Publications

Q. Z. Lv, Heiko Bauke
«Time and spaceresolved selective multipair creation»
peer reviewed article in Physical Review D, vol. 96, article 056017 (2017)
see also arXiv:1707.08450
AbstractThe
simultaneous creation of multiple electronpositron pairs by localized strong electric fields is studied by utilizing a
time and spaceresolved quantum field theory approach. It is demonstrated that the number of simultaneously created
pairs equals the number of the potential's supercritical quasibound states in the Dirac sea. This means it can be
controlled by tuning the potential parameters. Furthermore, the energy of the created particles corresponds to the
energy of the supercritical quasibound states. The simultaneously created electrons and positrons are statistically
correlated, which is reflected in the spatial distribution and the momentum distribution of these particles and
antiparticles.

Meng Wen, Christoph H. Keitel, Heiko Bauke
«Spinonehalf particles in strong electromagnetic fields: spin effects and radiation reaction»
peer reviewed article in Physical Review A, vol. 95, article 042102 (2017)
see also arXiv:1610.08951
AbstractVarious classical models of electrons including their spin degrees of freedom are commonly applied to describe the electron dynamics in strong electromagnetic fields. We demonstrate that different models can lead to different or even contradicting predictions regarding how the spin degree of freedom modifies the electron's orbital motion when the electron moves in strong electromagnetic fields. This discrepancy is rooted in the modelspecific energy dependency of the spininduced SternGerlach force acting on the electron. The Frenkel model and the classical FoldyWouthuysen model are compared exemplarily in the nonrelativistic and the relativistic limits in order to identify parameter regimes where these classical models make different predictions. This allows for experimental tests of these models. In ultrastrong laser setups in parameter regimes where effects of the SternGerlach force become relevant, radiationreaction effects are also expected to set in. We incorporate the radiation reaction classically via the LandauLifshitz equation and demonstrate that although radiationreaction effects can have a significant effect on the electron trajectory, the Frenkel model and the classical FoldyWouthuysen model remain distinguishable also if radiationreaction effects are taken into account. Our calculations are also suitable to verify the LandauLifshitz equation for the radiation reaction of electrons and other spin1/2 particles.

Meng Wen, Heiko Bauke, Christoph H. Keitel
«Identifying the SternGerlach force of classical electron dynamics»
peer reviewed article in Scientific Reports, vol. 6, article 31624 (2016)
see also arXiv:1510.09145
AbstractDifferent classical theories are commonly applied in various branches of physics to describe the
relativistic dynamics of electrons by coupled equations for the orbital motion and spin precession.
Exemplarily, we benchmark the Frenkel model and the classical FoldyWouthuysen model with spin
dependent forces (SternGerlach forces) to the quantum dynamics as predicted by the Dirac equation.
Both classical theories can lead to different or even contradicting predictions how the SternGerlach
forces modify the electron’s orbital motion, when the electron moves in strong electromagnetic field
configurations of emerging highintensity laser facilities. In this way, one may evaluate the validity and
identify the limits of these classical theories via a comparison with possible experiments to provide a
proper description of spininduced dynamics. Our results indicate that the FoldyWouthuysen model is
qualitatively in better agreement with the Dirac theory than the widely used Frenkel model.

Nicolas Teeny, Christoph H. Keitel, Heiko Bauke
«SaleckerWignerPeres quantum clock applied to strongfield tunnel ionization»
arXiv:1608.02854
Abstract The SaleckerWignerPeres quantumclock approach is applied in order to determine the tunneling time of an electron in strongfield tunnel ionization via a timedependent electric field. Our results show that the ionization of the electron takes a nonvanishing period of time. This tunneling time is of the order of the Keldysh time but strictly larger than the Keldysh time. Comparing the quantumclock tunneling time to the mean tunneling time as obtained by the virtualdetector approach, one finds that these two complementary methods give very similar results. Due to the asymmetric distribution of the tunneling time, there is a nonnegligible discrepancy between the mean tunneling time and the most probable tunneling time.

