On the dispersion decay for crystals in the linearized Schrödinger–Poisson model
Tài liệu tham khảo
Ambrosetti, 2008, On Schrödinger–Poisson systems, Milan J. Math., 76, 257, 10.1007/s00032-008-0094-z
Arnold, 1978
Bonetto, 2000, Fourier's law: a challenge to theorists, 128
Cancès, 1999, On the time-dependent, Hartree–Fock equations coupled with a classical nuclear dynamics, Math. Models Methods Appl. Sci., 9, 963, 10.1142/S0218202599000440
Cancès, 2012, A mathematical formulation of the random phase approximation for crystals, Ann. Inst. H. Poincaré Anal. Non Linéaire, 29, 887, 10.1016/j.anihpc.2012.05.004
Cancès, 2013, Mean-field models for disordered crystals, J. Math. Pures Appl. (9), 100, 241, 10.1016/j.matpur.2012.12.003
Catto, 1998
Catto, 2001, On the thermodynamic limit for Hartree–Fock type models, Ann. Inst. H. Poincaré Anal. Non Linéaire, 18, 687, 10.1016/s0294-1449(00)00059-7
Catto, 2002, On some periodic Hartree-type models for crystals, Ann. Inst. H. Poincaré Anal. Non Linéaire, 19, 143, 10.1016/s0294-1449(01)00071-3
Catto, 2013, Existence of steady states for the Maxwell–Schrödinger–Poisson system: exploring the applicability of the concentration-compactness principle, Math. Models Methods Appl. Sci., 23, 1915, 10.1142/S0218202513500541
Cuccagna, 2006, Stability of standing waves for NLS with perturbed Lamé potential, J. Differential Equations, 223, 112, 10.1016/j.jde.2005.07.017
Cuccagna, 2008, On dispersion for Schrödinger equation with periodic potential in 1D, Comm. Partial Differential Equations, 33, 2064, 10.1080/03605300802501582
Dyson, 1967, Ground-state energy of a finite system of charged particles, J. Math. Phys., 8, 1538, 10.1063/1.1705389
Firsova, 1996, On the time decay of a wave packet in a one-dimensional finite band periodic lattice, J. Math. Phys., 37, 1171, 10.1063/1.531454
Giuliani, 2005
Gohberg, 1970
Komech, 2015, On crystal ground state in the Schrödinger–Poisson model, SIAM J. Math. Anal., 47, 1001, 10.1137/130949932
Komech, 2014, On eigenfunction expansion of solutions to the Hamilton equations, J. Stat. Phys., 154, 503, 10.1007/s10955-013-0846-1
Komech, 2015, On the eigenfunction expansion for Hamilton operators, J. Spectr. Theory, 5, 331, 10.4171/JST/100
Komech, 2017, On stability of ground states for finite crystals in the Schrödinger–Poisson model, J. Math. Phys., 58, 10.1063/1.4978211
Komech, 2018, On orbital stability of ground states for finite crystals in fermionic Schrödinger–Poisson model, SIAM J. Math. Anal., 50, 64, 10.1137/17M1123249
Krein, 1963, The spectral function of a selfadjoint operator in a space with indefinite metric, Sov. Math., Dokl., 4, 1236
Langer, 1981, Spectral functions of definitizable operators in Krein spaces, 1
Le Bris, 2005, From atoms to crystals: a mathematical journey, Bull. Amer. Math. Soc. (N.S.), 42, 291, 10.1090/S0273-0979-05-01059-1
Lebowitz, 1969, Existence of thermodynamics for real matter with Coulomb forces, Phys. Rev. Lett., 22, 631, 10.1103/PhysRevLett.22.631
Lebowitz, 1973, Lectures on the Thermodynamic Limit for Coulomb Systems, vol. 20, 136
Lewin
Lewin
Lieb, 2009
Lions, 1981, Some remarks on Hartree equation, Nonlinear Anal., 5, 1245, 10.1016/0362-546X(81)90016-X
Nier, 1993, A variational formulation of Schrödinger–Poisson systems in dimension d≤3, Comm. Partial Differential Equations, 18, 1125, 10.1080/03605309308820966
Panati, 2003, Effective dynamics for Bloch electrons: Peierls substitution and beyond, Comm. Math. Phys., 242, 547, 10.1007/s00220-003-0950-1
Prill, 2015, Dispersive estimates for solutions to the perturbed one-dimensional Klein–Gordon equation with and without a one-gap periodic potential, ZAMM Z. Angew. Math. Mech., 95, 778, 10.1002/zamm.201300267
Reed, 1978
Rudin, 1991
Stratton, 2007