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Understanding the dynamics of bound state formation is one of the fundamentalquestions in confining quantum field theories such as Quantum Chromodynamics(QCD). One hadronization mechanism that has garnered significant attention isthe breaking of a string initially connecting a fermion and an anti-fermion.Deepening our understanding of real-time string-breaking dynamics with simpler,lower dimensional models like the Schwinger model can improve our understandingof the hadronization process in QCD and other confining systems found incondensed matter and statistical systems. In this paper, we consider thestring-breaking dynamics within the Schwinger model and investigate itsmodification inside a thermal medium, treating the Schwinger model as an openquantum system coupled to a thermal environment. Within the regime of weakcoupling between the system and environment, the real-time evolution of thesystem can be described by a Lindblad evolution equation. We analyze theLiouvillian gaps of this Lindblad equation and the time dependence of thesystem's von Neumann entropy. We observe that the late-time relaxation ratedecreases as the environment correlation length increases. Moreover, when theenvironment correlation length is infinite, the system exhibits two steadystates, one in each of the sectors with definite charge-conjugation-parity (CP)quantum numbers. For parameter regimes where an initial string breaks invacuum, we observe a delay of the string breaking in the medium, due to kineticdissipation effects. Conversely, in regimes where an initial string remainsintact in vacuum time evolution, we observe string breaking (melting) in thethermal medium. We further discuss how the Liouvillian dynamics of the openSchwinger model can be simulated on quantum computers and provide an estimateof the associated Trotter errors.

Liouvillian Dynamics of the Open Schwinger Model: String Breaking and Kinetic Dissipation in a Thermal Medium