University of Basel  >  Condensed Matter Theory

Michael N. Leuenberger


 
Address:  IPAPS 0360
Department of Physics 
University of San Diego 
La Jolla 
CA 92093
USA
e-mail:  mleuenbe@physics.ucsd.edu
phone (office):  +1 (858) 822-1081
fax:  +1 (858) 534-2232



Current affiliation
Assistant Professor in Theoretical Physics
Address: Nanoscience Technology Center and Department of Physics, University of Central Florida, 12424 Research Parkway Suite 400, Orlando, FL 32826
Phone: 1-407-882-2846
Fax: 1-407-882-2819
E-mail: mleuenbe@mail.ucf.edu


Biographical Data
Family name: Leuenberger
Given names: Michael, Niklaus
Born: September 7, 1973, in Basel, Switzerland.
Citizenship: Swiss.
Civil status: married.



Education
December 1992:
High-School examination/Baccalaureate with focus in German, French, English, Latin, Mathematics, Physics, and Chemistry (Gymnasium Münchenstein, Switzerland). Top 5% award recipient.

Spring/summer 1993:
Basic training in the Swiss military service.

November 1993:
Matriculation at the University of Basel as student in physics.

Winter 1997/98:
Diploma thesis entitled "Spin relaxation in Mn12-acetate" done under the supervision of Prof. D. Loss.

March 1998:
Diploma exam in theoretical physics (University of Basel, Switzerland). The diploma exam included as main subjects theoretical physics, experimental physics, mathematics, as subsidiary subject computer science, and as special subject gauge theories. My diploma mark was 5.7 (with the scale 6.0 for highest and 1.0 for lowest mark).

April 2002:
PhD exam in Theoretical Condensed Matter Physics (summa cum laude).


Professional Activities
March 1998 -- April 2002:
Research and teaching assistant in the group of Prof. D. Loss in Theoretical Physics, University of Basel, Switzerland.

May 2002 -- October 2002:
Postdoctoral research and teaching assistant in the group of Prof. D. Loss in Theoretical Physics, University of Basel, Switzerland.

November 2002 -- July 2004:
Postdoctoral researcher in the group of Prof. Michael E. Flatte in Theoretical Physics, University of Iowa, USA.

August 2004 -- July 2005:
Postdoctoral researcher in the group of Prof. Lu J. Sham in Theoretical Physics, University of California, San Diego, USA.

August 2005 -- :
Assistant Professor in Theoretical Physics in the Nanoscience Technology Center and the Department of Physics at the University of Central Florida, Orlando, FL, USA.


Teaching Experience
Summer semester 1998:
Course lectures on Quantum Mechanics II (assisting Prof. D. Loss), exercises in Quantum Mechanics II.

Winter semester 1998/99:
Exercises in Quantum Mechanics I.

Summer semester 1999:
Course lectures on Quantum Mechanics II (assisting Prof. D. Loss), exercises in Quantum Mechanics II.

Winter semester 1999/2000:
Course lectures on Quantum Mechanics I (assisting Prof. D. Loss), exercises in Quantum Mechanics I.

Summer semester 2000:
Exercises in Quantum Mechanics II.

Winter semester 2000/01:
Exercises in Theoretical Mechanics.

Summer semester 2001:
Exercises in Theoretical Electrodynamics.

March 9, 2005:
Lecture on Electrodynamics for undergraduate students at the University of Kansas, USA.

Fall semester 2005
PHY2049.0004: Lecture on Physics for Scientists and Engineers in the Dept. of Physics at the University of Central Florida


Publications
Berry Phase Oscillations of the Kondo Effect in Single-Molecule Magnets
Michael N. Leuenberger, Eduardo R. Mucciolo
cond-mat/0604380

We show that it is possible to topologically induce or quench the Kondo resonance in the conductance of a single-molecule magnet (S>1/2) strongly coupled to metallic leads. This can be achieved by applying a magnetic field perpendicular to the molecule easy axis and works for both full- and half-integer spin cases. The effect is caused by the Berry phase interference between two quantum tunneling paths of the molecule's spin. We have calculated the renormalized Berry phase oscillations of the Kondo peaks as a function of the transverse magnetic field as well as the conductance of the molecule by means of the poor man's scaling method. We propose to use a new variety of the single-molecule magnet Ni4 for the experimental observation of this phenomenon.


