessary to compute them in each calculations. Fixed building blocks, such as a parameterized expansion of the nuclear and electron–electron cusp can reduce the amount of necessary calculation. An algorithm for local expansion refinement is also given. It is possible to determine the significant expansion coefficients of a high resolution level without solving the Schrödinger equation using only lower resolution results.
    Theoretical Chemistry Accounts 03/2009; 125(3):471-479. DOI:10.1007/s00214-009-0653-6 · 2.14 Impact Factor
  • Source
    János Pipek, Szilvia Nagy
    [Show abstract] [Hide abstract]
    ABSTRACT: At any resolution level of wavelet expansions the physical observable of the kinetic energy is represented by an infinite matrix which is “canonically” chosen as the projection of the operator −Δ/2 onto the subspace of the given resolution. It is shown, that this canonical choice is not optimal, as the regular grid of the basis set introduces an artificial consequence of its periodicity, and it is only a particular member of possible operator representations. We present an explicit method of preparing a near optimal kinetic energy matrix which leads to more appropriate results in numerical wavelet based calculations. This construction works even in those cases, where the usual definition is unusable (i.e., the derivative of the basis functions does not exist). It is also shown, that building an effective kinetic energy matrix is equivalent to the renormalization of the kinetic energy by a momentum dependent effective mass compensating for artificial periodicity effects.
    Journal of Mathematical Chemistry 01/2009; 46(1):261-282. DOI:10.1007/s10910-008-9458-4 · 1.27 Impact Factor
  • János Pipek, Szilvia Nagy
    [Show abstract] [Hide abstract]
    ABSTRACT: Electron structure calculations over equidistant grids represent physical observables by matrices usually chosen as the projection of the corresponding operator in the Schrödinger picture onto the subspace expanded by the basis set of the given grid resolution. It is shown that any matrix representation compatible with the translational symmetry of the lattice suffers from essential difficulties. Especially the momentum and related operators like the kinetic energy show anomalous behavior, moreover, the required canonical commutation relation can never be satisfied.
    Chemical Physics Letters 10/2008; 464(1-3):103-106. DOI:10.1016/j.cplett.2008.08.091 · 1.99 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We study 12 parameter families of two qubit density matrices, arising from a special class of two-fermion systems with four single particle states or alternatively from a four-qubit state with amplitudes arranged in an antisymmetric matrix. We calculate the Wooters concurrences and the negativities in a closed form and study their behavior. We use these results to show that the relevant entanglement measures satisfy the generalized Coffman-Kundu-Wootters formula of distributed entanglement. An explicit formula for the residual tangle is also given. The geometry of such density matrices is elaborated in some detail. In particular an explicit form for the Bures metric is given. Comment: 21 pages, 1 figure
    Journal of Physics A Mathematical and Theoretical 07/2008; DOI:10.1088/1751-8113/41/50/505304 · 1.69 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: Correlation was detected between the thermal treatment parameters of the AuGe-GaAs system and surface fractal structure. Structural entropic calculations were used to confirm the results obtained by fractal calculations.
    Applied Physics Letters 08/2007; 91(7). DOI:10.1063/1.2768911 · 3.52 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Based on differences of generalized Rényi entropies nontrivial constraints on the shape of the distribution function of broadly distributed observables are derived introducing a new parameter in order to quantify the deviation from lognormality. As a test example the properties of the two-measure random Cantor set are calculated exactly and finally, using the results of numerical simulations, the distribution of the eigenvector components calculated in the critical region of the lowest Landau band is analyzed.
    EPL (Europhysics Letters) 01/2007; 36(6):437. DOI:10.1209/epl/i1996-00248-2 · 2.27 Impact Factor
  • Source
    János Pipek, Szilvia Nagy
    [Show abstract] [Hide abstract]
    ABSTRACT: The detail structure of the wave function is analyzed at various refinement levels using the methods of wavelet analysis. The eigenvalue problem of a model system is solved in granular Hilbert spaces, and the trajectory of the eigenstates is traced in terms of the resolution. An adaptive method is developed for identifying the fine structure localization regions, where further refinement of the wave function is necessary.
    The Journal of Chemical Physics 12/2006; 125(17):174107. DOI:10.1063/1.2363368 · 3.12 Impact Factor
  • János Pipek, Szilvia Nagy
    [Show abstract] [Hide abstract]
    ABSTRACT: The common experience that the distribution and interaction of electrons widely vary by scanning over various parts of a molecule is incorporated in the atomic-orbital expansion of wave functions. The application of Gaussian-type atomic orbitals suffers from the poor representation of nuclear cusps, as well as asymptotic regions, whereas Slater-type orbitals lead to unmanageable computational difficulties. In this contribution we show that using the toolkit of wavelet analysis it is possible to find an expansion of the electron density and density operators which is sufficiently precise, but at the same time avoids unnecessary complications at smooth and slightly detailed parts of the system. The basic idea of wavelet analysis is a coarse description of the system on a rough grid and a consecutive application of refinement steps by introducing new basis functions on a finer grid. This step could highly increase the number of required basis functions, however, in this work we apply an adaptive refinement only in those regions of the molecule, where the details of the electron structure require it. A molecule is split into three regions with different detail characteristics. The neighborhood of a nuclear cusp is extremely well represented by a moderately fine wavelet expansion; the domains of the chemical bonds are reproduced at an even coarser resolution level, whereas the asymptotic tails of the electron structure are surprisingly precise already at a grid distance of 0.5 a.u. The strict localization property of wavelet functions leads to an especially simple calculation of the electron integrals.