Nicolas Teeny, Christoph H. Keitel, Heiko Bauke
«Virtualdetector approach to tunnel ionization and tunneling times»
peer reviewed article in Physical Review A, vol. 94, article 022104 (2016)
see also
arXiv:1605.06411
AbstractTunneling times in atomic ionization are studied theoretically by a virtual detector approach. A virtual detector is a hypothetical device that allows one to monitor the wave function's density with spatial and temporal resolution during the ionization process. With this theoretical approach, it becomes possible to define unique moments when the electron enters and leaves with highest probability the classically forbidden region from first principles and a tunneling time can be specified unambiguously. It is shown that neither the moment when the electron enters the tunneling barrier nor when it leaves the tunneling barrier coincides with the moment when the external electric field reaches its maximum. Under the tunneling barrier as well as at the exit the electron has a nonzero velocity in the electric field direction. This nonzero exit velocity has to be incorporated when the free motion of the electron is modeled by classical equations of motion.

Anton Wöllert, Heiko Bauke, Christoph H. Keitel
«Multipair states in electronpositron pair creation»
peer reviewed article in Physics Letters B, vol. 760, pages 552557 (2016)
see also
arXiv:1511.07709
AbstractUltra strong electromagnetic fields can lead to spontaneous creation of single or multiple electron–positron pairs. A quantum field theoretical treatment of the pair creation process combined with numerical methods provides a description of the fermionic quantum field state, from which all observables of the multiple electron–positron pairs can be inferred. This allows to study the complex multiparticle dynamics of electron–positron pair creation indepth, including multipair statistics as well as momentum distributions and spin. To illustrate the potential benefit of this approach, it is applied to the intermediate regime of pair creation between nonperturbative Schwinger pair creation and perturbative multiphoton pair creation where the creation of multipair states becomes nonnegligible but cascades do not yet set in. Furthermore, it is demonstrated how spin and helicity of the created electrons and positrons are affected by the polarization of the counterpropagating laser fields, which induce the creation of electron–positron pairs.

Nicolas Teeny, Enderalp Yakaboylu, Heiko Bauke, Christoph H. Keitel
«Ionization time and exit momentum in strongfield tunnel ionization»
peer reviewed article in Physical Review Letters, vol. 116, article 063003 (2016)
see also arXiv:1502.05917
AbstractTunnel ionization belongs to the fundamental processes of atomic physics. The socalled twostep model, which describes the ionization as instantaneous tunneling at the electric field maximum and classical motion afterwards with zero exit momentum, is commonly employed to describe tunnel ionization in adiabatic regimes. In this contribution, we show by solving numerically the timedependent Schrödinger equation in one dimension and employing a virtual detector at the tunnel exit that there is a nonvanishing positive time delay between the electric field maximum and the instant of ionization. Moreover, we find a nonzero exit momentum in the direction of the electric field. To extract proper tunneling times from asymptotic momentum distributions of ionized electrons, it is essential to incorporate the electron’s initial momentum in the direction of the external electric field.

Q. Z. Lv, Heiko Bauke, Q. Su, C. H. Keitel, R. Grobe
«Bosonic pair creation and the SchiffSnyderWeinberg effect»
peer reviewed article in Physical Review A, vol. 93, article 012119 (2016)
see also arXiv:1510.05418
AbstractInteractions between different bound states in bosonic systems can lead to pair creation. We study this process in detail by solving the KleinGordon equation on spacetime grids in the framework of timedependent quantum field theory. By choosing specific external field configurations, two bound states can become pseudodegenerate, which is commonly referred to as the SchiffSnyderWeinberg effect. These pseudodegenerate bound states, which have complex energy eigenvalues, are related to the pseudoHermiticity of the KleinGordon Hamiltonian. In this work, the influence of the SchiffSnyderWeinberg effect on pair production is studied. A generalized SchiffSnyderWeinberg effect, where several pairs of pseudodegenerate states appear, is found in combined electric and magnetic fields. The generalized SchiffSnyderWeinberg effect likewise triggers pair creation. The particle number in these situations obeys an exponential growth law in time enhancing the creation of bosons, which cannot be found in fermionic systems.

Rico Erhard, Heiko Bauke
«Spin effects in KapitzaDirac scattering at light with elliptical polarization»
peer reviewed article in Physical Review A, vol. 92, article 042123 (2015)
see also arXiv:1509.01150
Abstract The KapitzaDirac effect, which refers to electron scattering at standing light waves, is studied in the Bragg regime with counterpropagating elliptically polarized electromagnetic waves having the same intensity, wavelength, and degree of polarization for two different setups. In the first setup, where the electric field components of the counterpropagating waves have the same sense of rotation, we find distinct spin effects. The spin of the scattered electrons and of the nonscattered electrons, respectively, precesses with a frequency that is of the order of the Braggreflection Rabi frequency. When the electric field components of the counterpropagating waves have opposite sense of rotation, which is the second considered setup, the standing wave has linear polarization and no spin effects can be observed. Our results are based on numerical solutions of the timedependent Dirac equation and the analytical solution of a relativistic Pauli equation, which accounts for the leading relativistic effects.

