J. Leconte and G. Chabrier, A new vision of giant planet interiors: Impact of double diffusive convection, Astronomy & Astrophysics, vol.540, p.20, 2012.
DOI : 10.1051/0004-6361/201117595

M. N. Saha, Ionisation in the Solar Chromosphere., Nature, vol.105, issue.2634, p.232, 1920.
DOI : 10.1038/105232b0

S. Eliezer, A. Ghatak, and H. Hora, Fundamentals of Equations of State, 2002.
DOI : 10.1142/4872

W. Pauli, Über den Zusammenhang des Abschlusses der Elektronengruppen im Atom mit der Komplexstruktur der Spektren, Z. Physik
DOI : 10.1007/bf02980631

L. Kaye, Tables of Physical and Chemical Constants, Journal of the R??ntgen Society, vol.17, issue.67, 2005.
DOI : 10.1259/jrs.1921.0043

M. D. Knudson, D. L. Hanson, J. E. Bailey, C. A. Hall, J. R. Asay et al., Principal Hugoniot, reverberating wave, and mechanical reshock measurements of liquid deuterium to 400

V. D. Mikhailova, G. V. Selemir, R. F. Simakov, I. P. Trunin, V. D. Trusov et al., Shock compression of solid deuterium, JETP Lett, issue.7, p.76433, 2002.

G. V. Boriskov, A. I. Bykov, R. I. Il-'kaev, V. D. Selemir, G. V. Simakov et al., Shock-wave compression of solid deuterium at a pressure of 120 GPa, Doklady Physics, vol.48, issue.10
DOI : 10.1134/1.1623535

G. N. Iosilevskii, S. I. Kashintseva, S. F. Kirshanov, V. B. Manachkin, A. L. Mintsev et al., Experimental measurements of the compressibility, temperature, and light absorption in dense shock-compressed gaseous deuterium, JETP Lett, vol.80, issue.6, pp.398-404, 2004.

J. D. Hammel, R. J. Kilkenny, M. Wallace, R. Ross, A. Cauble et al., Absolute equation of state measurements on shocked liquid deuterium up to 200 GPa (2 Mbar), Phys. Rev. Lett, vol.78, p.483, 1997.

K. S. Weber, R. Budil, and . Cauble, Measurements of the equation of state of deuterium at the fluid insulator-metal transition, Science AUG, vol.21, issue.5380, p.2811178, 1998.

D. G. Hicks, T. R. Boehly, P. M. Celliers, J. H. Eggert, S. J. Moon et al., Laser-driven single shock compression of

M. D. Knudson and M. P. Desjarlais, Shock Compression of Quartz to 1.6 TPa: Redefining a Pressure Standard, Physical Review Letters, vol.103, issue.22, p.225501, 2009.
DOI : 10.1103/PhysRevLett.103.225501

M. Ross, Linear-mixing model for shock-compressed liquid deuterium, Physical Review B, vol.58, issue.2, p.669, 1998.
DOI : 10.1103/PhysRevB.58.669

D. Saumon, G. Chabrier, and H. M. Van-horn, An Equation of State for Low-Mass Stars and Giant Planets, The Astrophysical Journal Supplement Series, vol.99, issue.2, p.713, 1995.
DOI : 10.1086/192204

H. Juranek and R. Redmer, Self-consistent fluid variational theory for pressure dissociation in dense hydrogen, The Journal of Chemical Physics, vol.112, issue.8, p.3780, 2000.
DOI : 10.1063/1.480939

L. Caillabet, S. Mazevet, and P. Loubeyre, calculations in the range 0.2 to 5 g/cc up to 10 eV, Physical Review B, vol.83, issue.9, p.94101, 2011.
DOI : 10.1103/PhysRevB.83.094101

L. Caillabet, Équation d'état ab initio de l'hydrogène dans la matière dense et tiède et application à l'implosion de cibles pour la fusion par confinement inertiel, 2011.

H. Mao and R. J. Hemley, Ultrahigh-pressure transitions in solid hydrogen, Reviews of Modern Physics, vol.66, issue.2, p.671, 1994.
DOI : 10.1103/RevModPhys.66.671

R. J. Hemley and H. K. Mao, Phase Transition in Solid Molecular Hydrogen at Ultrahigh Pressures, Physical Review Letters, vol.61, issue.7, p.857, 1988.
DOI : 10.1103/PhysRevLett.61.857

H. E. Lorenzana, I. F. Silvera, and K. A. Goettel, Evidence for a structural phase transition in solid hydrogen at megabar pressures, Physical Review Letters, vol.63, issue.19, p.2080, 1989.
DOI : 10.1103/PhysRevLett.63.2080

