Abstract
Here we summarize the most important results in this field of physics, which is growing due to the dominant role of these forms of matter in the cosmos. We describe the progress made in physical studies and the statistical theory of dense gases and nonideal plasmas, including their historical roots in the work of van der Waals, Debye, Saha, Planck, Einstein, and others. We present the basic tools required for the quantum statistical description of nonideal fluid systems, including analytical methods and computer simulations, and we discuss studies of plasma-like matter with high energy density.
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References
A.A. Abrikosov, L. Gorkov, I.E. Dzyaloshinskii, Methods of Quantum Field Theory in Statistical Physics (in Russian) (Moscow, 1962)
A. Alastuey, A. Perez, Virial expansion ot the equation of state of a quantum plasma, Europhys. Lett. 20, 19–24 (1992)
A. Alastuey, V. Ballenegger, W. Ebeling, Comment on direct linear term in the EOS of plasmas, Phys. Rev. E 92, 047101 (2015)
M. Badino, The odd couple: Boltzmann, Planck and applications of statistics to physics 1900–1913. Ann. Phys. (Berlin) 18, 81–101 (2009)
R. Balescu, Statistical Mechanics of Charged Particles (Wiley, London, 1963)
J.A. Barker, D. Henderson, Perturbation theory and EOS for fluids. J. Chem. Phys. 47, 2856 (1967)
K. Beneke, Erich Hückel und seine Arbeiten zur theoretischen Chemie, Mitt. Kolloid-Gesellschaft 274–304 (1999)
B.J. Berne, G. Ciccotti, D.F. Coker (eds.), Classical and Quantum Dynamics of Condensed Phase Simulation (World Scientific, Singapore, 1998)
K. Binder (ed.), Monte Carlo Methods in Statistical Physics (Springer, Berlin, 1979), p. 1986
D. Blaschke, D. Sedrakian, Superdense QCD Matter and Compact Stars (Springer, Berlin, 2006)
D. Blaschke, M. Buballa, A. Dubinin, G. Röpke, D. Zablocki, Generalized Beth–Uhlenbeck approach to mesons and diquarks in hot dense quark matter. Ann. Phys. 348, 228–255 (2014)
N.N. Bogolyubov, Collected Papers, vol. 1–12 (Fizmatlit, Moscow, 2005–2009)
N.N. Bogolyubov, N.N. Bogolyubov Jr., Introduction to Quantum Statistical Mechanics (Gordon and Breach, New York, 1992)
M. Bonitz, Quantum Kinetic Theory (B.G. Teubner, Stuttgart, 1998); 2nd edition (Springer, Berlin, 2016)
M. Bonitz, W.D. Kraeft (eds.), Kinetic theory of nonideal plasmas. J. Phys.: Conf. Ser. 11 (2005)
M. Bonitz, D. Semkat (eds.), Introduction to Computational Methods for Many Body Systems (Rinton Press, Princeton, 2006)
H.P. Bonzel, A.M. Bradshaw, G. Ertl (eds.), Physics and Chemistry of Alkali Metal Adsorption (Elsevier, Amsterdam, 1989)
L. Brillouin, Les statistiques quantiques et leurs applications, Paris 1930; German translation, Berlin (1931)
L.S. Brown, L.G. Yaffe, Effective field theory of highly ionized plasmas. Phys. Rep. 340, 1–164 (2001)
S.G. Brush, H.L. Sahlin, E. Teller, Monte Carlo study of a one-component plasma I. J. Chem. Phys. 45, 2102 (1966)
D.M. Ceperley, Path integrals in the theory of condensed Helium. Rev. Mod. Phys. 65, 279–356 (1995)
S. Chapman, T.G. Cowling, The Mathematical Theory of Non-uniform Gases: An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases, 3rd edn. (Cambridge Mathematical Library, Cambridge, 1991)
A.P. Chetverikov, W. Ebeling, M.G. Velarde. Local electron distributions and diffusion in anharmonic lattices mediated by thermally excited solitons. Eur. Phys. J. B 70, 217–227 (2011)
P. Debye, Handelingen Nederlandsch Natuuren Congres (1923)
P. Debye, E. Hückel, Theorie der Elektrolyte I. Physik Z. 24, 185 (1923)
C. Deutsch, Nodal expansion in a real matter plasma. Phys. Lett. A 60, 317–318 (1977)