Anton Wöllert, Heiko Bauke, Christoph H. Keitel
«Spin polarized electronpositron pair production via elliptical polarized laser fields»
peer reviewed article in Physical Review D, vol. 91, article 125026 (2015)
see also arXiv:1502.06414
AbstractWe study nonperturbative multiphoton electronpositron pair creation in ultrastrong electromagnetic fields formed by two counterpropagating pulses with elliptic polarization. Our numerical approach allows us to take into account the temporal as well as the spatial variation of the standing electromagnetic field. The spin and momentum resolved pair creation probabilities feature characteristic Rabi oscillations and resonance spectra. Therefore, each laser frequency features a specific momentum distribution of the created particles. We find that, depending on the relative polarization of both pulses, the created electrons may be spin polarized along the direction of field propagation.

Heiko Bauke, Sven Ahrens, Christoph H. Keitel, Rainer Grobe
«Spin dynamics in relativistic lightmatter interaction»
peer reviewed article in Proceedings of SPIE, Research Using Extreme Light: Entering New Frontiers with PetawattClass Lasers II, vol. 9515, article 95150L (2015)
see also arXiv:1504.03489
AbstractVarious spin effects are expected to become observable in lightmatter interaction at relativistic intensities. Relativistic quantum mechanics equipped with a suitable relativistic spin operator forms the theoretical foundation for describing these effects. Various proposals for relativistic spin operators have been offered by different authors, which are presented in a unified way. As a result of the operators' mathematical properties only the FoldyWouthuysen operator and the Pryce operator qualify as possible proper relativistic spin operators. The ground states of highly charged hydrogenlike ions can be utilized to identify a legitimate relativistic spin operator experimentally. Subsequently, the FoldyWothuysen spin operator is employed to study electronspin precession in highintensity standing light waves with elliptical polarization. For a correct theoretical description of the predicted electronspin precession relativistic effects due to the spin angular momentum of the electromagnetic wave has to be taken into account even in the limit of low intensities.

Anton Wöllert, Michael Klaiber, Heiko Bauke, Christoph H. Keitel
«Relativistic tunneling picture of electronpositron pair creation»
peer reviewed article in Physical Review D, vol. 91, article 065022 (2015)
see also arXiv:1410.2401
AbstractThe common tunneling picture of electronpositron pair creation in a strong electric field is generalized to pair creation in combined crossed electric and magnetic fields. This enhanced picture, being symmetric for electrons and positrons, is formulated in a gaugeinvariant and Lorentzinvariant manner for quasistatic fields. It may be used to infer qualitative features of the pair creation process. In particular, it allows for an intuitive interpretation of how the presence of a magnetic field modifies and, in particular cases, even enhances pair creation. The creation of electrons and positrons from the vacuum may be assisted by an energetic photon, which can also be incorporated into this picture of pair creation.

Heiko Bauke, Sven Ahrens, Rainer Grobe
«Electronspin dynamics in elliptically polarized light waves»
peer reviewed article in Physical Review A, vol. 90, article 052101 (2014)
see also arXiv:1409.2647
AbstractWe investigate the coupling of the spin angular momentum of light beams with elliptical polarization to the spin degree of freedom of free electrons. It is shown that this coupling, which is of similar origin as the wellknown spinorbit coupling, can lead to spin precession. The spinprecession frequency is proportional to the product of the laserfield's intensity and its spin density. The electronspin dynamics is analyzed by employing exact numerical methods as well as timedependent perturbation theory based on the fully relativistic Dirac equation and on the nonrelativistic Pauli equation that is amended by a relativistic correction that accounts for the light's spin density.

