Publications

• Quantum dynamics
• Computational physics
• Quantum dynamics
• Monte Carlo methods and random numbers
• Cluster computing
• Statistical mechanics
• Other scientific work


• List of peer reviewed publications at ResearcherID
• Publications in arXiv.org
• List of publications (books) at the German National Library

Quantum dynamics

• Michael Klaiber, Enderalp Yakaboylu, Heiko Bauke, Karen Z. Hatsagortsyan, and Christoph H. Keitel
  «Under-the-barrier dynamics in laser-induced relativistic tunneling»
  arXiv:1205.2004
  
  Abstract

  The tunneling dynamics in relativistic strong-field ionization is investigated with the aim to develop an intuitive picture for the relativistic tunneling regime. We demonstrate that the tunneling picture applies also in the relativistic regime by introducing position dependent energy levels. The relativistic quantum dynamics in the classically forbidden region features two characteristic time scales: the time for the formation of momentum components of the ionized electron wave packet (Keldysh time) and the time interval which the electron wave packet spends inside the barrier (Eisenbud-Wigner-Smith time delay). While the Keldysh time determines an electron momentum shift under the barrier along the laser propagation direction, the Eisenbud-Wigner-Smith time delay governs the corresponding wave-packet's spatial drift. The signature of the momentum shift is shown to be present in the ionization spectrum at the detector and, therefore, observable experimentally. In contrast, the signature of the Eisenbud-Wigner-Smith time delay disappears at far distances for pure tunneling dynamics.


• Sven Arens, Heiko Bauke, Christoph H. Keitel, and Carsten Müller
  «Spin dynamics in the Kapitza-Dirac effect»
  arXiv:1204.0239
  
  Abstract

  Electron spin dynamics in Kapitza-Dirac scattering from a standing laser wave of high frequency and high intensity is studied. We develop a fully relativistic quantum theory of the electron motion based on the time-dependent Dirac equation. Distinct spin dynamics, with Rabi oscillations and complete spin-flip transitions, is demonstrated for Kapitza-Dirac scattering involving three photons in a parameter regime accessible to future high-power X-ray laser sources. The Rabi frequency and, thus, the diffraction pattern is shown to depend crucially on the spin degree of freedom.


• Heiko Bauke, Henrik G. Hetzheim, Guido R. Mocken, Matthias Ruf, and Christoph H. Keitel
  «Relativistic ionization characteristics of laser-driven hydrogenlike ions»
  Peer reviewed article in Physical Review A, vol. 83, nr. 6, article 063414 (2011)
  
  Abstract

  In this contribution, we investigate the relativistic ionization characteristics of highly charged hydrogenlike ions in short intense laser pulses as a function of the laser pulse parameters by means of the numerical solution of the time-dependent Dirac equation and the time-dependent Klein-Gordon equation as well as by the classical phase-space averaging method. For this purpose, we generalize the phase-space averaging method such that it is applicable to relativistically driven particles in arbitrary central potentials. If the ionization probability is not too small, quantum mechanical and classical methods give similar results for laser wavelengths in the range from the near-infrared to soft x-ray radiation. We find that ionization in few-cycle intense laser pulses depends sensitively on the pulses' peak intensity but little on the pulse tails and on the pulse energy. The ionization probability is shown to be strongly linked to the peak intensity allowing for an estimation of the laser intensity via ionization yields.

Quantum dynamics

• Frederick Blumenthal and Heiko Bauke
  «A stability analysis of a real space split operator method for the Klein-Gordon equation»
  Peer reviewed article in Journal of Computational Physics, vol. 231, nr. 2, pp. 454–464 (2012)
  see also arXiv:1105.3660
  
  Abstract

  We carry out a stability analysis for the real space split operator method for the propagation of the time-dependent Klein–Gordon equation that has been proposed in Ruf et al. [M. Ruf, H. Bauke, C.H. Keitel, A real space split operator method for the Klein–Gordon equation, Journal of Computational Physics 228 (24) (2009) 9092–9106, doi:10.1016/j.jcp.2009.09.012]. The region of algebraic stability is determined analytically by means of a von-Neumann stability analysis for systems with homogeneous scalar and vector potentials. Algebraic stability implies convergence of the real space split operator method for smooth absolutely integrable initial conditions. In the limit of small spatial grid spacings $h$ in each of the $d$ spatial dimensions and small temporal steps $\tau$, the stability condition becomes for second order finite differences and for fourth order finite differences, respectively, with $c$ denoting the speed of light. Furthermore, we demonstrate numerically that the stability region for systems with inhomogeneous potentials coincides almost with the region of algebraic stability for homogeneous potentials.


