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Home page > Seminars > Séminaires théorie > Theory Club Friday March 13 2020 at 12:00 in room 412B. Alessandro Manacorda: "A numerical solution for the infinite-dimensional dynamics of spheres".

Theory Club Friday March 13 2020 at 12:00 in room 412B. Alessandro Manacorda: "A numerical solution for the infinite-dimensional dynamics of spheres"

Unless otherwise stated, seminars and defences take place at 11:30 in room 454A of Condorcet building.


A numerical solution for the infinite-dimensional dynamics of spheres

Alessandro Manacorda

Abstract: In the last years, a Dynamical Mean-Field Theory (DMFT) describing the dynamics of short-range interacting particles in infinite dimensions at equilibrium has been formulated [1-5]. The infinite-dimensional limit of the dynamical equations, obtained as the leading order of a perturbative expansion in 1/d, leads to theoretical predictions concerning the dynamical transition and the critical exponent of the diffusivity. However, an analytical solution of the DMFT equations is out of reach. I will present a numerical solution of the dynamics through a self-consistent algorithm, applied to hard and soft spheres, considering both overdamped and inertial dynamics [6]. The solution found confirms the theoretical predictions about the dynamical transition at high densities, and leads to new quantitative insights about the dynamical observables of the system, such as the memory kernel and the MSD. The solution for hard spheres is obtained through a non-trivial limit of the soft spheres one. The results both merge and extend kinetic theory and thermodynamics at infinite d, and represent a starting point for the study of several out-of-equilibrium systems [7-8].

[1] T Maimbourg, J Kurchan & F Zamponi. Phys. Rev. Lett. 116 015902 (2016) [2] J Kurchan, T Maimbourg & F Zamponi. J. Stat. Mech. 2016.3 033210 (2016) [3] G Szamel. Phys. Rev. Lett. 119 155502 (2017) [4] P Charbonneau et al. Annu. Rev. of Cond. Matter Phys. 8 265-288 (2017) [5] G Parisi, P Urbani & F Zamponi. Theory of Simple Glasses: Exact Solutions in Infinite Dimensions. Cambridge University Press (2020) [6] A Manacorda, G Schehr & F Zamponi. arXiv:2002.09216 (2020) [7] E Agoritsas, T Maimbourg & F Zamponi. J. Phys. A: Math. Theor. 52 144002 (2019) [8] E Agoritsas, T Maimbourg & F Zamponi. J. Phys. A: Math. Theor. 52 334001 (2019)

Friday March 13 at 12:00 in room 412B


Contact : Équipe séminaires / Seminar team - Published on / Publié le 10 March 2020


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