Heiko Bauke, Sven Ahrens, Christoph H. Keitel, Rainer Grobe
«Electronspin dynamics induced by photon spins»
peer reviewed article in New Journal of Physics, vol. 16, article 103028 (2014)
see also arXiv:1401.5976
Abstract
Strong rotating magnetic fields may cause a precession of the
electron's spin around the rotation axis of the magnetic field. The
superposition of two counterpropagating laser beams with circular
polarization and opposite helicity features such a rotating magnetic
field component but also carries spin. The laser's spin density, which
can be expressed in terms of the laser's electromagnetic fields and
potentials, couples to the electron's spin via a relativistic
correction to the Pauli equation. We show that the quantum mechanical
interaction of the electron's spin with the laser's rotating magnetic
field and with the laser's spin density counteract each other in such
a way that a net spin rotation remains with a precession frequency
that is much smaller than the frequency one would expect from the
rotating magnetic field alone. In particular, the frequency scales
differently with the laser's electric field strength depending on if
relativistic corrections are taken into account or not. Thus, the
relativistic coupling of the electron's spin to the laser's spin
density changes the dynamics not only quantitatively but also
qualitatively as compared to the nonrelativistic theory. The
electron's spin dynamics is a genuine quantum mechanical relativistic
effect.

Meng Wen, Heiko Bauke, Christoph H. Keitel
«Dynamical spin effects in ultrarelativistic laser pulses»
arXiv:1406.3659
Abstract
The dynamics of single laserdriven electrons and many particle systems with spin are investigated on the basis
of a classical theory. We demonstrate that the spin forces can alter the electron dynamics in an ultrarelativistic
laser field due to the coupling of the electron’s spin degree of freedom to its kinematic momentum. Highenergy
electrons can acquire significant spindependent transverse momenta while passing through a counterpropagating
ultrarelativistic infrared laser pulse. Numerical calculations show that the deflection of the electrons by the laser
pulse is determined by the laser intensity, the pulse duration, and the initial spin orientation of the electron. We
complement our investigation of these dynamical spin effects by performing particleincell simulations and point
out possibilities of an experimental realization of the predicted effect with available laser parameters.

Heiko Bauke, Sven Ahrens, Christoph H. Keitel, Rainer Grobe
«Relativistic spin operators in various electromagnetic environments»
peer reviewed article in Physical Review A, vol. 89, article 052101 (2014)
see also arXiv:1403.0550
Abstract
Different operators have been suggested in the literature to describe the electron's spin degree of freedom within the relativistic Dirac theory. We compare concrete predictions of the various proposed relativistic spin operators in different physical situations. In particular, we investigate the socalled Pauli, FoldyWouthuysen, Czachor, Frenkel, Chakrabarti, Pryce, and FradkinGood spin operators. We demonstrate that when a quantum system interacts with electromagnetic potentials the various spin operators predict different expectation values. This is explicitly illustrated for the scattering dynamics at a potential step and in a standing laser field and also for energy eigenstates of hydrogenic ions. Therefore, one may distinguish between the proposed relativistic spin operators experimentally.

Heiko Bauke, Sven Ahrens, Christoph H. Keitel, Rainer Grobe
«What is the relativistic spin operator?»
peer reviewed article in New Journal of Physics, vol. 16, article 043012 (2014)
see also arXiv:1303.3862
Abstract
Although the spin is regarded as a fundamental property of the electron, there is no
universally accepted spin operator within the framework of relativistic quantum
mechanics. We investigate the properties of different proposals for a relativistic
spin operator. It is shown that most candidates are lacking essential features
of proper angular momentum operators, leading to spurious zitterbewegung
(quivering motion) or violation of the angular momentum algebra. Only the
FoldyWouthuysen operator and the Pryce operator qualify as proper relativistic
spin operators. We demonstrate that ground states of highly charged hydrogenlike
ions can be utilized to identify a legitimate relativistic spin operator
experimentally.

Michael Klaiber, Enderalp Yakaboylu, Carsten Müller, Heiko Bauke, Gerhard G. Paulus, Karen Z. Hatsagortsyan
«Spin effects in relativistic ionization with highly charged ions in superstrong laser fields»
peer reviewed article in Journal of Physics B: Atomic, Molecular and Optical Physics, vol. 47, article 065603 (2014)
see also arXiv:1305.5379, the accompanying LabTalk article and Europhysics News vol. 45, no. 3, p. 13
Abstract
Spin effects in abovethreshold ionization of hydrogenlike highly
charged ions in superstrong laser fields are
investigated. Spinresolved ionization rates in the tunneling regime are
calculated by employing two versions of a relativistic Coulombcorrected
strongfield approximation (SFA). An intuitive simpleman model is
developed which explains the derived scaling laws for spinflip and
spinasymmetry effects. The intuitive model as well as our ab initio
numerical simulations support the analytical results for the spin
effects obtained in the dressed SFA where the impact of the laser field
on the electron spin evolution in the bound state is taken into
account. In contrast, the standard SFA is shown to fail in reproducing
spin effects at ionization even at a qualitative level. The anticipated
spineffects are expected to be measurable with modern laser techniques
combined with an ion storage facility.

