New Contact Information
NAME Burkhard Militzer
PHONE (510) 643-7414
FAX (510) 643-9980
E-MAIL militzer at berkeley dot edu
ADDRESS

( MAP IT )
University of California, Berkeley
Departments of Earth and Planetary Science
and Astronomy
407 McCone Hall #4767
Berkeley, CA 94720, USA

Research Interests
Path integral Monte Carlo simulation of metallic hydrogen My area of expertise lies in the field of theoretical condensed matter physics with a strong emphasis on computer simulations, in particular quantum Monte Carlo methods.

Path integral Monte Carlo simulation of molecular hydrogen
I am interested in theory and simulation of novel materials under extreme conditions and have studied a variety of liquids at high pressure. Examples include path integral Monte Carlo (PIMC) simulations of hot dense hydrogen and density functional molecular dynamics simulations of liquid oxygen under pressure.

See slides from a recent presentation on this topic.

Simulation of Hydrogen-Helium Mixtures in Planetary Interiors
Shock hugoniot curves for precompressed hydrogen and helium
Helium in molecular hydrogen
Shock hugoniot curves for precompressed hydrogen and helium
Helium in metallic hydrogen
We performed density functional molecular dynamics simulation to characterize hydrogen-helium mixtures in the interior of solar and extrasolar giant planets. In this article, the author team (Jan Vorberger, Isaac Tamblyn, B.M., and Stanimir Bonev) addresses outstanding questions about their structure and evolution e.g. whether Jupiter has a rocky core and if it was formed by a core accretion process. We describe how the presence of helium defers the molecular-to-metallic transition in hydrogen to higher pressures by stabilizing hydrogen molecules.
First Principles Simulation of Fluid Helium at High Pressure
Shock hugoniot curves for precompressed hydrogen and helium

Shock hugoniot curves for precompressed hydrogen and helium.
Shock wave experiments allow one to study a material's properties at high pressure and temperature. In this article (accepted for publication in Physical Review Letters), we used first-principles computer simulation to predict the properties of shock fluid helium at megabar pressures. The simulations show that the compressibility of helium is substantially increased by electronic excitations. A maximum compression ratio of 5.24-fold the initial density was predicted for 360 GPa and 150000 K. This result distinguishes helium from deuterium, for which simulations predicted a maximum compression ratio of 4.3. If the sample are precompressed statically the compression ratio is reduced, which is shown in the left graph.
Ab Initio Simulations of Liquid Oxygen under Pressure
Spin fluctuations in dense molecular oxygen