• Heiko Bauke and Christoph H. Keitel
  «Accelerating the Fourier split operator method via graphics processing units»
  Peer reviewed article in Computer Physics Communications, vol. 182, nr. 12, pp. 2454–2463 (2011)
  see also arXiv:1012.3911
  
  Abstract

  Current generations of graphics processing units have turned into highly parallel devices with general computing capabilities. Thus, graphics processing units may be utilized, for example, to solve time dependent partial differential equations by the Fourier split operator method. In this contribution, we demonstrate that graphics processing units are capable to calculate fast Fourier transforms much more efficiently than traditional central processing units. Thus, graphics processing units render efficient implementations of the Fourier split operator method possible. Performance gains of more than an order of magnitude as compared to implementations for traditional central processing units are reached in the solution of the time dependent Schrödinger equation and the time dependent Dirac equation.


• Heiko Bauke and Noya Ruth Itzhak
  «Visualizing quantum mechanics in phase space»
  arXiv:1101.2683
  
  Abstract

  We examine the visualization of quantum mechanics in phase space by means of the Wigner function and the Wigner function flow as a complementary approach to illustrating quantum mechanics in configuration space by wave functions. The Wigner function formalism resembles the mathematical language of classical mechanics of non-interacting particles. Thus, it allows a more direct comparison between classical and quantum dynamical features.


• Heiko Bauke and Christoph H. Keitel
  «Efficient integration of quantum mechanical wave equations»
  Contributed talk given at the workshop «Quantum Dynamic Imaging» at the Centre de recherches mathématiques, Université de Montréal, Canada, 19–23 October 2009
  


• Matthias Ruf, Heiko Bauke and Christoph H. Keitel
  «A real space split operator method for the Klein-Gordon equation»
  Peer reviewed article in Journal of Computational Physics, vol. 228, nr. 24, pp. 9092–9106 (2009)
  
  Abstract

  The Klein-Gordon equation is a Lorentz invariant equation of motion for spinless particles. We propose a real space split operator method for the solution of the time-dependent Klein-Gordon equation with arbitrary electromagnetic fields. Split operator methods for the Schrödinger equation and the Dirac equation typically operate alternately in real space and momentum space and, therefore, require the computation of a Fourier transform in each time step. However, the fact that the kinetic energy operator $K$ in the two-component representation of the Klein-Gordon equation is a nilpotent operator, that is $K^2$, allows us to implement the split operator method for the Klein-Gordon equation entirely in real space. Consequently, the split operator method for the Klein-Gordon equation does not require the computation of a Fourier transform and may be parallelized efficiently by domain decomposition.


• Heiko Bauke and Christoph H. Keitel
  «Canonical transforms and the efficient integration of quantum mechanical wave equations»
  Peer reviewed article in Physical Review E, vol. 80, nr. 1, article 016706 (2009)
  
  Abstract

  The integration of time-dependent quantum mechanical wave equations is a fundamental problem in computational physics and computational chemistry. The wave-function's energy spectrum as well as its momentum spectrum impose fundamental limits on the performance of numerical algorithms for the solution of wave equations. We demonstrate how canonical transforms may be applied to negotiate these limitations and to increase the performance of numerical algorithms by up to several orders of magnitude. Our approach includes the so-called Kramers-Henneberger transform as a special case and puts forward modifications toward an improved numerical efficiency.


• Heiko Bauke and Christoph H. Keitel
  «Efficient Integration of Quantum Mechanical Wave Equations by Unitary Transforms»
  Peer reviewed article in AIP Conference Proceedings, vol. 1148, nr. 1, pp. 17–20 (2009)
  
  Abstract

  The integration of time dependent quantum mechanical wave equations is a fundamental problem in computational physics and computational chemistry. The energy and momentum spectrum of a wave function imposes fundamental limits on the performance of numerical algorithms for this problem. We demonstrate how unitary transforms can help to surmount these limitations.


