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SUMMARY:Derivation of effective equations in the mean-field regime
DTSTART;VALUE=DATE-TIME:20230327T070000Z
DTEND;VALUE=DATE-TIME:20230331T090000Z
DTSTAMP;VALUE=DATE-TIME:20240624T161500Z
UID:indico-event-476@indico.gssi.it
DESCRIPTION:Speakers: Chiara Saffirio (University of Basel)\n\nLecturer: C
hiara Saffirio (University of Basel)Abstract: The derivation of effective
macroscopic theories approximating microscopic systems of interacting part
icles in some scaling limit is a major question in non-equilibrium statist
ical mechanics. In this course we will be concerned with the dynamics of s
ystems made of many interacting fermions. We will focus on the mean-field
regime\, i.e. weakly interacting particles whose collective effect can be
approximated by an averaged potential in convolution form\, and review rec
ent mean-field techniques based on second quantization approaches. As a fi
rst step we will obtain a reduced description given by the time-dependent
Hartree-Fock equation. As a second step we will look at longer time scales
\, where a semiclassical description starts to be relevant\, and approxima
te the many-body dynamics with the Vlasov equation\, which describes the e
volution of the effective probability density of particles on the one part
icle phase space. The structure of the initial data will play an important
role at each step of the approximation. References:N. Benedikter\, M. P
orta\, B. Schlein: Effective evolution equations from quantum dynamics. Sp
ringer Briefs in Mathematical Physics 7\, 2016. C. Saffirio: The Vlasov e
quation as the mean-field and semiclassical limit of many interacting ferm
ions. IAMP News Bulletin April 2022\, http://www.iamp.org/bulletins/Bullet
in-Apr2022-print.pdf. Information. This minicourse is part of the school
"Scaling Limits and Generalized Hydrodynamics"\, see https://indico.gssi.i
t/e/ScalingLimits.\n\nhttps://indico.gssi.it/event/476/
URL:https://indico.gssi.it/event/476/
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