János Pipek

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

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Publications (33)70.56 Total impact

  • János Pipek, Szilvia Nagy
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    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 10/2012; · 3.84 Impact Factor
  • A. Feher, S. Nagy, J. Pipek
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    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
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    János Pipek, Szilvia Nagy
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    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. · 1.23 Impact Factor
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    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; · 1.77 Impact Factor
  • János Pipek, Szilvia Nagy
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    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 01/2008; 464:103-106. · 2.15 Impact Factor
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    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. · 2.26 Impact Factor
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    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 01/2007; 91. · 3.52 Impact Factor
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    János Pipek, Szilvia Nagy
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    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. · 3.12 Impact Factor
  • János Pipek, Szilvia Nagy
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    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. · 3.12 Impact Factor
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    Péter Lévay, Szilvia Nagy, János Pipek
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    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; · 3.04 Impact Factor
  • J. Pipek, I. Varga, T. Nagy
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    ABSTRACT: The localization properties of the π-electron system of some aromatic and conjugated hydrocarbon molecules have been investigated. The π orbitals have been obtained using a standard PPP-SCF procedure. The shape analysis was carried out using the novel concept of the relation between the localization measure and structural entropy. According to our investigations the π-electron system of these aromatic molecules is more localized than expected. The eigenstates seem to show one-dimensional characteristics with a decay rate generally faster than exponential. Linear chains, on the other hand, have rather delocalized orbitals. As a byproduct we have found that in certain systems some states exhibit step-function–like behavior, similar to bond-centered charge density waves.
    International Journal of Quantum Chemistry 10/2004; 37(4):529 - 537. · 1.17 Impact Factor
  • János Pipek, Imre Varga
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    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. · 1.17 Impact Factor
  • János Pipek, Ferenc Bogár
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    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
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    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. · 3.12 Impact Factor
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    Imre Varga, János Pipek
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    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. · 2.31 Impact Factor
  • János Pipek, Szilvia Nagy
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    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). · 3.04 Impact Factor
  • Szilvia Nagy, János Pipek
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    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 05/2001; 84(5):523 - 529. · 1.17 Impact Factor
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    ABSTRACT: Numerical and analytical details are presented on the newly discovered superscaling property of the energy spacing distribution in the three dimensional Anderson model.
    Physica E Low-dimensional Systems and Nanostructures 09/2000; · 1.86 Impact Factor
  • J. Pipek
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    ABSTRACT: Although Mulliken's charge population concept is widely used in literature, it suffers from the main conceptual disadvantage of not describing a probability distribution of the electron on the constituent atoms; small negative population values can occur as well. This fact prohibits some practical applications, too. Mulliken's AO population can be written as the expectation value of a self-adjoint operator P̂μ, corresponding to each atomic orbital |μ〉. Using the algebra generated by P̂μ, we will give in this paper a positive definite extension of Mulliken's expressions which can be written as the expectation value of a proper self-adjoint operator; it is local in the sense of Mulliken's definition; and it remains in the framework of the usual LCAO techniques (i.e. only the atomic overlap matrix is required for calculations). It is shown that only non-physical populations change significantly, realistic values remain close to Mulliken ones. From computational point of view, the extra work required to calculate this positive definite distribution is practically negligible.
    Journal of Molecular Structure-theochem - J MOL STRUC-THEOCHEM. 01/2000; 501:395-401.
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    ABSTRACT: Coarse grained Langevin-type effective field equations may provide some guidance for the analysis of mesoscopic or microscopic molecular systems exhibiting fluctuations, or for systems of hundreds to thousands of atomic or subatomic particles produced in atomic or high-energy nuclear collisions. Suggestions for consistent realization of random fluctuations in discretized fluid dynamics will be presented. (c) 2000 The American Physical Society.
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 12/1999; 61(1).

Publication Stats

232 Citations
70.56 Total Impact Points

Institutions

  • 1990–2012
    • Budapest University of Technology and Economics
      • • Department of Theoretical Physics
      • • Institute of Physics
      Budapest, Budapest fovaros, Hungary
  • 1997
    • Hungarian Academy of Sciences
      Budapeŝto, Budapest, Hungary