Theory of Umklapp-assisted recombination of bound excitons in Si:P
Michael N. Leuenberger, Lu J. Sham
cond-mat/0507383

We present the calculations for the oscillator strength of the recombination of excitons bound to phosphorous donors in silicon. We show that the direct recombination of the bound exciton cannot account for the experimentally measured oscillator strength of the no-phonon line. Instead, the recombination process is assisted by an umklapp process of the donor electron state. We make use of the empirical pseudopotential method to evaluate the Umklapp-assisted recombination matrix element in second-order perturbation theory. Our result is in excellent agreement with the experiment. We also present two methods to improve the optical resolution of the optical detection of the spin state of a single nucleus in silicon.


Phonon Bottleneck Effect Leads to Observation of Quantum Tunneling of the Magnetization and Butterfly Hysteresis Loops in (Et4N)3Fe2F9
Ralph Schenker, Michael N. Leuenberger, Gregory Chaboussant, Daniel Loss, Hans U. G\"udel
Phys. Rev. B 72, 184403 (2005)

A detailed investigation of the unusual dynamics of the magnetization of (Et4N)3Fe2F9 (Fe2), containing isolated [Fe2F9]3– dimers, is presented and discussed. Fe2 possesses an S=5 ground state with an energy barrier of 2.40 K due to an axial anisotropy. Poor thermal contact between sample and bath leads to a phonon bottleneck situation, giving rise to butterfly-shaped hysteresis loops below 5 K concomitant with slow decay of the magnetization for magnetic fields Hz applied along the FeFe axis. The butterfly curves are reproduced using a microscopic model based on the interaction of the spins with resonant phonons. The phonon bottleneck allows for the observation of resonant quantum tunneling of the magnetization at 1.8 K, far above the blocking temperature for spin-phonon relaxation. The latter relaxation is probed by ac magnetic susceptibility experiments at various temperatures and bias fields HDC. At HDC=0, no out-of-phase signal is detected, indicating that at T1.8 K Fe2 does not behave as a single-molecule magnet. At HDC=1 kG, relaxation is observed, occurring over the barrier of the thermally accessible S=4 first excited state that forms a combined system with the S=5 state.


Fault-tolerant quantum computing with spins using the conditional Faraday rotation
Michael N. Leuenberger
cond-mat/0412114.

We propose a fault-tolerant scheme for deterministic quantum computing with spins that is based on a quantum teleportation scheme using the conditional Faraday rotation. The phase gate between two sets of noninteracting quantum dots, embedded in microcavities inside a photonic crystal, is mediated by single photons, which yields a Faraday rotation rate high enough for gate operation times of 100 ps. Using sets of quantum dots and error correction codes makes our scheme fault-tolerant. Single-qubit operations on encoded qubits can be implemented by means of the optical Stark effect combined with the optical RKKY interaction.


The generalized rotating frame
Michael N. Leuenberger
J. Mag. Mag. Mat. 272-276, 1974-1975 (2004).

I introduce the transformation of a large spin system externally driven by several oscillating magnetic fields to the generalized rotating frame, which is a natural generalization of the standard rotating frame. This method requires that the spin system has non-equidistant energy levels, which is usually satisfied by anisotropies. Possible applications include the implementation of the Grover algorithm in molecular magnets or in large nuclear spins of semiconductors and the coherent manipulation of large single-spin states of arbitrary dimension.


Teleportation of electronic many-qubit states via single photons
Michael N. Leuenberger, Michael E. Flatte, D. D. Awschalom,
Phys. Rev. Lett. 94, 107401 (2005); see cond-mat/0407499.

We propose a teleportation scheme that relies only on single-photon measurements and Faraday rotation, for teleportation of many-qubit entangled states stored in the electron spins of a quantum dot system. The interaction between a photon and the two electron spins, via Faraday rotation in microcavities, establishes Greenberger-Horne-Zeilinger entanglement in the spin-photon-spin system. The appropriate single-qubit measurements, and the communication of two classical bits, produce teleportation. This scheme provides the essential link between spintronic and photonic quantum information devices by permitting quantum information to be exchanged between them.


Measuring the entanglement of coupled spins by multiphoton interference
Michael N. Leuenberger, Michael E. Flatte, D. D. Awschalom
cond-mat/0307657

We propose an experimental method to measure the entanglement of coupled spins, each in a separate quantum dot, by means of multiphoton interference patterns generated through the scattering of two laser beams off the quantum dots. We calculate the N-photon quantum correlations measured by N detectors on an image plane. Using two perpendicular laser beams, either many correlation measurements on a time ensemble or a single correlation measurement on a spatial ensemble of the many-qubit state is sufficient to retrieve all the possible amplitudes of a many-qubit state.


