## Correlations of stress fluctuations in glass-forming liquids

Many fluids do not crystallize upon cooling, but form amorphous, glassy, solids at low temperature. As liquids, amorphous solids are on average isotropic so that static pair-correlation functions do not allow to distinguish between fluid and solid states. However, a distinction is possible under weak shear deformation which makes a fluid flow, while a solid deforms elastically. Glass-forming liquids 'interpolate' between fluid and solid behavior, as the slowing down of the dynamics on cooling is accompanied by the emergence of elastic features. To characterize this viscoelasticity the spatio-temporal correlation function Cxyxy(r,t) of the local shear stress, for vectorial distance r and time t, has attracted a lot of recent interest.

The talk is embedded in this topical context. We examine a two-dimensional (2D) polydisperse Lennard-Jones model for a glass-forming system. The model is studied by molecular simulations (molecular dynamics and Monte Carlo) [1,2] and theory [2,3]. Our major results are : At low temperature and long times, Cxyxy(r,t) does not depend on r only, but also on the angle θ. In agreement with other recent work [Lemaître, JCP (2018) ; Maier, Fuchs, Zippelius, JCP (2018)], we argue that this behavior arises because the system is isotropic and achiral. The octupolar dependence of Cxyxy(r,θ) on the angle θ is thus a necessary consequence for isotropic and achiral systems. (ii) Specifically chosen angular averages allow to extract the dependence of Cxyxy(r,θ) on r. This dependence is long-ranged, decaying as 1/r^2 in 2D with an amplitude being given by a particular elastic constant, the Young modulus E. Our theory is in good agreement with the simulation results [3].

[1] J. P. Wittmer, A. N. Semenov, J. Baschnagel, Phys. Rev. E 108, 015002 (2023).

[2] L. Klochko, J. Baschnagel, J. P. Wittmer, H. Meyer, O. Benzerara, A. N. Semenov, J. Chem. Phys. 156, 164505 (2022).

[3] L. Klochko, J. Baschnagel, J. P. Wittmer, A. N. Semenov, Soft Matter 14, 6835 (2018).