H.E. De Witt, Evaluation of the quantum-mechanical ring sum with Boltzmann statistics. J. Math. Phys. 3, 1216–1228 (1962)
H.E. De Witt, M. Schlanges, A.Y. Sakakura, W.D. Kraeft, Low density expansion of the equation of state for a quantum electron gas. Phys. Lett. A 197, 326 (1995)
W. Ebeling, Statistical thermodynamics of bound states in plasmas (in Dt.). Ann. Physik (Leipzig) 19, 104–112 (1967)
W. Ebeling, Derivation of free energy of quantum plasmas from exact scattering shifts (in Dt.). Ann. Physik 22, 33–39, 383–391 (1968)
W. Ebeling, Equation of state and Saha equation of partially ionized plasmas. Physica 38, 378 (1968); 73, 573–584 (1974)
W. Ebeling, On the possibility of diffusion instabilities in weak electrolytes. Z. Phys. Chem. 247, 340 (1971); Quantum statistics of ionization. Phys. Stat. Sol. (b) 46, 243–255 (1971)
W. Ebeling, D. Hoffmann, The Berlin school of thermodynamics founded by Helmholtz and Clausius. Eur. J. Phys. 12, 1–9 (1991)
W. Ebeling, D. Hoffmann, Eine Vorlage Einsteins in der Preuischen Akademie der Wissenschaften 1924, Leibniz Online, EbelingHoffmann.pdf (2014)
W. Ebeling, W.D. Kraeft, D. Kremp, Theory of Bound States and Ionisation Equilibrium in Plasmas and Solids (Akademie-Verlag, Berlin, 1976). Extended Russ. translation Mir, Moscow (1979)
W. Ebeling, V.F. Fortov, YuL Klimontovich, et al. (eds.), Transport Properties of Dense Plasmas (Birkhäuser, Boston, 1984)
W. Ebeling, A. Förster, V.E. Fortov, V.K. Gryaznov, AYa. Polishchuk, Thermophysical Properties of Hot Dense Plasmas (Teubner, Stuttgart, 1991)
W. Ebeling, A. Förster, V. Fortov, V. Gryaznov, A. Polishchuk, Thermophysical Properties of Hot Dense Plasmas (Teubner, Stuttgart, 1991) (Russ. transl. Moskva, Ishevsk, 2007)
W. Ebeling, M.Yu. Romanovsly, I.M. Sokolov, Velocity distributions and kinetic equations including Levy power law tails. Contr. Plasma Phys, 49, 704–712 (2009)
D. Ebert, Eichtheorien: Grundlage der Elementarteilchenphysik (VCH-Verlag, Weinheim, 1989)
J. Eggert, Über den Dissoziationzustand der Fixsterngase. Physikalische Zeitschrift 20, 570–574 (1919)
A. Einstein, Quantentheorie des einatomigen idealen gases. Sitzungsber. Preuss. Akad. Wiss. Phys.-math. Kl. 22, 261–267 (1924); 23, 3–14 (1925)
D. Enskog, Kinetische Theorie der Vorgänge in mässig verdünnten Gasen (författare) (Almqvist and Wiksell, Uppsala, 1917)
H. Falkenhagen, W. Ebeling, Equilibrium properties of ionized dilute electrolytes, in Ionic Interactions, ed. by S. Petrucci (Academic Press, New York, 1971)
R. Feistel, W. Ebeling, Evolution of Complex Systems (Kluwer, Dordrecht, 1989)
R. Feistel, W. Ebeling, Physics of Self-Organization and Evolution (Wiley-VCH, Weinheim, 2011)
H. Fehske, R. Schneider, A. Weibe (eds.), Computational Many-Particle Physics (Springer, Berlin, 2008)
R.P. Feynman, Statistical Mechanics (Benjamin, Reading Mass, 1972)
M.E. Fisher, Y. Levin, Criticality in ionic fluids: Debye–Hückel theory, Bjerrum, and beyond. Phys. Rev. Lett. 71, 2138 (1993)
H. Friedman, Ionic Solution Theory (Wiley Interscience, New York, 1962)
V. Fortov, M. Mochalov et al., Phys. Rev. Lett. 99, 185001 (2007)
V.E. Fortov, Extreme States of Matter (Russ) (FizMatGis, Moskva, 2009). New edition 2015
V.E. Fortov, Equation of State of Matter (FizMatGis, Moskva, 2013). (in Russian)
V.E. Fortov, Extreme States of Matter: On Earth and in the Cosmos, The Frontiers Collection (Springer, Berlin, 2011); Extreme States of Matter, High Energy Density Physics (Springer, Berlin, 2016)
V.L. Ginzburg, The Physics of a Lifetime: Reflections on the Problems and Personalities of 20th Century Physics (Springer, Berlin, 2001)
B. Greene, The Fabric of the Cosmos (Knopf, New York, 2004)