• Heiko Bauke and Christoph H. Keitel
  «Efficient Integration of Quantum Mechanical Wave Equations by Unitary Transforms»
  Contributed talk given at the Sixth International Conference of Computational Methods in Sciences and Engineering (ICCMSE 2008) Hotel Belvedere Imperial, Hersonissos, Crete, Greece, 25–30 September 2008

Monte Carlo methods and pseudo random numbers

• Heiko Bauke and Stephan Mertens
  «YARN generators in large scale distributed Monte Carlo: Practice»
  Invited talk given at the Eighth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC'08) at the Centre de recherches mathématiques, Université de Montréal, Canada, 6–11 July 2008
  see also Tina's Random Number Generator Library


• Heiko Bauke and Stephan Mertens
  «Random Numbers for Large Scale Distributed Monte Carlo Simulations»
  Peer reviewed article in Physical Review E, vol. 75, nr. 6, article 066701 (2007)
  see also arXiv:cond-mat/0609584 and Tina's Random Number Generator Library
  Abstract

  Monte Carlo simulations are one of the major tools in statistical physics, complex system science, and other fields, and an increasing number of these simulations is run on distributed systems like clusters or grids. This raises the issue of generating random numbers in a parallel, distributed environment. In this contribution we demonstrate that multiple linear recurrences in finite fields are an ideal method to produce high quality pseudorandom numbers in sequential and parallel algorithms. Their known weakness (failure of sampling points in high dimensions) can be overcome by an appropriate delinearization that preserves all desirable properties of the underlying linear sequence.


• Heiko Bauke and Stephan Mertens
  «Pseudo Random Coins Show More Heads Than Tails»
  Peer reviewed article in Journal of Statistical Physics, vol. 114, pp. 1149–1169 (2004)
  see also arXiv:cond-mat/0307138 or some articles in popular journals about our work:
  • «Random numbers hit and miss» by nature science update, 29 July 2003
  • «Heads it's zero» by NewScientist, 26 July 2003, issue 2405
  • «Zufallsgeneratoren bevorzugen die Null» by Frankfurter Allgemeine Zeitung, 20 August 2003
  • «The Bias of Random-Number Generators» by Ivars Peterson's MathTrek
  • «Digitale Dominanz der Null» by Deutschlandfunk, 15 September 2003, a radio report
  • «Die verflixte Null» by Berliner Zeitung
  • «Kopf oder Zahl» by spektrumdirekt.
  Abstract

  Tossing a coin is the most elementary Monte-Carlo experiment. In a computer the coin is replaced by a pseudo random number generator. It can be shown analytically and by exact enumerations that popular random number generators are not capable of imitating a fair coin: pseudo random coins show more “heads” than “tails.” This bias explains the empirically observed failure of some random number generators in random walk experiments. It can be traced down to the special role of the value zero in the algebra of finite fields.


• Stephan Mertens and Heiko Bauke
  «Entropy of Pseudo Random Number Generators»
  Peer reviewed article in Physical Review E, vol. 69, nr. 5, article 055702(R) (2004)
  See also arXiv:cond-mat/0305319.
  Abstract

  Since the work of Ferrenberg et al. [Phys. Rev. Lett. 69 3382 (1992)] some pseudo-random-number generators are known to yield wrong results in cluster Monte Carlo simulations. In this contribution the fundamental mechanism behind this failure is discussed. Almost all random-number generators calculate a new pseudo-random-number x_i from preceding values, x_i=f(x_i−1,x_i−2,…,x_i−q). Failure of these generators in cluster Monte Carlo simulations and related experiments can be attributed to the low entropy of the production rule f() conditioned on the statistics of the input values x_i−1,…,x_i−q. Being a measure only of the arithmetic operations in the generator rule, the conditional entropy is independent of the lag in the recurrence or the period of the sequence. In that sense it measures a more profound quality of a random-number generator than empirical tests with their limited horizon.