Spin fluctuations present molecular oxygen (left) are suppressed at high pressures (right).
In recent shock wave experiments [Phys. Rev. Lett. 86, 3108 (2001)], the conductivity of liquid oxygen was measured for pressures up to 1.8 Mbar and indications for a insulator-metal transition were found. In this article, we report results from density functional molecular dynamics simulations of dense liquid oxygen close to the metal-insulator transition. We have found that band gap closure occurs in the molecular liquid, with a slow transition from a semi-conducting to a poor metallic state occurring over a wide pressure range. At approximately 80 GPa, molecular dissociation is observed in the metallic fluid. Spin fluctuations play a key role in determining the electronic structure of the low pressure fluid, while they are suppressed at high pressure.
Dense Plasma Effects on Nuclear Reaction Rates
Many-body enhancement of nuclear reaction rates
Many-body enhancement of nuclear reaction rates h(0) as function of the coupling parameter.
Dense plasma effects can cause an exponenial change in charge particle nuclear reaction rates important in stellar evolution. In this article, reaction rates in dense plasmas are examined using path integral Monte Carlo. Quantum effects causes a reduction in the many body enhancement of the reaction rate, h(0), compared to the classical value. This is shown in figure on the left for different quantum parameters. This reduction can be attributed to the "quantum smearing" of the Coulomb interaction at the short range resulting in a reduced repulsion between the reacting pair and surrounding particles.
Lowering of the Kinetic Energy in Interacting Quantum Systems
Temperature density region of kinetic energy lowering
Temperature density region of kinetic energy lowering for dense hydrogen and the electron gas.
The equilibrium momentum distribution is of fundamental importance to characterize many-body systems. In contrast to classical systems where the distribution is always Maxwellian, in quantum systems the distribution depends on particle statistics, bosons or fermions, as well as on interactions and can display interparticle correlations, which are the basis of superfluidity and superconductivity. In this article, we report and explain a surprising effect of interactions in quantum systems on the one particle momentum distribution and kinetic energy. Interactions never lower the ground state kinetic energy of a quantum system. However, at nonzero temperature, where the system occupies a thermal distribution of states, interactions can reduce the kinetic energy below the noninteracting value. This is demonstrated using PIMC simulations for dense hydrogen and the electron gas.
Understanding hot dense hydrogen with PIMC simulations
Hydrogen at rs=4.0, T=5000K Hydrogen at rs=1.86, T=5000K Hydrogen at rs=1.6, T=6250K
Molecular liquid
Molecular metallic liquid
Metallic liquid
The high temperature phase diagram of hydrogen
Phase diagram of deuterium At which pressure and density does hydrogen become metallic? Thermal dissociation leads into a diminishing of the peak in the proton-proton pair correlation function with increasing temperature. At low densities up to about rs=2.6, the properties of hydrogen including the equation of state are well understood. Processes like the thermal dissociation of molecules can be modelled accurately with PIMC. The resulting proton-proton pair correlation functions are shown.
Single and double shock Hugoniot curves from PIMC simulations
Single Shock Results
Single shock hugoniot results
Phase diagram showing single and double shock hugoniot curves.
Single and double shock hugoniot in the phase diagram.
Double Shock Results
Double shock hugoniot results
Publications
37. P. Beck, A. F. Goncharov, V. Struzhkin, B. Militzer, H.-K. Mao, and R. J. Hemley "Measurement of thermal diffusivity at high pressure using a transient heating technique", Appl. Phys. Lett. 91 (2007) 181914.
36. B. Militzer, W. B. Hubbard, "Implications of Shock Wave Experiments with Precompressed Materials for Giant Planet Interiors", accepted for publication in proceedings volume for the American Physical Society meeting on Shock Compression of Condensed Matter, Hawaii, June, 2007.
35. J. Vorberger, I. Tamblyn, S.A. Bonev, B. Militzer, "Properties of Dense Fluid Hydrogen and Helium in Giant Gas Planets", Contrib. Plasma Phys. 47 (2007) 375.
34. S. Seager, M. Kuchner, C. A. Hier-Majumder, B. Militzer, "Mass-radius relationship of solid exoplanets", Astrophys. J. 669 (2007) 1279.
33. V. V. Struzhkin, B. Militzer, W. Mao, R. J. Hemley, H.-k. Mao, "Hydrogen Storage in Clathrates", Chem. Rev. 107 (2007) 4133.
32. G. D. Cody, H. Yabuta, T. Araki, L. D. Kilcoyne, C. M. Alexander, H. Ade, P. Dera, M. Fogel, B. Militzer, B. O. Mysen, "An Organic thermometer for Chondritic Parent Bodies", submitted to Earth. Planet. Sci. Lett. (2006).
31. J. Vorberger, I. Tamblyn, B. Militzer, S.A. Bonev, "Hydrogen-Helium Mixtures in the Interiors of Giant Planets", Phys. Rev. B 75 (2007) 024206, cond-mat/0609476.
30. B. Militzer, R. J Hemley, "Solid oxygen takes shape", Nature (News & Views), 443 (2006) 150.