S. A. Bonev, E. Schwegler, T. Ogitsu, and G. Galli, A quantum fluid of metallic hydrogen suggested by first-principles calculations, Nature, vol.52, issue.7009, p.669, 2004.
DOI : 10.1103/PhysRevB.65.052102

J. Vorberger, I. Tamblyn, B. Militzer, and S. A. Bonev, Hydrogen-helium mixtures in the interiors of giant planets, Physical Review B, vol.75, issue.2, p.24206, 2007.
DOI : 10.1103/PhysRevB.75.024206

W. Lorenzen, B. Holst, and R. Redmer, First-order liquid-liquid phase transition in dense hydrogen, Physical Review B, vol.82, issue.19, 2010.
DOI : 10.1103/PhysRevB.82.195107

I. Tamblyn and S. A. Bonev, Structure and Phase Boundaries of Compressed Liquid Hydrogen, Physical Review Letters, vol.104, issue.6, p.65702, 2010.
DOI : 10.1103/PhysRevLett.104.065702

B. Holst, M. French, and R. Redmer, simulations and application to dense liquid hydrogen, Physical Review B, vol.83, issue.23, p.235120, 2011.
DOI : 10.1103/PhysRevB.83.235120

M. A. Morales, C. Pierleoni, E. Schwegler, and D. M. Ceperley, Evidence of a first-order liquidliquid transition in high-pressure hydrogen from ab initio calculations, p.10712799, 2010.

P. M. Celliers, P. Loubeyre, J. H. Eggert, S. Brygoo, R. S. Mcwilliams et al., Insulator-to-Conducting Transition in Dense Fluid Helium, Physical Review Letters, vol.104, issue.18, p.184503, 2010.
DOI : 10.1103/PhysRevLett.104.184503

G. I. Kerley, Équation d'état hydrogène-hélium équimolaire

W. L. Vos, A. De-kuijper, J. Barrat, and J. A. Chouten, High pressure phase diagram of heliumhydrogen calculated through fluid integral equations and density functional theory of freezing, J

P. Loubeyre, R. Letoullec, J. P. Pinceaux, H. Mao, J. Hu et al., Equation of state and phase-diagram of solid He-4 from single-crystal X-ray-diffraction over a large P-T domain

W. Lorenzen, B. Holst, and R. Redmer, Demixing of Hydrogen and Helium at Megabar Pressures, Physical Review Letters, vol.102, issue.11, p.115701, 2009.
DOI : 10.1103/PhysRevLett.102.115701

C. Winisdoerffer and G. Chabrier, Free-energy model for fluid helium at high density, Physical Review E, vol.71, issue.2, p.26402, 2005.
DOI : 10.1103/PhysRevE.71.026402
URL : https://hal.archives-ouvertes.fr/hal-00012957

D. A. Young, A. K. Mcmahan, and M. Ross, Equation of state and melting curve of helium to very high pressure, Physical Review B, vol.24, issue.9, p.5119, 1981.
DOI : 10.1103/PhysRevB.24.5119

B. Militzer, Correlations in hot dense helium, Journal of Physics A: Mathematical and Theoretical, vol.42, issue.21, p.214001, 2009.
DOI : 10.1088/1751-8113/42/21/214001

P. M. Kowalski, S. Mazevet, D. Saumon, and M. Challacombe, Equation of state and optical properties of warm dense helium, Physical Review B, vol.76, issue.7, p.75112, 2007.
DOI : 10.1103/PhysRevB.76.075112

J. Eggert, S. Brygoo, P. Loubeyre, R. S. Mcwilliams, P. M. Celliers et al., Hugoniot Data for Helium in the Ionization Regime, Physical Review Letters, vol.100, issue.12, p.124503, 2008.
DOI : 10.1103/PhysRevLett.100.124503

V. E. Fortov, V. Y. Ternovoi, M. V. Zhernokletov, M. A. Mochalov, A. L. Mikhailov et al., Pressure-produced ionization of nonideal plasma in a megabar range of dynamic pressures, Journal of Experimental and Theoretical Physics, vol.97, issue.2, p.97259, 2003.
DOI : 10.1134/1.1608993

F. Soubiran, S. Mazevet, C. Winisdoerffer, and G. Chabrier, Helium gap in the warm dense matter regime and experimental reflectivity measurements, Physical Review B, vol.86, issue.11
DOI : 10.1103/PhysRevB.86.115102

W. B. Hubbard, Structure of Jupiter: Chemical Composition, Contraction, and Rotation, The Astrophysical Journal, vol.162, p.687, 1970.
DOI : 10.1086/150700

J. J. Fortney and W. B. Hubbard, Effects of Helium Phase Separation on the Evolution of Extrasolar Giant Planets, The Astrophysical Journal, vol.608, issue.2, p.1039, 2004.
DOI : 10.1086/420765

