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Effects of dissipation on phase diagram and bosonic excitations in the quark-meson model

Johannes V. Roth1,*, Yunxin Ye2,†, Sören Schlichting2, and Lorenz von Smekal1,3

  • 1Institut für Theoretische Physik, Justus-Liebig-Universität, 35392 Giessen, Germany
  • 2Fakultät für Physik, Universität Bielefeld, D-33615 Bielefeld, Germany
  • 3Helmholtz Research Academy Hesse for FAIR (HFHF), Campus Giessen, 35392 Giessen, Germany

  • *Present address: Fakultät für Physik, Universität Bielefeld, D-33615 Bielefeld, Germany.
  • †Present address: Theoretisch-Physikalisches Institut, Abbe Center of Photonics, Friedrich-Schiller-Universität Jena, 07743 Jena, Germany.
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Phys. Rev. D 113, 016016 – Published 14 January, 2026

DOI: https://doi.org/10.1103/mbl9-vdxc

Abstract

In this work we study the quark-meson model within a real-time formulation of the functional renormalization group (FRG) on the Schwinger-Keldysh contour. First, we discuss in detail the symmetry of thermal equilibrium for the fermionic sector of the Keldysh action. We take into account dissipation for the bosonic degrees of freedom in the spirit of the Caldeira-Leggett model by coupling the system to an O(4) invariant external heat bath. We study the effect of dissipation on static equilibrium properties, most prominently on the FRG flow of the effective potential and thus on the resulting phase diagram. We find that, unlike in classical systems, through the contributions from nonzero Matsubara modes the dissipative dynamics can in general have an effect on static observables. We investigate these effects within two phenomenological models for the temperature dependence of the pion damping to verify that they are quantitatively small. To estimate their largest possible influence, we consider limits where the damping constants approach infinity.

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Phys. Rev. D 113, 016016– Published 14 January, 2026
  • Received 12 May 2025
  • Accepted 10 December 2025
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