On the scattering problem for infinitely many fermions in dimensions $d ≥ 3$ at positive temperature

Thomas Chen; Younghun Hong; Nataša Pavlović

doi:10.1016/j.anihpc.2017.05.002

JournalsaihpcVol. 35, No. 2pp. 393–416

On the scattering problem for infinitely many fermions in dimensions $d \geq 3$ at positive temperature

Thomas Chen
Department of Mathematics, University of Texas at Austin, USA
Younghun Hong
Department of Mathematics, Yonsei University, Seoul, 120-749, Republic of Korea
Nataša Pavlović
Department of Mathematics, University of Texas at Austin, USA

On the scattering problem for infinitely many fermions in dimensions $d ≥ 3$ at positive temperature cover

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Abstract

In this paper, we study the dynamics of a system of infinitely many fermions in dimensions $d \geq 3$ near thermal equilibrium and prove scattering in the case of small perturbation around equilibrium in a certain generalized Sobolev space of density operators. This work is a continuation of our previous paper [11], and extends the important recent result of M. Lewin and J. Sabin in [19] of a similar type for dimension $d = 2$ . In the work at hand, we establish new, improved Strichartz estimates that allow us to control the case $d \geq 3$ .

Cite this article

Thomas Chen, Younghun Hong, Nataša Pavlović, On the scattering problem for infinitely many fermions in dimensions $d \geq 3$ at positive temperature. Ann. Inst. H. Poincaré Anal. Non Linéaire 35 (2018), no. 2, pp. 393–416

DOI 10.1016/J.ANIHPC.2017.05.002