Enderalp Yakaboylu, Michael Klaiber, Heiko Bauke, Karen Z. Hatsagortsyan, Christoph H. Keitel
«Relativistic features and time delay of laserinduced tunnelionization»
peer reviewed article in Physical Review A, vol. 88, article 063421 (2013)
see also arXiv:1309.0610
Abstract
The electron dynamics in the classically forbidden region during relativistic tunnel ionization is investigated. The classical forbidden region in the relativistic regime is identified by defining a gaugeinvariant totalenergy operator. Introducing positiondependent energy levels inside the tunneling barrier, we demonstrate that the relativistic tunnel ionization can be well described by a onedimensional intuitive picture. This picture predicts that, in contrast to the wellknown nonrelativistic regime, the ionized electron wave packet arises with a momentum shift along the laser's propagation direction. This is compatible with results from a strongfield approximation calculation where the binding potential is assumed to be zero ranged. Further, the tunneling time delay, stemming from Wigner's definition, is investigated for model configurations of tunneling and compared with results obtained from the exact propagator. By adapting Wigner's time delay definition to the ionization process, the tunneling time is investigated in the deeptunneling and in the nearthresholdtunneling regimes. It is shown that while in the deeptunneling regime signatures of the tunneling time delay are not measurable at remote distance, they are detectable, however, in the latter regime.

Sven Ahrens, Heiko Bauke, Christoph H. Keitel, Carsten Müller
«KapitzaDirac effect in the relativistic regime»
peer reviewed article in Physical Review A, vol. 88, article 012115 (2013)
see also arXiv:1305.5507
Abstract
A relativistic description of the KapitzaDirac effect in the socalled
Bragg regime with two and three interacting photons is presented by
investigating both numerical and perturbative solutions of the Dirac
equation in momentum space. We demonstrate that spin flips can be
observed in the twophoton and the threephoton KapitzaDirac effects
for certain parameters. During the interaction with the laser field the
electron's spin is rotated, and we give explicit expressions for the
rotation axis and the rotation angle. The offresonant KapitzaDirac
effect, that is, when the Bragg condition is not exactly fulfilled, is
described by a generalized Rabi theory. We also analyze the infield
quantum dynamics as obtained from the numerical solution of the Dirac
equation.

S. Ahrens, T.O. Müller, S. VillalbaChávez, H. Bauke, C. Müller
«Spin effects in strongfield laserelectron interactions»
peer reviewed article in Journal of Physics: Conference Series, vol. 414, nr. 1, article 012012 (2013)
see also arXiv:1308.0231
AbstractThe electron spin degree of freedom can play a significant role in relativistic scattering processes involving intense laser fields. In this contribution we discuss the influence of the electron spin on (i) KapitzaDirac scattering in an xray laser field of high intensity, (ii) photoinduced electronpositron pair production in a strong laser wave and (iii) multiphoton electronpositron pair production on an atomic nucleus. We show that in all cases under consideration the electron spin can have a characteristic impact on the process properties and their total probabilities. To this end, spinresolved calculations based on the Dirac equation in the presence of an intense laser field are performed. The predictions from Dirac theory are also compared with the corresponding results from the KleinGordon equation.

Michael Klaiber, Enderalp Yakaboylu, Heiko Bauke, Karen Z. Hatsagortsyan, and Christoph H. Keitel
«UndertheBarrier Dynamics in LaserInduced Relativistic Tunneling»
peer reviewed article in Physical Review Letters, vol. 110, article 153004 (2013)
see also arXiv:1205.2004,
press release 1
and press release 2, prophysik.de
Abstract
The tunneling dynamics in relativistic strongfield 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 quantum dynamics in the classically forbidden region features two time scales, the typical time that characterizes the probability density’s decay of the ionizing electron under the barrier (Keldysh time) and the time interval which the electron spends inside the barrier (EisenbudWignerSmith tunneling time). In the relativistic regime, an electron momentum shift as well as a spatial shift along the laser propagation direction arise during the underthebarrier motion which are caused by the laser magnetic field induced Lorentz force. The momentum shift is proportional to the Keldysh time, while the wavepacket’s spatial drift is proportional to the EisenbudWignerSmith time. 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 EisenbudWignerSmith time delay disappears at far distances for pure quasistatic tunneling dynamics.