The Grover algorithm with large nuclear spins in semiconductors
Michael N. Leuenberger, Daniel Loss
Phys. Rev. B 68, 165317 (2003), see cond-mat/0304674

We show a possible way to implement the Grover algorithm in large nuclear spins 1/2 < I < 9/2 in semiconductors. The Grover sequence is performed by means of multiphoton transitions that distribute the spin amplitude between the nuclear spin states. They are distinguishable due to the quadrupolar splitting, which makes the nuclear spin levels non-equidistant. We introduce a generalized rotating frame for an effective Hamiltonian that governs the non-perturbative time evolution of the nuclear spin states for arbitrary spin lengths I. The larger the quadrupolar splitting, the better the agreement between our approximative method using the generalized rotating frame and exact numerical calculations.


Discrete Fourier Transform in Nanostructures using Scattering
Michael N. Leuenberger, Daniel Loss, Michael E. Flatte, D. D. Awschalom
J. Appl. Phys. 95, 8167 (2004), see cond-mat/0302279

In this paper we show that the discrete Fourier transform can be performed by scattering a coherent particle or laser beam off a two-dimensional potential that has the shape of rings or peaks. After encoding the initial vector into the two-dimensional potential, the Fourier-transformed vector can be read out by detectors surrounding the potential. The wavelength of the laser beam determines the necessary accuracy of the 2D potential, which makes our method very fault-tolerant.


Quantum Spin Dynamics in Molecular Magnets
Michael N. Leuenberger, Florian Meier, Daniel Loss
Monatshefte für Chemie 134, 217 (2003),  see cond-mat/0205457.

The detailed theoretical understanding of quantum spin dynamics in various molecular magnets is an important step on the roadway to technological applications of these systems. Quantum effects in both ferromagnetic and antiferromagnetic molecular clusters are, by now, theoretically well understood. Ferromagnetic molecular clusters allow one to study the interplay of incoherent quantum tunneling and thermally activated transitions between states with different spin orientation. The Berry phase oscillations found in Fe8 are signatures of the quantum mechanical interference of different tunneling paths. Antiferromagnetic molecular clusters are promising candidates for the observation of coherent quantum tunneling on the mesoscopic scale. Although challenging, applications of molecular magnetic clusters for data storage and quantum data processing are within experimental reach already with present day technology.


Butterfly Hysteresis and Slow Relaxation of the Magnetization in (Et4N)3Fe2F9: Manifestations of a Single-Molecule Magnet
Ralph Schenker, Michael N. Leuenberger, Gregory Chaboussant, Hans U. Guedel, Daniel Loss
Chem. Phys. Lett. 358, 413-418 (2002), see cond-mat/0204445.

(Et4N)3Fe2F9 exhibits a butterfly--shaped hysteresis below 5 K when the magnetic field is parallel to the threefold axis, in accordance with a very slow magnetization relaxation in the timescale of minutes. This is attributed to an energy barrier Delta=2.40 K resulting from the S=5 dimer ground state of [Fe2F9]3- and a negative axial anisotropy. The relaxation partly occurs via thermally assisted quantum tunneling. These features of a single-molecule magnet are observable at temperatures comparable to the barrier height, due to an extremely inefficient energy exchange between the spin system and the phonons. The butterfly shape of the hysteresis arises from a phonon avalanche effect.


Quantum information processing with large nuclear spins in GaAs semiconductors
Michael N. Leuenberger, Daniel Loss, Martino Poggio, David D. Awschalom
Phys. Rev. Lett. 89, 207601 (2002), see cond-mat/0204355.

We propose an implementation for quantum information processing based on coherent manipulations of nuclear spins I=3/2 in GaAs semiconductors. We describe theoretically an NMR method which involves multiphoton transitions and which exploits the non-equidistance of nuclear spin levels due to quadrupolar splittings. Starting from known spin anisotropies we derive effective Hamiltonians in a generalized rotating frame, valid for arbitrary I, which allow us to describe the non-perturbative time evolution of spin states generated by magnetic rf fields. We identify an experimentally accessible regime where multiphoton Rabi oscillations are observable. In the nonlinear regime, we find Berry phase interference effects.