R. Smoluchowski, Internal Structure and Energy Emission of Jupiter, Nature, vol.1, issue.5102, p.691, 1967.
DOI : 10.1086/149052

R. Smoluchowski, Solid-State Convection on Jupiter, Physical Review Letters, vol.25, issue.10, p.693, 1970.
DOI : 10.1103/PhysRevLett.25.693

E. E. Salpeter, On Convection and Gravitational Layering in Jupiter and in Stars of Low Mass, The Astrophysical Journal, vol.181, p.83, 1973.
DOI : 10.1086/181190

D. J. Stevenson and E. E. Salpeter, The phase diagram and transport properties for hydrogen-helium fluid planets, The Astrophysical Journal Supplement Series, vol.35, p.221, 1977.
DOI : 10.1086/190478

W. B. Hubbard and H. E. Dewitt, Statistical mechanics of light elements at high pressure. VII - A perturbative free energy for arbitrary mixtures of H and He, The Astrophysical Journal, vol.290, p.388, 1985.
DOI : 10.1086/162996

W. B. Hubbard, T. Guillot, M. S. Marley, A. Burrows, J. I. Lunine et al., Comparative evolution of Jupiter and Saturn, Planetary and Space Science, vol.47, issue.10-11, pp.10-111175, 1999.
DOI : 10.1016/S0032-0633(99)00042-2

J. J. Fortney and W. B. Hubbard, Phase separation in giant planets: inhomogeneous evolution of Saturn, Icarus, vol.164, issue.1, p.228, 2003.
DOI : 10.1016/S0019-1035(03)00130-1

G. Chabrier, Plasma physics and planetary astrophysics. Plasma Physics and Controlled Fusion, p.124014, 2009.
DOI : 10.1088/0741-3335/51/12/124014
URL : http://arxiv.org/abs/0912.2968

P. Loubeyre, R. L. Toullec, and J. P. Pinceaux, -He mixtures at high temperature and high pressure, Physical Review B, vol.36, issue.7, p.3723, 1987.
DOI : 10.1103/PhysRevB.36.3723
URL : https://hal.archives-ouvertes.fr/hal-00595299

A. De-kuijper, B. Smit, J. A. Schouten, and J. P. Michels, Fluid-Fluid Phase Separation in a Repulsive ??-exp-6 Mixture: A Comparison with the Full ??-exp-6 Mixture by Means of Computer Simulations, Europhysics Letters (EPL), vol.13, issue.8, p.13679, 1990.
DOI : 10.1209/0295-5075/13/8/002

M. A. Morales, E. Schwegler, D. Ceperley, C. Pierleoni, S. Hamel et al., Phase separation in hydrogenâhelium mixtures at Mbar pressures, p.1324, 2009.

W. Lorenzen, B. Holst, and R. Redmer, Metallization in hydrogen-helium mixtures [1] M Born and R Oppenheimer. Quantum theory of molecules, Phys. Rev. B Annalen der Physik, vol.84, issue.20, p.457, 1927.

C. J. Cramer, Essentials of Computational Chemistry -Theories and models, 2004.

L. H. Thomas, The calculation of atomic fields, Proc. Camb. Phis. Soc, p.542, 1927.

E. Fermi, Un metodo statistico per la determinazione di alcune priorieta dell'atome, Rend. Accad. Naz. Lincei, vol.6, p.602, 1927.

P. Hohenberg and W. Kohn, Inhomogeneous Electron Gas, Physical Review, vol.136, issue.3B, p.864, 1964.
DOI : 10.1103/PhysRev.136.B864

R. G. Parr and W. Yang, Density Functional Theory of Atoms and Molecules, 1989.
DOI : 10.1007/978-94-009-9027-2_2

M. Levy, Universal variational functionals of electron densities, first-order density matrices, and natural spin-orbitals and solution of the v-representability problem, Proc. Natl. Acad. Sci. USA, p.766062, 1979.
DOI : 10.1073/pnas.76.12.6062

M. Levy, Electron densities in search of Hamiltonians, Physical Review A, vol.26, issue.3, p.1200, 1982.
DOI : 10.1103/PhysRevA.26.1200

J. P. Perdew and M. Levy, Extrema of the density functional for the energy: Excited states from the ground-state theory, Physical Review B, vol.31, issue.10, p.6264, 1985.
DOI : 10.1103/PhysRevB.31.6264

W. Kohn and L. J. Sham, Self-Consistent Equations Including Exchange and Correlation Effects, Physical Review, vol.140, issue.4A, p.1133, 1965.
DOI : 10.1103/PhysRev.140.A1133

