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Many-Body Perturbation Theory for Driven Dissipative Quasiparticle Flows and Fluctuations

Thomas Blommel, Enrico Perfetto, Gianluca Stefanucci, Vojtech Vlcek

Abstract

We present a unified many-body perturbation theory for open quantum systems, that treats dissipation, correlations, and external driving on equal footing. Using a Keldysh-Lindblad formalism, we introduce diagrammatic treatment of dissipative interaction lines representing quasiparticle flows and fluctuations. Two new Feynman rules render the evaluation of dissipative diagrams compact and systematically improvable, while preserving the Keldysh and anti-Hermitian symmetries of the closed-system theory. Consequently, the structure of the Kadanoff-Baym equations (KBE) remains unchanged, enabling existing numerical methods to be directly applied. To illustrate this, we derive dissipative versions of the second Born and GW approximations, identifying the physical content of the self-energy components. Moreover, we demonstrate that time-linear approximations to the full KBE retain their closed structure and can be efficiently used to simulate relaxation and decoherence dynamics. This framework establishes a general route toward first-principles modeling of correlated, driven, and dissipative quantum materials.

Many-Body Perturbation Theory for Driven Dissipative Quasiparticle Flows and Fluctuations

Abstract

We present a unified many-body perturbation theory for open quantum systems, that treats dissipation, correlations, and external driving on equal footing. Using a Keldysh-Lindblad formalism, we introduce diagrammatic treatment of dissipative interaction lines representing quasiparticle flows and fluctuations. Two new Feynman rules render the evaluation of dissipative diagrams compact and systematically improvable, while preserving the Keldysh and anti-Hermitian symmetries of the closed-system theory. Consequently, the structure of the Kadanoff-Baym equations (KBE) remains unchanged, enabling existing numerical methods to be directly applied. To illustrate this, we derive dissipative versions of the second Born and GW approximations, identifying the physical content of the self-energy components. Moreover, we demonstrate that time-linear approximations to the full KBE retain their closed structure and can be efficiently used to simulate relaxation and decoherence dynamics. This framework establishes a general route toward first-principles modeling of correlated, driven, and dissipative quantum materials.
Paper Structure (4 sections, 20 equations, 3 figures)

This paper contains 4 sections, 20 equations, 3 figures.

Table of Contents

  1. Appendix A: Feynman Rules
  2. Appendix B: Forward and Backward Functions
  3. Appendix C: Bubble diagram for $t<t'$
  4. Appendix D: Linear Scaling EOM Definitions

Figures (3)

  • Figure 1: The particle fluctuation (green) and flow (red) lines that appear in the perturbative expansion of the Lindblad open system Hamiltonian. Note that the distinct contour coincidence structure of $v^S$ and $\lozenge$ lead to different symmetries and generally distinct behavior upon index permutation.
  • Figure 2: Bubble diagram with interaction lines specified. Contour arguments of each interaction leg have also been included, showing the interaction legs that are contour coincident with each other.
  • Figure 3: $GW$ diagram with $W$ representing the screened particle fluctuation line.