    The Journal of Chemical Physics 11/2005; 123(14):144107. DOI:10.1063/1.2048600 · 3.12 Impact Factor
  • Source
    Péter Lévay, Szilvia Nagy, János Pipek
    [Show abstract] [Hide abstract]
    ABSTRACT: An elementary formula for the von Neumann and Renyi entropies describing quantum correlations in two-fermionic systems having four single particle states is presented. An interesting geometric structure of fermionic entanglement is revealed. A connection with the generalized Pauli principle is established.
    Physical Review A 02/2005; 72(2). DOI:10.1103/PhysRevA.72.022302 · 2.99 Impact Factor
  • János Pipek
    [Show abstract] [Hide abstract]
    ABSTRACT: A mathematically well-defined measure of localization is presented based on Mulliken's orbital populations. It is shown that this quantity equals 1 for core- and lone-pair orbitals, 2 for two-atomic bonds, 6 for benzene rings, etc., and it is applicable for delocalized canonical HF orbitals as well. The definition of this quantity is general in the sense that ab initio MOS with overlapping AO expansion, and semiempirical wave functions using the ZDO approximation as well, can be treated. The localization quantity is essentially “intrinsic,” i.e., no subdivision of the molecule is required. For N-electron wave functions, mean delocalization can be defined. This measure is not invariant to unitary transformations of the one-electron orbitals, characterizing in this way the localized or extended representation of the N-electron wave function. It can be proven, however, that for unitary transformed wave functions a maximum delocalization exists which depends only on the physical (N-electron) properties of the molecule. It is shown that inhomogeneous charge distribution can cause strong electron localization in molecular systems. The delocalization of the canonical Hartree–Fock orbitals, the Parr–Chen circulant orbitals, and the optimum delocalized orbitals is studied by numerical calculations in extended systems.
    International Journal of Quantum Chemistry 10/2004; 36(4):487 - 501. DOI:10.1002/qua.560360405 · 1.17 Impact Factor
  • János Pipek, Paul G. Mezey
    [Show abstract] [Hide abstract]
    ABSTRACT: Whereas localization of orbitals has long been a tool for a semiclassical interpretation of chemical properties, it is in fact electron delocalization that is a fundamental property of quantum mechanical molecules. A mathematically well-defined measure is suggested for the degree of delocalization of molecular orbitals. It is shown that an orbital set of maximum delocalization exists for which the degree of delocalization depends on the charge distribution of the molecule. Hartree-Fock canonical orbitals are definitely more localized than the most uniformaly distributed MO's giving an equivalent description of the molecule. The changes in the geometrical shape of molecular orbitals are studied passing (quasi-) continuously from the strongly localized description towards the most delocalized picture. In the case of charge-inhomogeneities even the most delocalized orbitals remain rather compact. The degree of maximum delocalization may be correlated with chemical properties such as reactivity. The shape distortion of MO's under the perturbing effect of other ions and small molecules is investigated in several examples.
    International Journal of Quantum Chemistry 10/2004; 34(S22):1 - 13. DOI:10.1002/qua.560340804 · 1.17 Impact Factor
  • János Pipek, Imre Varga
    [Show abstract] [Hide abstract]
    ABSTRACT: The availability of recent supercomputers and massively parallel computing facilities makes possible the calculation of the electronic structure of highly extended (mesoscopic) molecular networks. Disorder, which is practically always present in these systems, causes an extreme complexity of the wave function that typically shows multifractal behavior in the intermediate length scale. Multifractal analysis, however, is possible only on systems that cover several orders of length scales. Though such calculation can be carried out on model systems, it is beyond the bounds of present ab initio or semiempirical treatments. In this contribution, a shape-analysis method of the wave function is given that is applicable both for localized and multifractal one-particle states even in moderately large networks without a regular geometrical structure. No boxing of the distributions is necessary through several orders of magnitude of scaling distances. Multifractal behavior and different regularly decaying localization shape functions can be distinguished. Finite-size multifractal distributions are also discussed. The described method is intended to serve as an easily applicable and efficient tool for bridging over the gap between the wave-function analysis of systems containing macroscopic and moderately large number of particles. © 1994 John Wiley & Sons, Inc.
