Open quantum systems in Euclidean and real-time approaches

• Applicant: Dr. Ralf-Arno Tripolt
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 523702416

The proposed project aims at making a significant contribution to gaining a deeper understanding of the dynamical properties of open quantum systems. This will eventually allow for a description of the dynamics near the (chiral) critical endpoint in the phase diagram of Quantum Chromodynamics. A robust understanding of these critical dynamics is not only of fundamental theoretical interest but also needed for the interpretation of experimental data, for example on event-by-event fluctuations as obtained in heavy-ion collisions. The theoretical description of realistic open quantum systems that are subject to effects like dissipation and diffusion is however a very challenging task. First-principle lattice QCD calculations are for example hampered by the fermion sign problem at finite chemical potential and, in addition, only give access to close-to-equilibrium information. Functional approaches such as Dyson-Schwinger equations and the Functional Renormalization Group (FRG) framework can here provide valuable alternatives. In particular the FRG, based on Wilson's coarse graining idea, is ideally suited to investigate critical phenomena and aspects of universality. In this project we aim at describing dynamical critical properties of open quantum systems with both Euclidean and real-time approaches near equilibrium. As the method of choice to describe such systems, in particular near phase transitions where quantum and thermal fluctuations are essential, we will use the Functional Renormalization Group (FRG) framework. Using both a Euclidean FRG formulation and a real-time formulation on the Keldysh contour, we will aim at describing the critical near-equilibrium dynamics of non-equilibrium phase transitions in dissipative and diffusive systems in terms of dynamic critical exponents, spectral functions and dynamic scaling functions. By systematically developing and comparing the Euclidean and the real-time approach, we will be able to assess the extent to which the Euclidean setup can be used to describe such dynamic properties, and to identify the most suited method in a given situation: if applicable, the (analytically continued) Euclidean setup can often be technically favorable over the more general but typically very demanding real-time formulation.

• DFG Programme: Research Grants