29. B. Militzer, "First Principles Calculations of Shock Compressed Fluid Helium", Phys. Rev. Lett. 97 (2006) 175501.
28. B. Militzer, R. L. Graham, "Simulations of Dense Atomic Hydrogen in the Wigner Crystal Phase", J. Phys. Chem. Solids, 67 (2006) 2136.
27. B. Militzer, "Hydrogen-Helium Mixtures at High Pressure", J. Low Temp. Phys. 139 (2005) 739.
26. B. Militzer, E. L. Pollock, "Equilibrium Contact Probabilities in Dense Plasmas", Phys. Rev. B, 71 (2005) 134303.
25. J.-F. Lin, B. Militzer, V. V. Struzhkin, E. Gregoryanz, R. J. Hemley, H.-k. Mao, "High Pressure-Temperature Raman Measurements of H2O Melting to 22 GPa and 900 K", J. Chem. Phys. 121 (2004) 8423.
24. B. Militzer, E. L. Pollock, D. Ceperley, "Path Integral Monte Carlo Calculation of the Momentum Distribution of the Homogeneous Electron Gas at Finite Temperature", submitted to Phys. Rev. B (2003).
23. E. L. Pollock, B. Militzer, "Dense Plasma Effects on Nuclear Reaction Rates", Phys. Rev. Lett. 92 (2004) 021101.
22. S. A. Bonev, B. Militzer, G. Galli, "Dense liquid deuterium: Ab initio simulation of states obtained in gas gun shock wave experiments", Phys. Rev. B 69 (2004) 014101.
21. F. Brglez, X.Y. Li, M.F. Stallmann, and B. Militzer, "Evolutionary and Alternative Algorithms: Reliable Cost Predictions for Finding Optimal Solutions to the LABS Problem", Information Sciences, in press, 2004.
20. B. Militzer, F. Gygi, G. Galli, "Structure and Bonding of Dense Liquid Oxygen from First Principles Simulations", Phys. Rev. Lett. 91 (2003) 265503.
19. F. Brglez, X.Y. Li, M.F. Stallmann, and B. Militzer, "Reliable Cost Predictions for Finding Optimal Solutions to LABS Problem: Evolutionary and Alternative Algorithms", Proceedings of The Fifth International Workshop on Frontiers in Evolutionary Algorithms, Cary, NC (2003).
18. B. Militzer, "Path Integral Calculation of Shock Hugoniot Curves of Precompressed Liquid Deuterium", J. Phys. A: Math. Gen. 63 (2003) 6159.
17. B. Militzer, E. L. Pollock, "Lowering of the Kinetic Energy in Interacting Quantum Systems", Phys. Rev. Lett. 89 (2002) 280401.
16. B. Militzer, D. M. Ceperley, J. D. Kress, J. D. Johnson, L. A. Collins, S. Mazevet, "Calculation of a Deuterium Double Shock Hugoniot from Ab Initio Simulations", Phys. Rev. Lett. 87 (2001) 275502.
15. B. Militzer, D. M. Ceperley, "Path Integral Monte Carlo Simulation of the Low-Density Hydrogen Plasma", Phys. Rev. E 63 (2001) 066404.
14. B. Militzer, D. M. Ceperley, "Path Integral Monte Carlo Calculation of the Deuterium Hugoniot", Phys. Rev. Lett. 85 (2000) 1890.
13. B. Militzer, "Path Integral Monte Carlo Simulations of Hot Dense Hydrogen", Ph.D. thesis, University of Illinois at Urbana-Champaign (2000).
12. B. Militzer, E. L. Pollock, "Variational Density Matrix Method for Warm Condensed Matter and Application to Dense Hydrogen", Phys. Rev. E 61 (2000) 3470.
11. B. Militzer, E. L. Pollock, "Introduction to the Variational Density Matrix Method and its Application to Dense Hydrogen", in Strongly Coupled Coulomb Systems 99, ed. by C. Deutsch, B. Jancovici, and M.-M. Gombert, J. Phys. France IV 10 (2000) 315.
10. B. Militzer, W. Magro, and D. Ceperley, "Characterization of the State of Hydrogen at High Temperature and Density", Contr. Plasma Physics 39 (1999) 1-2, 151.
9. W. Magro, B. Militzer, D. Ceperley, B. Bernu, and C. Pierleoni, "Restricted Path Integral Monte Carlo Calculations of Hot, Dense Hydrogen", in Strongly Coupled Coulomb Systems, ed. by G. J. Kalman, J. M. Rommel and K. Blagoev, Plenum Press, New York NY, 1998.
8. W. Ebeling, B. Militzer, and F. Schautz, "Quasi-Classical Theory and Simulation of Two-Component Plasmas", in Strongly Coupled Coulomb Systems, ed. by G. J. Kalman, J. M. Rommel and K. Blagoev, Plenum Press, New York NY, 1998.
7. B. Militzer, W. Magro, and D. Ceperley, "Fermionic Path-Integral Simulation of Dense Hydrogen", in Strongly Coupled Coulomb Systems, ed. by G. J. Kalman, J. M. Rommel and K. Blagoev, Plenum Press, New York NY, 1998.
6. B. Militzer, M. Zamparelli, and D. Beule, "Evolutionary Search for Low Autocorrelated Binary Sequences", IEEE Trans. Evol. Comput. 2 (1998) 34-39.
5. W. Ebeling, B. Militzer, and F. Schautz, "Quasi-classical Theory and Simulations of Hydrogen-like Quantum Plasmas", Contr. Plasma Physics 37 (1997) 2-3, 137.
4. W. Ebeling and B. Militzer, "Quantum Molecular Dynamics of Partially Ionized Plasmas", Phys. Lett. A 226 (1997) 298
3. B. Militzer, "Quanten-Molekular-Dynamik mit reaktiven Freiheitsgraden", in Dynamik, Evolution, Strukturen, ed. J. Freund, Dr. Köster publishing company, Berlin, 1996.
2. B. Militzer, "Quanten-Molekular-Dynamik von Coulomb-Systemen", Logos publishing company, Berlin, 1996, ISBN 3-931216-08-X
1. B.-D. Dörfel and B. Militzer, "Test of Modular Invariance for Finite XXZ Chains", J. Phys. A: Math. Gen. 26 (1993) 4875.

Other interests: low auto-correlated binary sequences (LABS), traffic jams

[My previous research group at the Lawrence Livermore Nat. Laboratory, 2000-2003]
[My research group at the University of Illinois at Urbana-Champaign, 1996-2000]
[My research group at the Humboldt University at Berlin, 1994-1996]

[Geophysical Laboratory | Carnegie Institution of Washington]

Last modified: 10/17/06.