Efficient energy resolved quantum master equation for transport calculations in large strongly correlated systems

Gerhard Dorn*, Enrico Arrigoni, Wolfgang von der Linden

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We introduce a systematic approximation for an efficient evaluation of Born–Markov master equations for steady state transport studies in open quantum systems out of equilibrium: the energy resolved master equation approach. The master equation is formulated in the eigenbasis of the open quantum system and build successively by including eigenstates with increasing grandcanonical energies. In order to quantify convergence of the approximate scheme we introduce quality factors to check preservation of trace, positivity and hermiticity. Furthermore, we discuss different types of master equations that go beyond the commonly used secular approximation in order to resolve coherences between quasi-degenerate states. For the discussion of complete positivity we introduce a canonical Redfield–Bloch master equation and compare it to a previously derived master equations in Lindblad form with and without using the secular approximation. The approximate scheme is benchmarked for a six orbital quantum system which shows destructive quantum interference under the application of a bias voltage. The energy resolved master equation approach presented here makes quantum transport calculations in many-body quantum systems numerically accessible also beyond six orbitals with a full Hilbert space of the order of ∼ 10 6

Original languageEnglish
Article number075301
JournalJournal of Physics A: Mathematical and Theoretical
Issue number7
Publication statusPublished - 19 Feb 2021


  • quantum master equation, destructive interference, complete posi-tivity, efficient evaluation
  • Destructive interference
  • Quantum master equation
  • Complete positivity
  • Efficient evaluation

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Mathematical Physics
  • Modelling and Simulation

Fields of Expertise

  • Advanced Materials Science


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