R. M. Martin, Electronic Structure -Basic Theory and Practical Methods, 2010.

N. D. Mermin, Thermal Properties of the Inhomogeneous Electron Gas, Physical Review, vol.137, issue.5A, p.1441, 1965.
DOI : 10.1103/PhysRev.137.A1441

P. A. Dirac, Note on Exchange Phenomena in the Thomas Atom, Proc. Camb, p.376, 1930.
DOI : 10.1017/S0305004100016108

D. M. Ceperley and B. J. Alder, Ground State of the Electron Gas by a Stochastic Method, Physical Review Letters, vol.45, issue.7, p.566, 1980.
DOI : 10.1103/PhysRevLett.45.566

J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized Gradient Approximation Made Simple, Physical Review Letters, vol.77, issue.18, p.3865, 1996.
DOI : 10.1103/PhysRevLett.77.3865

L. Caillabet, Équation d'état ab initio de l'hydrogène dans la matière dense et tiède et application à l'implosion de cibles pour la fusion par confinement inertiel, 2011.

F. Perrot and M. W. Dharma-wardana, Exchange and correlation potentials for electron-ion systems at finite temperatures, Physical Review A, vol.30, issue.5, p.2619, 1984.
DOI : 10.1103/PhysRevA.30.2619

M. Born and K. Huang, Dynamical Theory of Crystal Lattices, American Journal of Physics, vol.23, issue.7, 1954.
DOI : 10.1119/1.1934059

M. C. Payne, M. P. Teter, D. C. Allan, T. A. Arias, and J. D. Joannopoulos, Iterative minimization techniques for ab initio total-energy calculations : molecular dynamics and conjugate gradients
DOI : 10.1103/revmodphys.64.1045

H. J. Monkhorst and J. D. Pack, Special points for Brillouin-zone integrations, Physical Review B, vol.13, issue.12, p.5188, 1976.
DOI : 10.1103/PhysRevB.13.5188

E. Antoncik, A new formulation of the method of nearly free electrons, Czechoslovak Journal of Physics, vol.4, issue.4, p.439, 1954.
DOI : 10.1007/BF01687834

E. Antoncik, Approximate formulation of the orthogonalized plane-wave method, Journal of Physics and Chemistry of Solids, vol.10, issue.4, p.314, 1959.
DOI : 10.1016/0022-3697(59)90007-1

J. C. Phillips and L. Kleinman, New Method for Calculating Wave Functions in Crystals and Molecules, Physical Review, vol.116, issue.2, p.287, 1959.
DOI : 10.1103/PhysRev.116.287

W. C. Herring, A New Method for Calculating Wave Functions in Crystals, Physical Review, vol.57, issue.12, p.1169, 1940.
DOI : 10.1103/PhysRev.57.1169

D. R. Hamann, M. Schlüter, and C. Chiang, Norm-Conserving Pseudopotentials, Physical Review Letters, vol.43, issue.20, p.1494, 1979.
DOI : 10.1103/PhysRevLett.43.1494

P. E. Blöchl, Projector augmented-wave method, Physical Review B, vol.50, issue.24, p.17953, 1994.
DOI : 10.1103/PhysRevB.50.17953

C. Rostgaard, The Projector Augmented-wave Method. eprint arXiv :0910, 2009.

P. E. Blöchl, C. J. Först, and J. Schimpl, Projector augmented-wave method, Physical Review B, vol.50, issue.24, 2002.
DOI : 10.1103/PhysRevB.50.17953

N. A. Holzwarth, A. R. Tackett, and G. E. Matthews, A Projector Augmented Wave (PAW) code for electronic structure calculations, Part I: atompaw for generating atom-centered functions, Computer Physics Communications, vol.135, issue.3
DOI : 10.1016/S0010-4655(00)00244-7

P. Loubeyre, R. Letoullec, J. P. Pinceaux, H. Mao, J. Hu et al., Equation of state and phase-diagram of solid He-4 from single-crystal X-ray-diffraction over a large P-T domain

L. Verlet, Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules, Physical Review, vol.159, issue.1, p.98, 1967.
DOI : 10.1103/PhysRev.159.98

M. E. Tuckerman, C. J. Mundy, and G. J. Martyna, On the classical statistical mechanics of non-Hamiltonian systems, Europhysics Letters (EPL), vol.45, issue.2, p.149, 1999.
DOI : 10.1209/epl/i1999-00139-0

D. J. Evans and G. P. Morriss, The isothermal/isobaric molecular dynamics ensemble, Physics Letters A, vol.98, issue.8-9, p.433, 1983.
DOI : 10.1016/0375-9601(83)90256-6

