The Derivation of the Compressible Euler Equation from Quantum Many-Body Dynamics
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Xuwen Chen | Shunlin Shen | Jiahao Wu | Zhifei Zhang | Zhifei Zhang | Xuwen Chen | Jiahao Wu | Shunlin Shen
[1] O. Lanford. Time evolution of large classical systems , 1975 .
[2] Xuwen Chen. On the Rigorous Derivation of the 3D Cubic Nonlinear Schrödinger Equation with a Quadratic Trap , 2012, 1204.0125.
[3] Paul Smith,et al. On the unconditional uniqueness of solutions to the infinite radial Chern-Simons-Schrödinger hierarchy , 2014, 1406.2649.
[4] T. Paul,et al. Mean‐Field and Classical Limit for the N‐Body Quantum Dynamics with Coulomb Interaction , 2019, Communications on Pure and Applied Mathematics.
[5] Matthew Rosenzweig,et al. From Quantum Many-Body Systems to Ideal Fluids , 2021, 2110.04195.
[6] E. Madelung,et al. Quantentheorie in hydrodynamischer Form , 1927 .
[7] Zhifei Zhang,et al. The unconditional uniqueness for the energy-supercritical NLS , 2021 .
[8] Philip T. Gressman,et al. On the uniqueness of solutions to the periodic 3D Gross–Pitaevskii hierarchy , 2012, 1212.2987.
[9] Laure Saint-Raymond,et al. Hydrodynamic Limits of the Boltzmann Equation , 2009 .
[10] Justin Holmer,et al. Quantitative Derivation and Scattering of the 3D Cubic NLS in the Energy Space , 2021 .
[11] R. Illner,et al. The mathematical theory of dilute gases , 1994 .
[12] J. Holmer,et al. The Derivation of the Energy-critical NLS from Quantum Many-body Dynamics , 2018 .
[13] Thomas Chen,et al. The quintic NLS as the mean field limit of a boson gas with three-body interactions , 2008, 0812.2740.
[14] Shunlin Shen,et al. The rigorous derivation of the T2 focusing cubic NLS from 3D , 2021 .
[15] Horng-Tzer Yau,et al. Derivation of the Gross‐Pitaevskii hierarchy for the dynamics of Bose‐Einstein condensate , 2004, math-ph/0410005.
[16] Zhihui Xie,et al. Unconditional Uniqueness of the cubic Gross-Pitaevskii Hierarchy with Low Regularity , 2014, SIAM J. Math. Anal..
[17] Sergiu Klainerman,et al. On the Uniqueness of Solutions to the Gross-Pitaevskii Hierarchy , 2007 .
[18] Horng-Tzer Yau,et al. Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensate , 2004, math-ph/0606017.
[19] Phan Thanh Nam,et al. Derivation of Hartree's theory for generic mean-field Bose systems , 2013, 1303.0981.
[20] Pair Excitations and the Mean Field Approximation of Interacting Bosons, I , 2012, 1208.3763.
[21] J. Holmer,et al. On the Klainerman–Machedon conjecture for the quantum BBGKY hierarchy with self-interaction , 2013, 1303.5385.
[22] Sergiu Klainerman,et al. Space-time estimates for null forms and the local existence theorem , 1993 .
[23] Mean field limit for Coulomb-type flows , 2018, 1803.08345.
[24] Z. Xie. Derivation of a nonlinear Schrödinger equation with a general power-type nonlinearity in $d=1,2$ , 2015, Differential and Integral Equations.
[25] M. Grillakis,et al. Pair Excitations and the Mean Field Approximation of Interacting Bosons, I , 2012, 1208.3763.
[26] Gross-Pitaevskii Equation as the Mean Field Limit of Weakly Coupled Bosons , 2004, math-ph/0410038.
[27] C. David Levermore,et al. The Semiclassical Limit of the Defocusing NLS Hierarchy , 1999 .
[28] J. Holmer,et al. Focusing Quantum Many-body Dynamics II: The Rigorous Derivation of the 1D Focusing Cubic Nonlinear Schr\"{o}dinger Equation from 3D , 2014, 1407.8457.
[29] On the Quantum Boltzmann Equation , 2003, math-ph/0302034.
[30] B. Schlein,et al. Gross–Pitaevskii dynamics for Bose–Einstein condensates , 2017, Analysis & PDE.