Sven Ahrens, Heiko Bauke, Christoph H. Keitel, and Carsten Müller
«Spin dynamics in the KapitzaDirac effect»
peer reviewed article in Physical Review Letters, vol. 109, article 043601 (2012)
see also arXiv:1204.0239
Abstract
Electron spin dynamics in KapitzaDirac 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 timedependent Dirac equation. Distinct spin dynamics, with Rabi
oscillations and complete spinflip transitions, is demonstrated for
KapitzaDirac scattering involving three photons in a parameter regime
accessible to future highpower Xray 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 laserdriven hydrogenlike ions»
peer reviewed article in Physical Review A, vol. 83, nr. 6, article 063414 (2011)
AbstractIn
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 timedependent Dirac equation and the
timedependent KleinGordon equation as well as by the classical
phasespace averaging method. For this purpose, we generalize the
phasespace 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 nearinfrared to soft xray radiation. We find that
ionization in fewcycle 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.

Heiko Bauke
«Timedependent relativistic wave equations: Numerics of the Dirac and the Klein–Gordon equation»
in Computational StrongField Quantum Dynamics edited by Dieter Bauer, De Gruyter (2017)

Randolf Beerwerth, Heiko Bauke
«Krylov subspace methods for the Dirac equation»
peer reviewed article in Computer Physics Communications, vol. 188, pp. 189–197 (2015)
see also arXiv:1407.7370
AbstractThe Lanczos algorithm is evaluated for solving the timeindependent
as well as the timedependent Dirac equation with arbitrary
electromagnetic fields. We demonstrate that the Lanczos algorithm
can yield very precise eigenenergies and allows very precise time
propagation of relativistic wave packets. The Dirac Hamiltonian's
property of not being bounded does not hinder the applicability of
the Lanczos algorithm. As the Lanczos algorithm requires only
matrixvector and inner products, which both can be efficiently
parallelized, it is an ideal method for largescale calculations.
The excellent parallelization capabilities are demonstrated by a
parallel implementation of the Dirac Lanczos propagator utilizing
the Message Passing Interface standard.

Heiko Bauke, Michael Klaiber, Enderalp Yakaboylu, Karen Z. Hatsagortsyan, Sven Ahrens, Carsten Müller, Christoph H. Keitel
«Computational relativistic quantum dynamics and its application to relativistic tunneling and KapitzaDirac scattering»
peer reviewed article in Proceedings of SPIE, HighPower, HighEnergy, and HighIntensity Laser Technology; and Research Using Extreme Light: Entering New Frontiers with PetawattClass Lasers, vol. 8780, article 87801Q (2013)
see also arXiv:1306.0702
AbstractComputational methods are indispensable to study the quantum dynamics of relativistic lightmatter interactions in parameter regimes where analytical methods become inapplicable. We present numerical methods for solving the timedependent Dirac equation and the timedependent KleinGordon equation and their implementation on high performance graphics cards. These methods allow us to study tunneling from hydrogenlike highly charged ions in strong laser fields and KapitzaDirac scattering in the relativistic regime.

Frederick Blumenthal and Heiko Bauke
«A stability analysis of a real space split operator method for the KleinGordon equation»
peer reviewed article in Journal of Computational Physics,
vol. 231, nr. 2, pp. 454–464 (2012)
see also arXiv:1105.3660
AbstractWe
carry out a stability analysis for the real space split operator
method for the propagation of the timedependent 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 vonNeumann 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
$\frac{h}{\tau}<\sqrt{d}c$
for second order finite differences and
$\frac{1}{2}\frac{\sqrt{3}h}{\tau}<\sqrt{d}c$
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
noninteracting particles. Thus, it allows a more direct comparison
between classical and quantum dynamical features.