D. J. Evans and G. P. Morriss, Isothermal-isobaric molecular dynamics, Chemical Physics, vol.77, issue.1, p.63, 1983.
DOI : 10.1016/0301-0104(83)85065-4

P. Minary, G. J. Martyna, and M. E. Tuckerman, Algorithms and novel applications based on the isokinetic ensemble. II. Ab initio molecular dynamics, The Journal of Chemical Physics, vol.118, issue.6, p.2527, 2003.
DOI : 10.1063/1.1534583

F. Zhang, Operator-splitting integrators for constant-temperature molecular dynamics, The Journal of Chemical Physics, vol.106, issue.14, pp.6102-6106, 1997.
DOI : 10.1063/1.473273

M. D. Knudson, D. L. Hanson, J. E. Bailey, C. A. Hall, J. R. Asay et al., Principal Hugoniot, reverberating wave, and mechanical reshock measurements of liquid deuterium to 400

V. D. Mikhailova, G. V. Selemir, R. F. Simakov, I. P. Trunin, V. D. Trusov et al., Shock compression of solid deuterium, JETP Lett, issue.7, p.76433, 2002.

G. V. Boriskov, A. I. Bykov, R. I. Il-'kaev, V. D. Selemir, G. V. Simakov et al., Shock-wave compression of solid deuterium at a pressure of 120 GPa, Doklady Physics, vol.48, issue.10
DOI : 10.1134/1.1623535

G. N. Iosilevskii, S. I. Kashintseva, S. F. Kirshanov, V. B. Manachkin, A. L. Mintsev et al., Experimental measurements of the compressibility, temperature, and light absorption in dense shock-compressed gaseous deuterium, JETP Lett, vol.80, issue.6, pp.398-404, 2004.

J. D. Hammel, R. J. Kilkenny, M. Wallace, R. Ross, A. Cauble et al., Absolute equation of state measurements on shocked liquid deuterium up to 200 GPa (2 Mbar), Phys. Rev. Lett, vol.78, p.483, 1997.

K. S. Weber, R. Budil, and . Cauble, Measurements of the equation of state of deuterium at the fluid insulator-metal transition, Science AUG, vol.21, issue.5380, p.2811178, 1998.

D. G. Hicks, T. R. Boehly, P. M. Celliers, J. H. Eggert, S. J. Moon et al., Laser-driven single shock compression of

M. D. Knudson and M. P. Desjarlais, Shock Compression of Quartz to 1.6 TPa: Redefining a Pressure Standard, Physical Review Letters, vol.103, issue.22, p.225501, 2009.
DOI : 10.1103/PhysRevLett.103.225501

M. Ross, Linear-mixing model for shock-compressed liquid deuterium, Physical Review B, vol.58, issue.2, p.669, 1998.
DOI : 10.1103/PhysRevB.58.669

D. Saumon, G. Chabrier, and H. M. Van-horn, An Equation of State for Low-Mass Stars and Giant Planets, The Astrophysical Journal Supplement Series, vol.99, issue.2, p.713, 1995.
DOI : 10.1086/192204

H. Juranek and R. Redmer, Self-consistent fluid variational theory for pressure dissociation in dense hydrogen, The Journal of Chemical Physics, vol.112, issue.8, p.3780, 2000.
DOI : 10.1063/1.480939

L. Caillabet, S. Mazevet, and P. Loubeyre, calculations in the range 0.2 to 5 g/cc up to 10 eV, Physical Review B, vol.83, issue.9, p.94101, 2011.
DOI : 10.1103/PhysRevB.83.094101

L. Caillabet, Équation d'état ab initio de l'hydrogène dans la matière dense et tiède et application à l'implosion de cibles pour la fusion par confinement inertiel, 2011.

W. Lorenzen, B. Holst, and R. Redmer, First-order liquid-liquid phase transition in dense hydrogen, Physical Review B, vol.82, issue.19, 2010.
DOI : 10.1103/PhysRevB.82.195107

J. Eggert, S. Brygoo, P. Loubeyre, R. S. Mcwilliams, P. M. Celliers et al., Hugoniot Data for Helium in the Ionization Regime, Physical Review Letters, vol.100, issue.12, p.124503, 2008.
DOI : 10.1103/PhysRevLett.100.124503

P. M. Celliers, P. Loubeyre, J. H. Eggert, S. Brygoo, R. S. Mcwilliams et al., Insulator-to-Conducting Transition in Dense Fluid Helium, Physical Review Letters, vol.104, issue.18, p.184503, 2010.
DOI : 10.1103/PhysRevLett.104.184503

P. M. Kowalski, S. Mazevet, D. Saumon, and M. Challacombe, Equation of state and optical properties of warm dense helium, Physical Review B, vol.76, issue.7, p.75112, 2007.
DOI : 10.1103/PhysRevB.76.075112

M. A. Morales, E. Schwegler, D. Ceperley, C. Pierleoni, S. Hamel et al., Phase separation in hydrogenâhelium mixtures at Mbar pressures, p.1324, 2009.