H. Haken, P. Plath, W. Ebeling, YuM Romanovsky, Beiträge zur Geschichte der Synergetik (Springer, Berlin, 2016)
J.P. Hansen, I.R. McDonald, Theory of Simple Liquids (Academic Press, New York, 1976); J.N. Henn, J.C. Plefka, Scattering Amplitudes in Gauge Theories, Lecture Notes in Physics (Springer, Berlin, 2014)
P.C. Hemmer, H. Holden, S. Kjelstrup Ratkje (eds.), The Collected Works of Lars Onsager (World Scientific, Singapore, 1996)
F. Hensel, S. Juengst, F. Noll, R. Winter, in Localisation and Metal Insulator Transitions, ed. by D. Adler, H. Fritsche (Plenum, New York, 1985)
T.L. Hill, Statistical Mechanics, Principles and Selected Applications (McGraw Hill, New York, 1956)
J.O. Hirschfelder, C.F. Curtis, R.B. Bird, Molecular Theory of Gases and Liquids (Wiley, New York, 1954)
P. Hoyng, Relativistic Astrophysics and Cosmology (Springer, Dordrecht, 2006)
S. Ichimaru, Statistical Plasma Physics (Addison-Wesley, Redwood, 1992)
D.R. Inglis, E. Teller, Astrophysics 90, 430 (1939)
G. Kalman (ed.), Strongly Coupled Coulomb Systems (Pergamon Press, Oxford, 1998)
G. Kelbg, Quantenstatistik der Plasmen. Annalen der Physik 12, 354 (1963)
G. Kelbg, Einige Methoden der statistischen Thermodynamik hochionisierter Plasmen, Ergebnisse der Plasmaphysik aund Gaselektronik, vol. 3 (Akademie-Verlag, Berlin, 1972)
C. Kirsten, H.-G. Körber (eds.), Physiker über Physiker (Akademie-Verlag, Berlin, 1975)
H. Kleinert, Path integrals in quantum mechaniscs, statistics, polymer physics and financial markets, World Scientific, Singapore (1995)
Yu.L. Klimontovich, Statistical Theory of Nonequilibrium Processes in Plasmas (Izdat MGU, Moscow, 1964); English translation (Pergamon, Oxford, 1967)
Yu.L. Klimontovich, Statistical Physics (Russ.) (Nauka, Moscow, 1982); English translation (Harwood, New York, 1986)
W.D. Kraeft, D. Kremp, W. Ebeling, G. Röpke, Quantum Statistics of Charged Particle Systems (Akademie-Verlag and Pergamon Press, Berlin and New York, 1986)
W.D. Kraeft, D. Kremp, G. Röpke, Direct linear term in the equation of state of plasmas. Phys. Rev. E 91, 013108 (2015)
M.D. Knudson, M.P. Desjarlais, A. Becker, R.W. Lemke, K.R. Cochrane, M.E. Savage, D.E. Bliss, T.R. Mattsson, R. Redmer, Science 348(6242), 1455–1460 (2015)
G. Kalman, P. Carini (eds.), Strongly Coupled Plasma (Plenum Press, New York, 1978)
V.P. Krainov, M.B. Smirnov, Cluster beams in the super-intense femtosecond laser pulse. Phys. Rep. 370, 237–331 (2002)
V.P. Krainov, M.B. Smirnov, B.M. Smirnov, Femtosecond excitation of cluster beams. Phys. Usp. 50, 907–931 (2007)
D. Kremp, M. Schlanges, W.D. Kraeft, Quantum Statistics of Nonideal Plasmas (Springer, Berlin, 2005)
A.I. Larkin, Thermodynamic functions of a low-temperature plasma. JETP 11, 1363–1364 (1960)
J.D. Landau, E.M. Lifshits,Statistical Physics (Part I), Nauka Moska 1976, German translation Berlin 1979, English translation Statistical Physics, Part 1, vol. 5, 3rd edn. (Butterworth–Heinemann, London, 1980)
E.M. Lifshitz, L.P. Pitaevskii, Physical Kinetics, Course of Theoretical Physics, vol. X (Publishing Science, Moscow, 1979)
A. Linde, What Energy Drives the Universe (Stanford University, Stanford, 2005)
W.R. Magro, D.M. Ceperley, C. Pierleoni, B. Bernu, Phys. Rev. Lett. 76, 1240 (1996)
P.C. Martin, J. Schwinger, Theory of many-particle systems. Phys. Rev. 115, 1342–1432 (1959)
J.E. Mayer, Theory of ionic solutions. J. Chem. Phys. 18, 1426–1436 (1950)
B. Militzer, R. Pollock, Variational density matrix method for warm condensed matter and dense hydrogen. Phys. Rev. E 61, 3470–382 (2000)
E. Montroll, J. Ward, Quantum statistics of interacting particles. Phys. Fluids 1, 55 (1958)