Quantum Computing in Molecular Magnets
Michael N. Leuenberger and Daniel Loss
Nature 410, 789-793 (2001), see cond-mat/0011415.

Shor and Grover demonstrated that a quantum computer can outperform any classical computer in factoring numbers[1] and in searching a database[2] by exploiting the parallelism of quantum mechanics. Whereas Shor's algorithm requires both superposition and entanglement of a many-particle system[3], the superposition of single-particle quantum states is sufficient for Grover's algorithm[4]. Recently, the latter has been successfully implemented[5] using Rydberg atoms. Here we propose an implementation of Grover's algorithm that uses molecular magnets[6,7,8,9,10], which are solid-state systems with a large spin; their spin eigenstates make them natural candidates for single-particle systems. We show theoretically that molecular magnets can be used to build dense and efficient memory devices based on the Grover algorithm. In particular, one single crystal can serve as a storage unit of a dynamic random access memory device. Fast electron spin resonance pulses can be used to decode and read out stored numbers of up to 105, with access times as short as 10-10 seconds. We show that our proposal should be feasible using the molecular magnets Fe8 and Mn12.


Spintronics and Quantum Computing: Switching Mechanisms for Qubits
Michael N. Leuenberger and Daniel Loss
Physica E 10, 452-457 (2001), see cond-mat/0010434.

Quantum computing and quantum communication are remarkable examples of new information processing technologies that arise from the coherent manipulation of spins in nanostructures. We review our theoretical proposal for using electron spins in quantum-confined nanostructures as qubits. We present single- and two-qubit gate mechanisms in laterally as well as vertically coupled quantum dots and discuss the possibility to couple spins in quantum dots via exchange or superexchange. In addition, we propose a new stationary wave switch, which allows to perform quantum operations with quantum dots or spin-1/2 molecules placed on a 1D or 2D lattice.


Spin tunneling and topological selection rules for integer spins
Michael N. Leuenberger and Daniel Loss.
Phys. Rev. B 63, 054414 (2001), see cond-mat/0006075.

We present topological interference effects for the tunneling of a single large spin, which are caused by the symmetry of a general class of magnetic anisotropies. The interference originates from spin Berry phases associated with different tunneling paths exposed to the same dynamics. Introducing a generalized path integral for coherent spin states, we evaluate transition amplitudes between ground as well as low-lying excited states. We show that these interference effects lead to topological selection rules and spin-parity effects for integer spins that agree with quantum selection rules and which thus provide a generalization of the Kramers degeneracy to integer spins. Our results apply to the molecular magnets Mn12 and Fe8.


Incoherent Zener tunneling and its application to molecular magnets
Michael N. Leuenberger and Daniel Loss.
Phys. Rev. B 61, 12200-12203 (2000), see cond-mat/9911065

We generalize the Landau-Zener theory of coherent tunneling transitions by taking thermal relaxation into account. The evaluation of a new generalized master equation containing a dynamic tunneling rate that includes the interaction between the relevant system and its environment leads to an incoherent Zener transition probability with an exponent that is twice as large as the one of the coherent Zener probability in the limit T -> 0. We apply our results to molecular clusters, in particular to recent measurements of the tunneling transition of spins in Fe8 crystals performed by Wernsdorfer and Sessoli [Science 284, 133 (1999)].


Reply to the comment of Chudnovsky&Garanin on "Spin relaxation in Mn12-acetate"
Michael N. Leuenberger and Daniel Loss.
Europhys. Lett. 52 (2), 247-248 (2000), see cond-mat/0006149.

Reply to the comment of E.M. Chudnovsky and D.A. Garanin on Europhys. Lett. 46, 692 (1999).


Spin tunneling and phonon-assisted relaxation in Mn12-acetate
Michael N. Leuenberger and Daniel Loss.
Phys. Rev. B 61, 1286-1302 (2000), see cond-mat/9907154.