W. Lorenzen, B. Holst, and R. Redmer, Demixing of Hydrogen and Helium at Megabar Pressures, Physical Review Letters, vol.102, issue.11, p.115701, 2009.
DOI : 10.1103/PhysRevLett.102.115701

G. I. Kerley, Équation d'état hydrogène-hélium équimolaire, Com. priv, vol.23

P. Loubeyre, P. M. Celliers, D. G. Hicks, E. Henry, A. Dewaele et al., Coupling static and dynamic compressions: first measurements in dense hydrogen, High Pressure Research, vol.24, issue.1, p.25, 2004.
DOI : 10.1016/S0032-0633(99)00043-4

W. L. Vos, A. De-kuijper, J. Barrat, and J. A. Chouten, High pressure phase diagram of heliumhydrogen calculated through fluid integral equations and density functional theory of freezing, J

W. Lorenzen, B. Holst, and R. Redmer, Demixing of Hydrogen and Helium at Megabar Pressures, Physical Review Letters, vol.102, issue.11, p.115701, 2009.
DOI : 10.1103/PhysRevLett.102.115701

L. Caillabet, S. Mazevet, and P. Loubeyre, calculations in the range 0.2 to 5 g/cc up to 10 eV, Physical Review B, vol.83, issue.9, p.94101, 2011.
DOI : 10.1103/PhysRevB.83.094101

I. Tamblyn and S. A. Bonev, Structure and Phase Boundaries of Compressed Liquid Hydrogen, Physical Review Letters, vol.104, issue.6, p.65702, 2010.
DOI : 10.1103/PhysRevLett.104.065702

W. Lorenzen, B. Holst, and R. Redmer, First-order liquid-liquid phase transition in dense hydrogen, Physical Review B, vol.82, issue.19, 2010.
DOI : 10.1103/PhysRevB.82.195107

J. Hansen and I. R. Mcdonald, Theory of simple liquids, 1986.

R. Kubo, The fluctuation-dissipation theorem, Reports on Progress in Physics, vol.29, issue.1, p.255, 1966.
DOI : 10.1088/0034-4885/29/1/306

C. Caccamo, Integral equation theory description of phase equilibria in classical fluids, Physics Reports, vol.274, issue.1-2, p.1, 1996.
DOI : 10.1016/0370-1573(96)00011-7

E. Matteoli and G. A. Mansoori, A simple expression for radial distribution functions of pure fluids and mixtures, The Journal of Chemical Physics, vol.103, issue.11, p.4672, 1995.
DOI : 10.1063/1.470654

J. Vorberger, I. Tamblyn, B. Militzer, and S. A. Bonev, Hydrogen-helium mixtures in the interiors of giant planets, Physical Review B, vol.75, issue.2, p.24206, 2007.
DOI : 10.1103/PhysRevB.75.024206

B. Holst, M. French, and R. Redmer, simulations and application to dense liquid hydrogen, Physical Review B, vol.83, issue.23, p.235120, 2011.
DOI : 10.1103/PhysRevB.83.235120

P. M. Kowalski, S. Mazevet, D. Saumon, and M. Challacombe, Equation of state and optical properties of warm dense helium, Physical Review B, vol.76, issue.7, p.75112, 2007.
DOI : 10.1103/PhysRevB.76.075112

S. Hamel, M. A. Morales, and E. Schwegler, Signature of helium segregation in hydrogen-helium mixtures, Physical Review B, vol.84, issue.16, p.165110, 2011.
DOI : 10.1103/PhysRevB.84.165110

D. A. Young, A. K. Mcmahan, and M. Ross, Equation of state and melting curve of helium to very high pressure, Physical Review B, vol.24, issue.9, p.5119, 1981.
DOI : 10.1103/PhysRevB.24.5119

C. Winisdoerffer and G. Chabrier, Free-energy model for fluid helium at high density, Physical Review E, vol.71, issue.2, p.26402, 2005.
DOI : 10.1103/PhysRevE.71.026402
URL : https://hal.archives-ouvertes.fr/hal-00012957

P. M. Celliers, P. Loubeyre, J. H. Eggert, S. Brygoo, R. S. Mcwilliams et al., Insulator-to-Conducting Transition in Dense Fluid Helium, Physical Review Letters, vol.104, issue.18, p.184503, 2010.
DOI : 10.1103/PhysRevLett.104.184503