• Heiko Bauke
  «Theorie und Implementation von parallelisierten Pseudozufallszahlengeneratoren»
  Forschungsbeleg

Cluster computing

• Heiko Bauke
  «Digitale Auferstehung»
  Linux-Magazin, October 2007, pp. 78–81


• Heiko Bauke und Stephan Mertens
  «Cluster Computing»
  Praktische Einführung in das Hochleistungsrechnen auf Linux-Clustern
  Springer Verlag, 2005, ISBN 3-540-42299-4
  buy at amazon.de
  


• Heiko Bauke
  «MPI – Programming clusters»
  Linux-Magazine, Issue 31, June 2003, pp. 70–74


• Heiko Bauke
  «Zahlenbeißer für alle – Cluster programmieren mit MPI»
  Linux-Magazin, May 2003, pp. 84–89


• Heiko Bauke
  «Linux-Beowulf-Cluster; Herausforderung im High Performance Computing and Networking»
  Talk given at the Linuxtag in Magdeburg 2001

Statistical mechanics

• Heiko Bauke
  «Passing messages to lonely numbers»
  Invited talk given at the Carl von Ossietzky Universität Oldenburg in the Theoretical Comutational Physics Group on 1 July 2008


• Heiko Bauke and David Sherrington
  «Topological phase transition in complex networks»
  arXiv:0710.0831
  Abstract

  Preferential attachment is a central paradigm in the theory of complex networks. In this contribution we consider various generalizations of preferential attachment including for example node removal and edge rewiring. We demonstrate that generalized preferential attachment networks can undergo a topological phase transition. This transition separates networks having a power-law tail degree distribution from those with an exponential tail. The appearance of the phase transition is closely related to the breakdown of the continuous variable description of the network dynamics.


• Heiko Bauke
  «Structural phase transition in complex networks»
  Contributed talk presented at the conference «Common Concepts in Statistical Physics and Computer Science» at the ICTP, Trieste, Italy, 1–6 July 2007


• Heiko Bauke and David Sherrington
  «Local attachment in networks under churn»
  arXiv:0706.0018
  Abstract

  In this contribution we introduce local attachment as an universal network-joining protocol for peer-to-peer networks, social networks, or other kinds of networks. Based on this protocol nodes in a finite-size network dynamically create power-law connectivity distributions. Nodes or peers maintain them in a self-organized statistical way by incorporating local information only. We investigate the structural and macroscopic properties of such local attachment networks by extensive numerical simulations, including correlations and scaling relations between exponents. The emergence of the power-law degree distribution is further investigated by considering preferential attachment with a nonlinear attractiveness function as an approximative model for local attachment. This study suggests the local attachment scheme as a procedure to be included in future peer-to-peer protocols to enable the efficient production of stable network topologies in a continuously changing environment.


• Heiko Bauke
  «Parameter estimation for power-law distributions by maximum likelihood methods»
  Peer reviewed article in The European Physical Journal B, vol. 58, no. 2, pp. 167–173 (2007)
  see also arXiv:0704.1867, supplementary software:
  • hzeta.c, Matlab MEX function that computes the Hurwitz-zeta-function (needs the GNU Scientific Library)
  • powerlaw_ml.m, Matlab function that computes maximum likelihood estimates for power-law exponents
  Abstract

  Distributions following a power-law are an ubiquitous phenomenon. Methods for determining the exponent of a power-law tail by graphical means are often used in practice but are intrinsically unreliable. Maximum likelihood estimators for the exponent are a mathematically sound alternative to graphical methods.


• Heiko Bauke
  «Passing messages to lonely numbers»
  Peer reviewed article in Computing in Science & Engineering, vol. 10, no. 2, pp. 32–40 (2008)
  Abstract

  Message-passing methods provide powerful approximation algorithms for problems that can be formulated in terms of (probabilistic) graphical models. These methods find applications in statistical physics, inference, and combinatorial optimization. Sudoku, a popular number puzzle, is a simple optimization problem that message-passing algorithms can help solve. Therefore, Sudoku is an ideal vehicle to demonstrate these methods' strengths and limitations.