[31] J. Holmer,et al. Correlation structures, Many-body Scattering Processes and the Derivation of the Gross-Pitaevskii Hierarchy , 2014, 1409.1425.
[32] B. Schlein,et al. Bogoliubov theory in the Gross–Pitaevskii limit , 2018, Acta Mathematica.
[33] A. Majda. Compressible fluid flow and systems of conservation laws in several space variables , 1984 .
[34] F. Lin,et al. Semiclassical Limit of the Gross-Pitaevskii Equation in an Exterior Domain , 2006 .
[35] Xuwen Chen. Collapsing estimates and the rigorous derivation of the 2d cubic nonlinear Schrödinger equation with anisotropic switchable quadratic traps , 2011, 1102.0593.
[36] V. Sohinger,et al. Local existence of solutions to Randomized Gross-Pitaevskii hierarchies , 2014, 1401.0326.
[37] J. Holmer,et al. On the Rigorous Derivation of the 2D Cubic Nonlinear Schrödinger Equation from 3D Quantum Many-Body Dynamics , 2012, 1212.0787.
[38] H. Yau,et al. Rigorous Derivation of the Gross-Pitaevskii Equation with a Large Interaction Potential , 2008, 0802.3877.
[39] G. Staffilani,et al. Derivation of the two-dimensional nonlinear Schrödinger equation from many body quantum dynamics , 2008, 0808.0505.
[40] Thomas Chen,et al. Derivation of the Cubic NLS and Gross–Pitaevskii Hierarchy from Manybody Dynamics in d = 3 Based on Spacetime Norms , 2011, 1111.6222.
[41] N. Masmoudi. Hydrodynamic Limits of the Boltzmann Equation , 2004 .
[42] Horng-Tzer Yau,et al. Derivation of the cubic non-linear Schrödinger equation from quantum dynamics of many-body systems , 2005, math-ph/0508010.
[43] Rémi Carles,et al. Semi-Classical Analysis For Nonlinear Schrodinger Equations , 2008 .
[44] Isabelle Gallagher,et al. From Newton to Boltzmann: Hard Spheres and Short-range Potentials , 2012, 1208.5753.
[45] J. Holmer,et al. Focusing Quantum Many-body Dynamics: The Rigorous Derivation of the 1D Focusing Cubic Nonlinear Schrödinger Equation , 2013, 1308.3895.
[46] S. Herr,et al. The Gross–Pitaevskii Hierarchy on General Rectangular Tori , 2014, 1410.5338.
[47] R. Seiringer,et al. Unconditional Uniqueness for the Cubic Gross‐Pitaevskii Hierarchy via Quantum de Finetti , 2013, 1307.3168.
[48] V. Sohinger,et al. A rigorous derivation of the defocusing cubic nonlinear Schrödinger equation on T3 from the dynamics of many-body quantum systems , 2014, 1405.3003.
[49] G. Staffilani,et al. Randomization and the Gross–Pitaevskii Hierarchy , 2013, 1308.3714.
[50] Robert S. Strichartz,et al. Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations , 1977 .
[51] B. Schlein,et al. Quantitative Derivation of the Gross‐Pitaevskii Equation , 2012, 1208.0373.
[52] H. Spohn. Kinetic equations from Hamiltonian dynamics: Markovian limits , 1980 .
[53] Ping Zhang,et al. Wigner Measure and Semiclassical Limits of Nonlinear Schrodinger Equations , 2008 .
[54] E. Grenier,et al. Semiclassical limit of the nonlinear Schrödinger equation in small time , 1998 .
[55] Yan Guo,et al. On the weak coupling limit of quantum many-body dynamics and the quantum Boltzmann equation , 2014, 1412.1775.
[56] S. Herr,et al. Unconditional uniqueness results for the nonlinear Schrödinger equation , 2018, Communications in Contemporary Mathematics.
[57] Derivation of the Euler equations from many-body quantum mechanics , 2002, math-ph/0210036.
[58] Thomas Chen,et al. On the emergence of quantum Boltzmann fluctuation dynamics near a Bose-Einstein Condensate , 2021 .
[59] B. Schlein,et al. Quantum Many-Body Fluctuations Around Nonlinear Schrödinger Dynamics , 2015, 1509.03837.
[60] F. Golse,et al. Rigorous Derivation of the Cubic NLS in Dimension One , 2007 .
[61] Younghun Hong,et al. Uniqueness of solutions to the 3D quintic Gross-Pitaevskii Hierarchy , 2014, 1410.6961.