F. Soubiran, S. Mazevet, C. Winisdoerffer, and G. Chabrier, Helium gap in the warm dense matter regime and experimental reflectivity measurements, Physical Review B, vol.86, issue.11
DOI : 10.1103/PhysRevB.86.115102

L. A. Collins, S. R. Bickham, J. D. Kress, S. Mazevet, T. J. Lenosky et al., Dynamical and optical properties of warm dense hydrogen, Physical Review B, vol.63, issue.18, p.184110, 2001.
DOI : 10.1103/PhysRevB.63.184110

I. Tamblyn and S. A. Bonev, Structure and Phase Boundaries of Compressed Liquid Hydrogen, Physical Review Letters, vol.104, issue.6, p.65702, 2010.
DOI : 10.1103/PhysRevLett.104.065702

M. A. Morales, C. Pierleoni, E. Schwegler, and D. M. Ceperley, Evidence of a first-order liquidliquid transition in high-pressure hydrogen from ab initio calculations, p.10712799, 2010.

M. A. Morales, C. Pierleoni, and D. M. Ceperley, Equation of state of metallic hydrogen from coupled electron-ion Monte Carlo simulations, Physical Review E, vol.81, issue.2, p.21202, 2010.
DOI : 10.1103/PhysRevE.81.021202

L. Caillabet, S. Mazevet, and P. Loubeyre, calculations in the range 0.2 to 5 g/cc up to 10 eV, Physical Review B, vol.83, issue.9, p.94101, 2011.
DOI : 10.1103/PhysRevB.83.094101

W. A. Harrison, Solid State Theory, 1970.

J. Callaway, Quantum Theory of the Solid State, 1974.

G. D. Mahan, Many Particle Physics, 1981.

R. Kubo, Statistical-Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems, Journal of the Physical Society of Japan, vol.12, issue.6, p.570, 1957.
DOI : 10.1143/JPSJ.12.570

D. A. Greenwood, The Boltzmann Equation in the Theory of Electrical Conduction in Metals, Proc. Phys. Soc. (London), p.585, 1958.
DOI : 10.1088/0370-1328/71/4/306

R. Kubo, The fluctuation-dissipation theorem, Reports on Progress in Physics, vol.29, issue.1, p.255, 1966.
DOI : 10.1088/0034-4885/29/1/306

L. Onsager, Reciprocal Relations in Irreversible Processes. I., Physical Review, vol.37, issue.4, p.405, 1931.
DOI : 10.1103/PhysRev.37.405

G. V. Chester and A. Thellung, The Law of Wiedemann and Franz, Proc. Phys. Soc, p.1005, 1961.
DOI : 10.1088/0370-1328/77/5/309

V. Recoules and J. Crocombette, determination of electrical and thermal conductivity of liquid aluminum, Physical Review B, vol.72, issue.10, p.104202, 2005.
DOI : 10.1103/PhysRevB.72.104202

V. Recoules, F. Lambert, A. Decoster, B. Canaud, and J. Clérouin, Determination of Thermal Conductivity of Dense Hydrogen Plasmas, Physical Review Letters, vol.102, issue.7, p.75002, 2009.
DOI : 10.1103/PhysRevLett.102.075002

H. J. Monkhorst and J. D. Pack, Special points for Brillouin-zone integrations, Physical Review B, vol.13, issue.12, p.5188, 1976.
DOI : 10.1103/PhysRevB.13.5188

J. Clérouin, P. Renaudin, Y. Laudernet, P. Noiret, and M. P. Desjarlais, Electrical conductivity and equation-of-state study of warm dense copper: Measurements and quantum molecular dynamics calculations, Physical Review B, vol.71, issue.6, p.64203, 2005.
DOI : 10.1103/PhysRevB.71.064203

S. Mazevet, M. Torrent, V. Recoules, and F. Jollet, Calculations of the transport properties within the PAW formalism, High Energy Density Physics, vol.6, issue.1, p.84, 2010.
DOI : 10.1016/j.hedp.2009.06.004

D. Pelat, Bruits et signaux, 1998.
URL : https://hal.archives-ouvertes.fr/cel-00092937

A. Y. Potekhin, D. A. Baiko, P. Haensel, and D. G. Yakovlev, Transport properties of degenerate electrons in neutron star envelopes and white dwarf cores, A&A, vol.346, p.345, 1999.

J. Leconte and G. Chabrier, A new vision of giant planet interiors: Impact of double diffusive convection, Astronomy & Astrophysics, vol.540, p.20, 2012.
DOI : 10.1051/0004-6361/201117595

G. Wiedemann and R. Franz, Über die Wärme Leistungsfähigkeit der Metalle, Ann. Phys. Chem, vol.165, issue.8, p.497, 1853.