• Heiko Bauke
  «Message passing in statistical physics and optimisation»
  Internal talk presented at the Informal Condensed Matter Theory Seminar in October 2006 in Oxford


• Heiko Bauke
  «Sudoku – An application of message passing»
  Contributed talk presented at the «Les Houches Summer School on Complex Systems» in July 2006 in Les Houches, France


• Heiko Bauke
  «Zur Universalität des Random-Energy-Modells»
  Ph.D. thesis, Books on Demand, 2006, ISBN 3-8334-5425-3
  buy at amazon.de


• Heiko Bauke and Stephan Mertens
  «Ubiquity of the Random-Energy Model»
  Poster presented at the «International Summer School Fundamental Problems in Statistical Physics XI» in September 2005 in Leuven (Belgium)


• Heiko Bauke and Stephan Mertens
  «Universality in the level statistics of disordered systems»
  Peer reviewed article in Physical Review E, vol. 70, article 025102(R) (2004)
  see also arXiv:cond-mat/0404470
  Abstract

  Energy spectra of disordered systems share a common feature: If the entropy of the quenched disorder is larger than the entropy of the dynamical variables, the spectrum is locally that of a random energy model and the correlation between energy and configuration is lost. We demonstrate this effect for the Edwards-Anderson model, but we also discuss its universality.


• Heiko Bauke, Silvio Franz and Stephan Mertens
  «Number partitioning as a random energy model»
  Peer reviewed article in Journal of Statistical Mechnics: Theory and Experiment, article P04003 (2004)
  see also arXiv:cond-mat/0402010
  Abstract

  Number partitioning is a classical problem from combinatorial optimization. In physical terms it corresponds to a long range anti-ferromagnetic Ising spin glass. It has been rigorously proven that the low lying energies of number partitioning behave like uncorrelated random variables. We claim that neighbouring energy levels are uncorrelated almost everywhere on the energy axis, and that energetically adjacent configurations are uncorrelated, too. Apparently there is no relation between geometry (configuration) and energy that could be exploited by an optimization algorithm. This 'local random energy' picture of number partitioning is corroborated by numerical simulations and heuristic arguments.


• Heiko Bauke
  «Statistische Mechanik des Zahlenaufteilungsproblems»
  Invited talk given on May 8th 2003 at Junior Research Group "Complex Ground States of Disordered Systems" at University of Göttingen.


• Heiko Bauke, Stephan Mertens and Andreas Engel
  «Phase Transition in Multiprocessor Scheduling»
  Peer reviewed article in Physical Review Letters, vol. 90, nr. 15, article 158701 (2003)
  see also arXiv:cond-mat/0208081 or read the report «Physics tackles processor problem» about our work by Kimberly Patch in Technology Research News
  Abstract

  An “easy-hard” phase transition is shown to characterize the multiprocessor scheduling problem in which one has to distribute the workload on a parallel computer such as to minimize the overall run time. The transition can be analyzed in detail by mapping it on a mean-field antiferromagnetic Potts model. The static phase transition, characterized by a vanishing ground state entropy, corresponds to a transition in the performance of practical scheduling algorithms.


• Heiko Bauke
  «Statistische Mechanik des Zahlenaufteilungsproblems»
  Diplomarbeit (diploma thesis)

• Heiko Bauke
  «Performance studies for the TESLA forward tracking system with different layouts»
  LCnotes, LC-DET-2001-078


• Heiko Bauke
  «Performance studies for the TESLA forward tracking system with different layouts»
  Talk given at the TESLA-meeting in Hamburg at DESY in October 2001


• Alexander V. Lebedev, Andreas Engel, Konstantin I. Morozov and Heiko Bauke
  «Ferrofluid drops in rotating magnetic fields»
  Peer reviewed article in New Journal of Physics, vol. 5, nr. 6, article 57 (2003)
  This paper was one of the top 30 downloaded articles in the New Journal of Physics in 2003.
  Abstract

  Drops of a ferrofluid floating in a non-magnetic liquid of the same density and spun by a rotating magnetic field are investigated experimentally and theoretically. The parameters for the experiment are chosen such that different stationary drop shapes including non-axis-symmetric configurations could be observed. Within an approximate theoretical analysis the character of the occurring shape bifurcations, the different stationary drop forms, as well as the slow rotational motion of the drop is investigated. The results are in qualitative, and often quantitative agreement, with the experimental findings. It is also shown that a small eccentricity of the rotating field may have a substantial impact on the rotational motion of the drop.


• G. Mook, H. Bauke, V. Uchanin
  «Wirbelstromprüfung mit hohen Eindringtiefen – Theorie und Praxis»
  Beitrag zu der DGZfP (Gesellschaft zur Förderung zerstörungsfreier Prüfverfahren e.V.) Jahrestagung, Innsbruck, 29–31 May 2000