Speaker
Description
Our understanding of ordinary liquid matter is based on the statistical physics of Brownian motion and self-diffusion, as embodied in the complementary descriptions of Einstein and Langevin. The Langevin equation as a stochastic equation of motion which comprises all physical effects of atomic motion in liquids (from conservative interactions to dissipation) is used ubiquitously to predict the macroscopic properties of matter based on microscopic dynamics and interactions. In nuclear physics, the viscosity is a key quantity which plays a pivotal role in various high-energy processes, from fusion-fission nuclear reactions [1] to heavy-ion collisions and the quark-gluon plasma [2]. Apart from numerical simulations, the viscosity of liquid matter cannot be predicted as an expansion around the gaseous state (e.g. Boltzmann equation plus Chapman-Enskog closure) due to the high packing density of the microscopic building blocks [3]. The only alternative is, thus, the Green-Kubo relation. This is, however, a macroscopic description that heavily relies on numerics. I will show how a relativistic Langevin equation can be derived from a microscopic relativistic particle-bath (Caldeira-Leggett) Lagrangian [5]. Contrary to previous approaches to the relativistic Langevin equation which were not based on a first-principles derivation, this treatment reveals the intrinsically non-Markovian nature of the dynamics, as a result of the relativistic locality principle. The corresponding fluctuation-dissipation theorem is therefore also non-Markovian, implying that the white noise assumption is, generally, incompatible with special relativity and with causality [5]. This result calls for a fundamental revisiting of previously approaches in high-energy theory and QCD matter, such as the Parisi-Wu quantization. I will then show how the relativistic Langevin equation can be used as a starting point for a microscopic derivation of the viscosity of dense strongly-correlated high-energy liquids, where it predicts the cubic scaling of viscosity with temperature observed in quark-gluon plasma [6].
[1] C. Eccles, S. Roy, T. H. Gray, and A. Zaccone, Phys. Rev. C 96, 054611 (2017).
[2] J. E. Bernhard, J. Scott Moreland & S. A. Bass, Nat. Phys. 15, 1113–1117 (2019).
[3] V. G. Jervell and Ø. Wilhelmsen, J. Chem. Phys. 158, 224101 (2023).
[4] S. Borsanyi, et al. Phys. Rev. D 98, 014512 (2018).
[5] A. Petrosyan and A. Zaccone, J. Phys. A: Math. Theor. 55 015001 (2022); F. E. Zadra, A. Petrosyan, A. Zaccone, Phys. Rev. D 108, 096012 (2023).
[6] A. Zaccone, Nucl. Phys. B 1000, 116483 (2024).