J. Committee, . Guides, and . Metrology, Évaluation des données de mesure ? guide pour l'expression de l'incertitude de mesure, 2008.

L. Spitzer and R. Härm, Transport Phenomena in a Completely Ionized Gas, Physical Review, vol.89, issue.5, p.977, 1953.
DOI : 10.1103/PhysRev.89.977

W. Lorenzen, B. Holst, and R. Redmer, First-order liquid-liquid phase transition in dense hydrogen, Physical Review B, vol.82, issue.19, 2010.
DOI : 10.1103/PhysRevB.82.195107

A. Bondi, van der Waals Volumes and Radii, The Journal of Physical Chemistry, vol.68, issue.3, p.441, 1964.
DOI : 10.1021/j100785a001

R. Smoluchowski, Internal Structure and Energy Emission of Jupiter, Nature, vol.1, issue.5102, p.691, 1967.
DOI : 10.1086/149052

R. Smoluchowski, Solid-State Convection on Jupiter, Physical Review Letters, vol.25, issue.10, p.693, 1970.
DOI : 10.1103/PhysRevLett.25.693

J. J. Fortney and W. B. Hubbard, Phase separation in giant planets: inhomogeneous evolution of Saturn, Icarus, vol.164, issue.1, p.228, 2003.
DOI : 10.1016/S0019-1035(03)00130-1

M. A. Morales, E. Schwegler, D. Ceperley, C. Pierleoni, S. Hamel et al., Phase separation in hydrogenâhelium mixtures at Mbar pressures, p.1324, 2009.

W. Lorenzen, B. Holst, and R. Redmer, Demixing of Hydrogen and Helium at Megabar Pressures, Physical Review Letters, vol.102, issue.11, p.115701, 2009.
DOI : 10.1103/PhysRevLett.102.115701

P. Loubeyre, R. L. Toullec, and J. P. Pinceaux, -He mixtures at high temperature and high pressure, Physical Review B, vol.36, issue.7, p.3723, 1987.
DOI : 10.1103/PhysRevB.36.3723
URL : https://hal.archives-ouvertes.fr/hal-00595299

G. I. Kerley, Équation d'état hydrogène-hélium équimolaire

S. Hamel, M. A. Morales, and E. Schwegler, Signature of helium segregation in hydrogen-helium mixtures, Physical Review B, vol.84, issue.16, p.165110, 2011.
DOI : 10.1103/PhysRevB.84.165110

. Ainsi, En effet, il est fortement couplé au niveau coulombien (? ? 1) et partiellement quantique (? n /a n < 1 mais ? e /a e > 1) Par ailleurs, le système électronique présente une dégénérescence élevée (? F ,e /k B T ? 1) et le rapport entre l'énergie potentielle et l'énergie de Fermi des électrons montre que l'on ne peut pas traiter les effets coulombiens perturbativement (R s ? 1), Tout ceci indique qu'il est nécessaire de prendre en compte les effets quantiques et de dégénérescence au moins pour les électrons si l'on souhaite une description réaliste du système. En revanche, les noyaux ont plutôt un comportement classique, même si ceci doit être modulé par le fait que le paramètre ? est proche de 1

E. L. Pollock and J. P. Hansen, Statistical Mechanics of Dense Ionized Matter. II. Equilibrium Properties and Melting Transition of the Crystallized One-Component Plasma, Physical Review A, vol.8, issue.6, p.3110, 1973.
DOI : 10.1103/PhysRevA.8.3110

S. G. Brush, H. L. Sahlin, and E. Teller, Monte Carlo Study of a One???Component Plasma. I, The Journal of Chemical Physics, vol.45, issue.6, p.2102, 1966.
DOI : 10.1063/1.1727895

S. Eliezer, A. Ghatak, and H. Hora, Fundamentals of Equations of State, 2002.
DOI : 10.1142/4872

G. Chabrier, Quantum effects in dense coulombic matter : application to the cooling of white dwarfs, Astrophys. J, vol.414, p.195, 1993.

Y. B. Zel-'dovich and Y. P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena, 2002.

L. Landau and E. Lifchitz, Mécanique des fluides, 1989.

J. Hansen and I. R. Mcdonald, Theory of simple liquids, 1986.

G. and A. Mansoori, Radial distribution functions and their role in modeling of mixtures behavior, Fluid Phase Equilibria, vol.87, issue.1, 1993.
DOI : 10.1016/0378-3812(93)85015-E

E. Matteoli and G. A. Mansoori, A simple expression for radial distribution functions of pure fluids and mixtures, The Journal of Chemical Physics, vol.103, issue.11, p.4672, 1995.
DOI : 10.1063/1.470654