On Orbital Stability of Ground States for Finite Crystals in Fermionic Schrödinger-Poisson Model

We consider the Schrodinger--Poisson--Newton equations for finite crystals under periodic boundary conditions with one ion per cell of a lattice. The electron field is described by the $N$-particle...

[1]  J. Swinburne.  Electromagnetic Theory , 1894, Nature.

[2]  Mathieu Lewin,et al.  Mean-field models for disordered crystals , 2012, 1203.0402.

[3]  G. Stoltz,et al.  A mathematical formulation of the random phase approximation for crystals , 2011, 1109.2416.

[4]  Mathieu Lewin,et al.  The Hartree Equation for Infinitely Many Particles I. Well-Posedness Theory , 2013, 1310.0603.

[5]  Mathieu Lewin,et al.  The Hartree equation for infinitely many particles, II: Dispersion and scattering in 2D , 2013, 1310.0604.

[6]  A. Komech.  Quantum Mechanics: Genesis and Achievements , 2012 .

[7]  E. Lieb,et al.  The Stability of Matter in Quantum Mechanics , 2009 .

[8]  J. Ziman.  The Calculation of Bloch Functions , 1971 .

[9]  A. I. Komech.  On the Crystal Ground State in the Schrödinger-Poisson Model , 2015, SIAM J. Math. Anal..

[10]  Kristian Kirsch,et al.  Methods Of Modern Mathematical Physics , 2016 .

[11]  C. Kittel.  Introduction to solid state physics , 1954 .

[12]  L. Hörmander.  The analysis of linear partial differential operators , 1990 .

[13]  Pierre-Louis Lions,et al.  The Mathematical Theory of Thermodynamic Limits: Thomas--Fermi Type Models , 1998 .

[14]  A. Komech.  On the crystal ground state in the Schrödinger–Poisson model with point ions , 2016 .

[15]  Pierre-Louis Lions,et al.  On the thermodynamic limit for Hartree–Fock type models , 2001 .

[16]  On the Linear Stability of Crystals in the Schrödinger–Poisson Model , 2015, Journal of statistical physics.

[17]  Elliott H. Lieb,et al.  Existence of Thermodynamics for Real Matter with Coulomb Forces , 1969 .

[18]  A. Komech,et al.  On stability of ground states for finite crystals in the Schrödinger-Poisson model , 2017 .

[19]  Giovanni Vignale,et al.  Quantum Theory of the Electron Liquid , 2005 .

[20]  E. Lieb,et al.  Lectures on the Thermodynamic Limit for Coulomb Systems , 1973 .

[21]  Pierre-Louis Lions,et al.  On some periodic Hartree-type models for crystals , 2002 .

[22]  G. Burton.  Sobolev Spaces , 2013 .

[23]  V. Arnold.  Mathematical Methods of Classical Mechanics , 1974 .

[24]  M. Born,et al.  Dynamical Theory of Crystal Lattices , 1954 .

[25]  Pierre-Louis Lions,et al.  From atoms to crystals: a mathematical journey , 2005 .

[26]  J. Lebowitz,et al.  Fourier's Law: a Challenge for Theorists , 2000, math-ph/0002052.

[27]  J. Shatah,et al.  Stability theory of solitary waves in the presence of symmetry, II☆ , 1990 .

[28]  Freeman J. Dyson,et al.  Stability of Matter. II , 1967 .

[29]  F. Dyson.  Ground‐State Energy of a Finite System of Charged Particles , 1967 .

[30]  J. Lions.  Quelques méthodes de résolution de problèmes aux limites non linéaires , 1969 .

[31]  THE HARTREE EQUATION FOR INFINITELY MANY PARTICLES , 2013 .