We present a comprehensive theory of the magnetization relaxation in a Mn12-acetate crystal in the high temperature regime (T>1K), which is based on phonon-assisted spin tunneling induced by quartic magnetic anisotropy and weak transverse magnetic fields. The overall relaxation rate as function of the longitudinal magnetic field is calculated and shown to agree well with experimental data including all resonance peaks measured so far. The Lorentzian shape of the resonances, which we obtain via a generalized master equation that includes spin tunneling, is also in good agreement with recent data. We derive a general formula for the tunnel splitting energy of these resonances. We show that fourth-order diagonal terms in the Hamiltonian lead to satellite peaks. A derivation of the effective linewidth of a resonance peak is given and shown to agree well with experimental data. In addition, previously unknown spin-phonon coupling constants are calculated explicitly. The values obtained for these constants and for the sound velocity are also in good agreement with recent data. We show that the spin relaxation in Mn12-acetate takes place via several transition paths of comparable weight. These transition paths are expressed in terms of intermediate relaxation times, which are calculated and which can be tested experimentally.


Spin relaxation in Mn12-acetate
Michael N. Leuenberger and Daniel Loss.
Europhys. Lett. 46 (5), 692-698 (1999),  see cond-mat/9810156.

We present a comprehensive derivation of the magnetization relaxation in a Mn12-acetate crystal based on thermally assisted spin tunneling induced by quartic anisotropy and weak transverse magnetic fields. The overall relaxation rate as function of the magnetic field is calculated and shown to agree well with data including all resonance peaks. The Lorentzian shape of the resonances is also in good agreement with recent data. A generalized master equation including resonances is derived and solved exactly. It is shown that many transition paths with comparable weight exist that contribute to the relaxation process. Previously unknown spin-phonon coupling constants are calculated explicitly.



Invited Talks
Fault-tolerant quantum computing with spins using the conditional Faraday rotation
Condensed matter seminar, University of Kansas, USA, March 9, 2005.
Condensed matter seminar, Vanderbilt University, USA, February 8, 2005.
Condensed matter seminar, University of California, San Diego, USA, February 2, 2005.
Materials physics/solid state seminar, Department of Physics and Astronomy, University of Iowa, USA, January 25, 2004.

Teleportation of electronic many-qubit states via single photons
Condensed matter seminar, Department of Physics and Astronomy, University of Central Florida, USA, April 6, 2005.
Physics colloquium, Department of Physics and Astronomy, University of Kansas, USA, March 8, 2005.
Physics colloquium, Department of Physics and Astronomy, Vanderbilt University, USA, February 7, 2005.
Physics colloquium, Department of Physics and Astronomy, University of Iowa, USA, January 24, 2005.
Condensed matter seminar, University of California, San Diego, USA, October 22, 2004.
Materials physics/solid state/math seminar, Department of Physics and Astronomy, University of Iowa, USA, May 4, 2004.
Condensed matter seminar, University of Basel, Switzerland, February 11, 2004.

Proposal for measuring the entanglement of coupled spins by multiphoton interference
Materials physics/solid state seminar, Department of Physics and Astronomy, University of Iowa, USA, November 11, 2003.
Condensed matter seminar, University of California, San Diego, USA, November 7, 2003.
Condensed matter seminar, Jet Propulsion Lab of NASA, California Institute of Technology, Pasadena, USA, November 3, 2003.
Condensed matter seminar, University of Basel, Switzerland, August 4, 2003.

Quantum information processing with large spins
Condensed matter seminar, Department of Physics, New York University, USA, May 9, 2003.

Quantum information processing with large nuclear spins in GaAs semiconductors
Condensed matter seminar, University of California, San Diego, USA, November 5, 2003.
Condensed matter seminar, Centre for Quantum Computer Technology, Sydney, Australia, July 26, 2002.
Condensed matter seminar, Department of Physics, Mahidol University, Bangkok, Thailand, July 10, 2002.
Materials physics/solid state seminar, Department of Physics and Astronomy, University of Iowa, USA, April 22, 2002.
Condensed matter seminar, Department of Physics, University of Illinois at Urbana-Champaign, USA, April 19, 2002.

Quantum Computing in Molecular Magnets
Condensed matter seminar, Quantum Institute of the UCSB, Santa Barbara, USA, March 27, 2001.
Condensed matter seminar, LMU Fakultät für Physik, München, Germany, June 28, 2001.
GdR POMMES, Journées Thématiques Physique et Chimie des Nanomolécules Magnétiques , Dourdan, France, October 29-30, 2001.


Contributed Talks
Teleportation of electronic many-qubit states via single photons
APS march meeting, Los Angeles, USA, March 21-25, 2005.
PASPS III meeting, Santa Barbara, USA, July 21-23, 2004.

Proposal for measuring the entanglement of coupled spins by multiphoton interference
APS march meeting, Montreal, Canada, March 22-26, 2004.

