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First of all, I would like to thank my advisor, Prof. David M. Ceperley, for his guidance, stimulating discussions and support. He has made my graduate experience at the University of Illinois at Urbana-Champaign an excellent one. I also learned a great deal about exactness in numerical simulations.

I am particularly thankful to benefit from all the previous work that has been done to develop the PIMC method. This also includes Roy Pollock who was my advisor for two summers when I worked as a student at Lawrence Livermore National Laboratory. We developed on the variational density matrix together but I would also like to mention his bike-riding and vine-making skills.

Furthermore, I got a lot of support from Bill Magro who had worked on dense hydrogen before me and shared all his experience, taught me many computational skills and spent nights with me to parallelize the fermionic part of the path integral code.

I am very grateful to Prof. Richard M. Martin and Lubos Mitas for support and many helpful discussions. I would also like to thank all my fellow graduate students in the group, in particular John Shumway, Mark Dewing, Tommaso Torelli, and Fengua Zong. The numerous discussions helped me tremendously in my research and pointed out a lot of things I did not understand.

I also got a lot of support from Gregory Bauer who helped me with many things I needed as a German in America. Furthermore, I remember many useful discussions with him and the other post-docs Carmen Gordillo, Tadashi Ogitsu, and Fabrice Douchin.

I also wish to thank Prof. Bernard Bernu in Paris who was a kind host during my visits and an good collaborator interested in all PIMC details.

I would also like to thank for the support I got from the people at the National Center for Supercomputing Applications (NCSA). In particular, I would like to mention Rachael Brady, who provided me with her fancy visualization program so that I could modify it to show my path integral simulations in the CAVE virtual reality system at NCSA, for which I almost got more attention than for the numbers I calculated. Jeff Carpenter and Holly Korup are listed because they produced the video about our research on hot, dense hydrogen.

Furthermore, I would like to acknowledge the work by Nan Zhong and Guochun Shi who wrote the library that dumps the data of my simulation code.

Foremost, I am thankful to my girl-friend Nicole for her loving support and understanding for my work demands. It also should be mentioned that her proof-reading skills had a significant impact on this work. Last but not least, I thank my parents who have taught me many skills, were always there for me and gave me a lot of support even during my years in America.

I am grateful for the support by the Department of Physics at the University of Illinois and by the U.S. Department of Energy through the University of California under Subcontract number B341494.

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Burkhard Militzer 2003-01-15