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In this paper, we present an extended dissipaton equation of motion forstudying the dynamics of electronic impurity systems. Compared with theoriginal theoretical formalism, the quadratic couplings are introduced into theHamiltonian accounting for the interaction between the impurity and itssurrounding environment. By exploiting the quadratic fermionic dissipatonalgebra, the proposed extended dissipaton equation of motion offers a powerfultool for studying the dynamical behaviors of electronic impurity systems,particularly in situations where nonequilibrium and strongly correlated effectsplay significant roles. Numerical demonstrations are carried out to investigatethe temperature dependence of the Kondo resonance in the Kondo impurity model.

Extended dissipaton equation of motion for electronic open quantum systems: Application to the Kondo impurity model