Quantum information processing with large nuclear spins in GaAs semiconductors
Spintech II, Brugge, Belgium, August 4-8, 2003.
International Conference on Magnetism (ICM 2003), Rome, Italy, July 28 - August 1, 2003.
MRS spring meeting, San Francisco, CA, USA, April 21-25, 2003.
APS march meeting, Austin, TX, USA, March 3-7, 2003.

Quantum Computing in Molecular Magnets
March meeting of the APS, Indianapolis, USA, March 18-23, 2002.
Mid-term review meeting of the MolNanoMag network, Dourdan, France, December 13-15, 2001.

Incoherent Zener Tunneling and Berry Phase Oscillations in Molecular Magnets
Mid-term review meeting of the MolNanoMag network, Dourdan, France, December 13-15, 2001.

Spin tunneling in molecular magnets
Tutorial presentation at the workshop on the theoretical concepts and techniques for spin clusters and single molecule magnets of the MolNanoMag network, Florence, Italy, November 17-19, 2000.

Incoherent Zener tunneling and its application to molecular magnets
International conference on magnetism (ICM2000), Recife, Brazil, August 6-11, 2000.

Phonon-assisted and incoherent Zener tunneling of the spin in molecular magnets
ESF seminar on molecular magnets, Luebeck, Germany, May 20-23, 2000.
18th general conference of the condensed matter division of the European Physical Society, Montreux, Switzerland, March 13-17, 2000.

Spin relaxation in Mn12-acetate
Contributed talk at the 1999 Annual Meeting of the Swiss Physical Society, Berne, Switzerland, February 27, 1999.


Posters
Teleportation of electronic many-qubit states via single photons
Gordon Research Conference on Quantum Information Science, Ventura, CA, USA, February 27 - March 4, 2005.

Measuring the entanglement of coupled spins by multiphoton interference
Annual DARPA DSO SpinS Spintronics PI Review, Santa Monica, CA, USA, October 13-16, 2003.

Quantum information processing with large nuclear spins in GaAs semiconductors
Gordon Research Conference on Quantum Information Science, Ventura, CA, USA, March 23-28, 2003.

Quantum Computing in Molecular Magnets
Gordon Research Conference on Magnetic Nanostructures, Il Ciocco, Lucca, Italy, May 12-17, 2002.
Twannberg Workshop on Nanoscience, Hotel Feriendorf Twannberg, Switzerland, October 16-19, 2001.
Spintech-I, The 1st International Conference and School on Spintronics and Quantum Information Technology, Maui, Hawaii, May 13-18, 2001.

Incoherent Zener tunneling and Berry phase oscillations in molecular magnets
International Workshop on Mesoscopic Physics, Monte Verità, Switzerland, October 8-13, 2000.

Spin relaxation in Mn12-acetate
Swiss-US Nanoforum, ETH Zurich, Switzerland, September 20-21, 1999. 
LT22 Conference, Helsinki University of Technology, Otaniemi, Espoo, Finland, August 4-11, 1999.
Molecular Clusters, Magnetism and Quantum Size Effects, ESF Workshop, Florence, Italy, November 28-December 1, 1998.
Magnetism Today, Euroconference, Évora, Portugal, October 4-9, 1998.


Scientific Visits
Group of Prof. David Awschalom
Physics Department, UCSB, Santa Barbara, USA, May 26 - 31, 2003; June 27 - July 4, 2003.

Group of Prof. David Awschalom
Physics Department, UCSB, Santa Barbara, USA, April 23 - May 3, 2002.

Workshop on Quantum Information: Entanglement, Decoherence and Chaos
Institute of Theoretical Physics (ITP), University of California, Santa Barbara (UCSB), Santa Barbara, USA, November 12-24, 2001.

Group of Prof. David Awschalom
Physics Department, UCSB, Santa Barbara, USA, March 24-30, 2001.


Other Activities and Skills
Computational skills:
Basic, Pascal, C, C++, Assembler (Apple Macintosh), Super-Pascal (low-level parallel computing language), Alwan (high-level parallel computing language), hardware assembly, Windows, Mac OS, Microsoft Office, Latex, Maple, Mathematica.

Languages:
German (native language), English (written and spoken fluently), French (written and spoken fluently), Spanish (basic knowledge), Morse.

Sports:
Karate, aikido, tennis, swimming (brevet I rescue pass), skiing, dancing.

Hobbies:
Reading books, listening to music, watching movies.