T. Morita, Equation of state of high temperature plasma. Prog. Theor. Phys. (Kyoto) 22, 757–774 (1959)
N. Mott, The transition to the metallic state. Phil. Mag. 6, 287–309 (1961)
V. Mukhanov, S. Winitzki, Introduction to Quantum Effects in Gravity (NOOK Book, 2007)
V. Mukhanov, Quantum Universe (Plenary lecture DPG, Berlin, 2015)
J. von Neumann, Mathematische Grundlagen der Quantenmechanik (Springer, Berlin, 1932)
G.E. Norman, A. Starostin, High Temp. 6, 394 (1968); 8, 381 (1970)
D. Pines, The Many Body Problem (Benjamin, New York, 1961)
D. Pines, P. Nozieres, The Theory of Quantum Liquids (Benjamin, New York, 1966); Russ. Translation Mir, Moskva (1967)
M. Planck, Zur Quantenstatistik des Bohrschen Atommodells. Annalen der Physik 75, 673–684 (1924)
R. Redmer, G. Röpke, Progress in the theory of dense strongly coupled plasmas. Contr. Plasma Phys. 50, 970–985 (2010)
R. Redmer, B. Holst, F. Hensel (eds.), Metal to Non-Metal Transitions (Springer, Berlin, 2010)
K. Riewe, R. Rompe, Ann. Phys. (Leipzig) 17, 126 (1938)
R. Rompe, H. Treder, W. Ebeling, Zur grossen Berliner Physik (Teubner, Leipzig, 1987)
H.J. Rothe, Lattice Gauge Theories (World Scientific, Singapore, 2005)
M.N. Saha, Phil. Mag. 40, 472 (1920); Z. Phys. 6, 40 (1921)
H. Satz, Extreme States of Matter in Strong Interaction Physics: An Introduction (Springer, Berlin, 2012)
H. Satz, Ultimate Horizons: Probing the Limits of the Universe (Springer, Berlin, 2013)
K. Simonyi, Kulturgeschichte der Physik (Urania Verlag and Harri Deutsch, Frankfurt, 1990)
V. Sizyuk, A. Hassanein, T. Sizyuk, J. Appl. Phys. 100, 103106 (2006)
L. Spitzer, Physics of Fully Ionized Plasmas (Wiley, New York, 1961)
V.Ya. Ternovoi, A.S. Filimonov, V.E. Fortov, S.V. Kvitov, D.D. Nikolaev, A.A. Pyalling, Phys. B 265, 6 (1999)
G.E. Uhlenbeck, E. Beth, The quantum theory of the non-ideal gas I. Deviations from the classical theory. Physica 3, 729–745 (1936)
E.A. Uehling, G.E. Uhlenbeck, Phys. Rev. 43, 552 (1933)
J.D. van der Waals, Over de Continuiteit van den Gas- en Vloeistoftoestand (Continuity of fluid and gaseous state). Dissertation, University of Leiden (1873)
A.A. Vedenov, A.I. Larkin, Equation of state of plasmas (in Russ.). Zh. eksp. teor. Fiz. 36, 1133–1142 (1959); Sov. Phys. JETP 9, 806–821 (1959)
J. Von Neumann, Mathematische Grundlagen der Quantenmechanik (1932)
P.N. Voronzov-Veliaminov, A.M. Eliashevich, V.P. Morgenstern, V.P. Chassovskich, Teplophys. Vysokh. Temp. 8, 277 (1970); 14, 199 (1976)
S.T. Weir, A.C. Mitchell, W.J. Nellis, Phys. Rev. Lett. 76, 860 (1996)
H. Whitley, A. Alastuey, J.A. Gaffney, R. Cauble, W.D. Kraeft, M. Bonitz, A tribute to the pioneers of the strongly coupled plasmas: Hugh E. De Witt, Bernard Jancovici, Forest A. Rogers. Contr. Plasma Phys. 55, 102–115 (2015)
K. Yagi, T. Hatsuda, Y. Miake, Quark-Gluon Plasma: From Big Bang to Little Bang (Cambridge University Press, Cambridge, 2005)
E.P. Wigner, Interaction of electrons in metals. Phys. Rev. 46, 1002–1011 (1934)
V.M. Zamalin, G.E. Norman, V.S. Filinov, Monte Carlo Method in Statistical Mechanics (in Russ.) (Nauka, Moscow, 1977)
D. Zubarev, V. Morozov, G. Röpke, Statistical Mechanics of Nonequilibrium Processes (Akademie, Berlin, 1996)
J. Zweiback, T.E. Cowan, T. Dimitre et al., Phys. Rev. Lett. 85, 3640 (2000)
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Ebeling, W., Fortov, V.E., Filinov, V. (2017). Physics of Dense Gases, Nonideal Plasmas, and High Energy Density Matter. In: Quantum Statistics of Dense Gases and Nonideal Plasmas. Springer Series in Plasma Science and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-66637-2_1
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