    International Journal of Quantum Chemistry 09/2004; 51(6):539 - 553. DOI:10.1002/qua.560510619 · 1.17 Impact Factor
  • János Pipek, Ferenc Bogár
    [Show abstract] [Hide abstract]
    ABSTRACT: In this contribution the application of localized molecular orbitals for the separation of local and long-range correlation effects in extended systems is studied in the framework of the many-body perturbation theory. We first summarize the basic ideas developed by Professor Kapuy for extending diagrammatic methods based on localized one-electron states in correlation energy calculations. After describing some possible ways for characterizing the extension and separation of localized MOs we give a flexible procedure for the truncation of long-range correlation effects with the remarkable property that the range of the Coulomb interaction is still kept infinite. Analyzing numerical results the convergence of localization corrections is discussed and the separation of local correlation terms show that only the immediate neighborhood of a localized MO plays a considerable role in excitation processes.
    07/2004: pages 233-254;
  • János Pipek, Szilvia Nagy
    [Show abstract] [Hide abstract]
    ABSTRACT: Multiresolution (or wavelet) analysis offers a strictly local basis set for a systematic introduction of new details into Hilbert space operators. Using this tool we have previously developed an expansion method for density matrices. The set of density operators providing a given electron density plays an essential role in density functional theory, in the minimization of energy expectation values with the constraint that the electron density is fixed. In this contribution, using multiresolution analysis, we present an excellent quality density matrix expansion yielding a prescribed electron density, and compare it to other known methods. Due to the strictly local nature of the applied basis functions, our construction has the specific advantage that the resulting density matrix is correlated and N-representable in the infinite resolution limit. As a further consequence of this scheme we can conclude that the deviation of the exact kinetic energy functional from the Weizsäcker term is not a necessary consequence of the particle statistics. © 2003 American Institute of Physics.
    The Journal of Chemical Physics 10/2003; 119(16):8257-8265. DOI:10.1063/1.1611176 · 3.12 Impact Factor
  • Source
    Imre Varga, János Pipek
    [Show abstract] [Hide abstract]
    ABSTRACT: We discuss some properties of the generalized entropies, called Rényi entropies, and their application to the case of continuous distributions. In particular, it is shown that these measures of complexity can be divergent; however, their differences are free from these divergences, thus enabling them to be good candidates for the description of the extension and the shape of continuous distributions. We apply this formalism to the projection of wave functions onto the coherent state basis, i.e., to the Husimi representation. We also show how the localization properties of the Husimi distribution on average can be reconstructed from its marginal distributions that are calculated in position and momentum space in the case when the phase space has no structure, i.e., no classical limit can be defined. Numerical simulations on a one-dimensional disordered system corroborate our expectations.
    Physical Review E 09/2003; 68(2 Pt 2):026202. DOI:10.1103/PhysRevE.68.026202 · 2.33 Impact Factor
  • János Pipek, Szilvia Nagy
    [Show abstract] [Hide abstract]
    ABSTRACT: Since Kato proved his singularity condition for Coulomb potentials in 1957, there has been interest in the creation of wave functions that meet the prescriptions of the cusp conditions, necessary for high-precision quantum-mechanical calculations. It is well known, that wave-function expansions based on Slater determinants of one-electron functions are poorly convergent with respect to satisfying the electron-electron cusp condition. In this contribution we show that with the wavelet expansion of density operators even the local form of the electron-electron cusp condition is easily representable by Slater determinants of one-electron wavelet functions with a proper asymptotics of the expansion coefficients, which is explicitly calculated for Haar wavelets.
    Physical Review A 10/2001; 64(5). DOI:10.1103/PhysRevA.64.052506 · 2.99 Impact Factor
  • Szilvia Nagy, János Pipek
    [Show abstract] [Hide abstract]
    ABSTRACT: Numerical calculations show that, in extended electronic systems, complex one-particle states appear with different shape characteristics at different length scales. New results in the theory of wavelets are applied in this contribution for a consistent description of densities and density operators with a continuous kernel at various length scales. It is proved here that, for real physical systems, according to physical intuition, neither arbitrarily fine nor arbitrarily rough details of the wave function and density operators can exist. It is also shown that the calculation of both kinetic energy and interaction energy expectation values can be reduced to the determination of some universal functions defined on integer-valued arguments. © 2001 John Wiley & Sons, Inc. Int J Quant Chem, 2001
    International Journal of Quantum Chemistry 01/2001; 84(5):523 - 529. DOI:10.1002/qua.1406 · 1.17 Impact Factor

Publication Stats

1k Citations
88.10 Total Impact Points

Institutions

  • 1981–2013
    • Budapest University of Technology and Economics
      • • Department of Theoretical Physics
      • • Institute of Physics
      Budapeŝto, Budapest, Hungary
  • 2012
    • Széchenyi István University, Gyor
      Pinnyéd, Győr-Moson-Sopron, Hungary
  • 2004
    • University of Saskatchewan
      • Department of Chemistry
      Saskatoon, Saskatchewan, Canada
  • 1997
    • Hungarian Academy of Sciences
      Budapeŝto, Budapest, Hungary
  • 1985–1986
    • Friedrich-Alexander Universität Erlangen-Nürnberg
      • Chair of Theoretical Chemistry
      Erlangen, Bavaria, Germany