Derivation of the cubic non-linear Schrödinger equation from quantum dynamics of many-body systems

[1]  Manfred Salmhofer,et al.  Renormalization: An Introduction , 2007 .

[2]  F. Golse,et al.  Rigorous Derivation of the Cubic NLS in Dimension One , 2007 .

[3]  H. Yau,et al.  Derivation of the Gross‐Pitaevskii hierarchy for the dynamics of Bose‐Einstein condensate , 2004, math-ph/0410005.

[4]  E. Lieb,et al.  The Mathematics of the Bose Gas and its Condensation , 2005, cond-mat/0610117.

[5]  A. Elgart,et al.  Mean field dynamics of boson stars , 2005, math-ph/0504051.

[6]  YeYaojun.  GLOBAL SOLUTIONS OF NONLINEAR SCHRODINGER EQUATIONS , 2005 .

[7]  H. Yau,et al.  Gross-Pitaevskii Equation as the Mean Field Limit of Weakly Coupled Bosons , 2004, math-ph/0410038.

[8]  Horng-Tzer Yau,et al.  Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensate , 2004, math-ph/0606017.

[9]  J. Froehlich,et al.  Mean-Field Limit of Quantum Bose Gases and Nonlinear Hartree Equation , 2004, math-ph/0409019.

[10]  F. Golse,et al.  Towards a rigorous derivation of the cubic NLSE in dimension one , 2004 .

[11]  T. Cazenave.  Semilinear Schrodinger Equations , 2003 .

[12]  E. Lieb,et al.  Proof of Bose-Einstein condensation for dilute trapped gases. , 2001, Physical review letters.

[13]  H. Yau,et al.  Derivation of the nonlinear Schr\"odinger equation from a many body Coulomb system , 2001, math-ph/0111042.

[14]  R. Weikard,et al.  The ground state energy of a dilute Bose gas , 2000 .

[15]  François Golse,et al.  Weak Copling Limit of the N-Particle Schrödinger Equation , 2000 .

[16]  E. Lieb,et al.  The Ground State Energy of a Dilute Bose Gas , 1999, math-ph/9910033.

[17]  H. Yau,et al.  Linear Boltzmann equation as the weak coupling limit of a random Schrödinger equation , 1999, math-ph/9901020.

[18]  P. Bassanini,et al.  Elliptic Partial Differential Equations of Second Order , 1997 .

[19]  Séminaire sur les équations aux dérivées partielles,et al.  Séminaire equations aux dérivées partielles , 1988 .

[20]  H. Spohn.  Kinetic equations from Hamiltonian dynamics: Markovian limits , 1980 .

[21]  The classical field limit of scattering theory for non-relativistic many-boson systems. II , 1979 .

[22]  K. Hepp.  The classical limit for quantum mechanical correlation functions , 1974 .

[23]  R. Courant,et al.  Methods of Mathematical Physics , 1962 .

[24]  Dr. M. G. Worster.  Methods of Mathematical Physics , 1947, Nature.