From Hartree Dynamics to the Relativistic Vlasov Equation

被引：0
|
作者：
Elia Dietler
Simone Rademacher
Benjamin Schlein
机构：
[1] University of Zurich,Institute for Mathematics
来源：
Journal of Statistical Physics | 2018年 / 172卷
关键词：
Hartree theory; Relativistic Vlasov equation; Many-body quantum mechanics;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We derive the relativistic Vlasov equation from quantum Hartree dynamics for fermions with relativistic dispersion in the mean-field scaling, which is naturally linked with an effective semiclassic limit. Similar results in the non-relativistic setting have been recently obtained in Benedikter et al. (Arch Rat Mech Anal 221(1): 273–334, 2016). The new challenge that we have to face here, in the relativistic setting, consists in controlling the difference between the quantum kinetic energy and the relativistic transport term appearing in the Vlasov equation.
引用
收藏
页码：398 / 433
页数：35
相关论文
共 50 条
  • [41] Derivation of transient relativistic fluid dynamics from the Boltzmann equation
    Denicol, G. S.
    Niemi, H.
    Molnar, E.
    Rischke, D. H.
    PHYSICAL REVIEW D, 2012, 85 (11):
  • [42] Multicomponent relativistic dissipative fluid dynamics from the Boltzmann equation
    Fotakis, Jan A.
    Molnar, Etele
    Niemi, Harri
    Greiner, Carsten
    Rischke, Dirk H.
    PHYSICAL REVIEW D, 2022, 106 (03)
  • [43] Rate of Convergence Towards Semi-Relativistic Hartree Dynamics
    Ji Oon Lee
    Annales Henri Poincaré, 2013, 14 : 313 - 346
  • [44] Rate of Convergence Towards Semi-Relativistic Hartree Dynamics
    Lee, Ji Oon
    ANNALES HENRI POINCARE, 2013, 14 (02): : 313 - 346
  • [45] Ground states for the pseudo-relativistic Hartree equation with external potential
    Cingolani, Silvia
    Secchi, Simone
    PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2015, 145 (01) : 73 - 90
  • [46] A MODIFIED RELATIVISTIC HARTREE APPROXIMATION TO THE NUCLEAR-MATTER EQUATION OF STATE
    HEIDE, EK
    RUDAZ, S
    PHYSICS LETTERS B, 1991, 262 (04) : 375 - 382
  • [47] Nuclear response from the Vlasov equation
    Abrosimov, VI
    Dellafiore, A
    Matera, F
    TRANSPORT THEORY AND STATISTICAL PHYSICS, 2005, 34 (3-5): : 407 - 415
  • [48] Controlling the propagation of the support for the relativistic Vlasov equation with a selfconsistent Lorentz invariant field
    Andreasson, H
    INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1996, 45 (03) : 617 - 642
  • [49] Equation of Vlasov-Maxwell-Einstein Type and Transition to a Weakly Relativistic Approximation
    Vedenyapin, V. V.
    Fimin, N. N.
    Chechetkin, V. M.
    COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2019, 59 (11) : 1816 - 1831
  • [50] The Hartree and Vlasov equations at positive density
    Lewin, Mathieu
    Sabin, Julien
    COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2020, 45 (12) : 1702 - 1754
12345