Matthias Ruf, Heiko Bauke and Christoph H. Keitel
«A real space split operator method for the KleinGordon equation»
peer reviewed article in Journal of Computational Physics, vol. 228, nr. 24, pp. 9092–9106 (2009)
Abstract
The KleinGordon equation is a Lorentz invariant equation of motion
for spinless particles. We propose a real space split operator method
for the solution of the timedependent KleinGordon 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 twocomponent representation of the KleinGordon equation is a
nilpotent operator, that is
${K}^{2}$, allows us to
implement the split operator method for the KleinGordon equation
entirely in real space. Consequently, the split operator method for
the KleinGordon 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)
AbstractThe
integration of timedependent quantum mechanical wave equations
is a fundamental problem in computational physics and computational
chemistry. The wavefunction'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 socalled KramersHenneberger 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)
AbstractThe
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 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:condmat/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:condmat/0307138
or some articles in popular journals about our work:
Abstract
Tossing a coin is the most elementary MonteCarlo 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:condmat/0305319
Abstract
Since the work of Ferrenberg et al. [Phys. Rev. Lett. 69 3382 (1992)] some pseudorandomnumber 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 randomnumber generators calculate a new pseudorandomnumber 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 randomnumber generator than empirical tests with their limited horizon.

Heiko Bauke
«Theorie und Implementation von parallelisierten Pseudozufallszahlengeneratoren»
Forschungsbeleg
 Heiko Bauke
«Digitale Auferstehung»
LinuxMagazin, October 2007, pp. 78–81
 Heiko Bauke und Stephan Mertens
«Cluster Computing»
Praktische Einführung in das Hochleistungsrechnen auf LinuxClustern
Springer Verlag, 2005, ISBN 3540422994
buy from
Springer (hardcover and ebook),
amazon.de,
Google play
 Heiko Bauke
«MPI – Programming clusters»
LinuxMagazine, Issue 31, June 2003, pp. 70–74
 Heiko Bauke
«Zahlenbeißer für alle – Cluster programmieren mit
MPI»
LinuxMagazin, May 2003, pp. 84–89
 Heiko Bauke
«LinuxBeowulfCluster;
Herausforderung im High Performance Computing and Networking»
Talk given at the Linuxtag in Magdeburg 2001

H. Bauke, C. Moore, J. B. Rouquier, D. Sherrington
«Topological phase transition in a network model with preferential attachment and node removal»
peer reviewed article in The European Physical Journal B, vol. 83, pp. 519–524 (2011)
see also arXiv:1201.4044
Abstract
Preferential attachment is a popular model of growing networks. We consider a generalized model with random node removal, and a combination of preferential and random attachment. Using a highdegree expansion of the master equation, we identify a topological phase transition depending on the rate of node removal and the relative strength of preferential vs. random attachment, where the degree distribution goes from a power law to one with an exponential tail.

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 powerlaw
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 and David Sherrington
«Local attachment in networks under churn»
arXiv:0706.0018
Abstract
In this contribution we introduce local attachment as an universal
networkjoining protocol for peertopeer networks, social networks,
or other kinds of networks. Based on this protocol nodes in a
finitesize network dynamically create powerlaw connectivity
distributions. Nodes or peers maintain them in a selforganized
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 powerlaw 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 peertopeer protocols to enable the efficient production of
stable network topologies in a continuously changing environment.
 Heiko Bauke
«Parameter estimation for powerlaw 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:
Abstract
Distributions following a powerlaw are an ubiquitous
phenomenon. Methods for determining the exponent of a powerlaw 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
Messagepassing 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 messagepassing
algorithms can help solve. Therefore, Sudoku is an ideal vehicle to
demonstrate these methods' strengths and limitations.
 Heiko Bauke
«Zur Universalität des RandomEnergyModells»
Ph.D. thesis, Books on Demand, 2006, ISBN 3833454253
buy from
amazon.de
 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:condmat/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 EdwardsAnderson 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:condmat/0402010
Abstract
Number partitioning is a classical problem from combinatorial
optimization. In physical terms it corresponds to a long range
antiferromagnetic 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, 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:condmat/0208081
or read the report «Physics
tackles processor problem» about our work by
Kimberly Patch in Technology Research News
Abstract
An “easyhard” 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 meanfield 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, LCDET2001078

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 nonmagnetic 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
nonaxissymmetric 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»
in ZfP im Übergang zum 3. Jahrtausend (Jahrestagung Zerstörungsfreie Materialprüfung 2000 Innsbruck, 29.–31. Mai 2000),
DGZfPBerichtsband 73.1, pp. 145–154 (2000)
