Humboldt Universitt Berlin Institut fr Physik Plasma physics

Humboldt Universität Berlin Institut für Physik Plasma physics in Rostock with Gerd Röpke from the work in the seventies to new developments Werner Ebeling Humboldt University Berlin 1

Content • I. Quantum statistics in Rostock in the early seventies • II. Some of the new developments with Gerd Röpke • III. A special problem: the relations between physical • and chemical picture • IV. Conclusions

I. QS in Rostock before GR arrived. Plasma group in Rostock 1971 • First row: from r. Sändig, Krienke, Kelbg, guest, Ulbricht, Ebeling, guest, • the guests: Harold Friedman (USA) and Jan Stecki (Poland) • 2 nd row: from l. Kraeft, Kremp, Kilimann

In the center of interest was the bound state problem for plasmas and electrolytes, the divergence of the partition f. in plasmas • Coulombic phase transitions in class ionic solutions/plasmas with Grigo/Sändig/Richert, • Quantum statistics, virial coefficients, atomic partition function, density dependent minimum of ionization, energy levels with Kraeft/Kremp/Kilim. • <---- the RED BOOK

Exact thermodynamic results: 4 virial coeffcients are exactly known Higher vspa orders=3 part b. s. , 4 part b. s. , . .

A special problem: First order Coulombic phase transitions in electrolytes and quantum plasmas • Simplest model of a first order phase transition is the van der Waals gas, • A model of similar simplicity exists for a phase transition in Coulomb systems (CPT or PPT) based on Debye-Hückel approximation and Bjerrum-Saha MAL (E. /Sändig/Grigo/Fisher/Levin et al. )

Excess chemical potential in Debye-Hueckel approximation

The two-phase region

Quantum Debye-Hückel a --> a(T) = Lambda/8

The critical point of the PPT ~12000 - 18000 K

No data for plasmas were available in the 70 ties, except Kormer-group (wrong? ), Observed transitions in semiconductor plasmas, metal-amm. ? • Recently: • new observations in e-h plasmas, • new exp for ionic liquids (tetraalkylamm salts - Schröer) • New exp for high pressure plasmas (Trunin & Fortov groups) • Now: existence of PPT is rather sure!

II. Quantum statistics in Rostock since 1977 with GR • GR started his career in Leipzig with Prof. Heber (dissertation on theory of magnetism), then he moved with Heber to Dresden and finally got 1977 a position at U Rostock • a large influence on Gerd had his russian teacher and friend Dmitri N. Zubarev • several longer stays Moscow e. g. in 1968, books with Zubarev and Morosov • later close collaboration with JINR Dubna

Gerd in Rostock since 1977 • He was appointed for theoretical physics at Rostock University at 01. 02. 1977 • lectures in thermodynamics, quantum theory, statistical physics etc. • wrote several textbooks e. g. Quantum Theory, Nonequil. Statistics • In research he joined the group of G. Kelbg and worked with DK, WE and others

. . . the group • • • Günter Kelbg, Heinz Ulbricht, Dietrich Kremp, Wolf-D. Kremp, Klaus Kilimann, Hartmut Krienke, Lutz Schimansky-Geier Ahlbehrend, Malchow, Engel-H, Meister

In collaboration with GR new tools were applied and developed, as Green functions, Zubarev formalism, transport theory • New results are summarized 1986 in the green book • Quantum theory of density-dependent energy levels, Bethe. Salpeter equation etc. Kilimann/Kraeft/ Kremp/Röpke/Rösler/ Zimmermann

BSE: Closing the gap between Hlevels and continuuum (ZKKKR)

The valley of bound states, transition to highly ionized states (Mott transition)

Phase diagram ne, cm-3 1028 Metallic plasma ne e 3 = 1 r. D = 0. 84 a 0 H 2 = 0. 5 1024 rs = 1 =1 1020 1016 2 10 molecul ars atoms Calculations 104 = 0. 5 Strongly Ionized plasma 106 T, K

New results in TD: advanced Pade appr. (Sändig, Zimdahl, Richert, Förster, Kahlbaum). Example=electronic part of energy:

rr ee aa s o n a b l e e a r

90 -. . : many calculations for H-plasma (BFJRR) pressure and PPT in Mbar region

Coexistence line /diss. /ioniz.

How to reach the PPT transition line? Hugoniots or (quasi-adiabatic) multishocks?

Transport theory • D. N. Zubarev, G. Röpke, A. A. Morosov: Statistical mechanics of nonequilibrium processes. • Wiley, Vol. I 1996, Vol. II 1997 • Few words about him. . • Go to special problem. .