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Partial Differential Equations01:21

Partial Differential Equations

A stone dropped into a still pond generates waves that propagate outward in circular patterns, creating a dynamic surface whose elevation depends on both position and time. At any given location, the water level oscillates as the wave passes, while at any fixed moment, the surface exhibits smooth, curved structures extending across space. This dual dependence requires a mathematical description that accounts for variation in multiple variables simultaneously.At a fixed point on the water...
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Many-Body Perturbation Theory for Driven Dissipative Quasiparticle Flows and Fluctuations.

Thomas Blommel1,2, Enrico Perfetto3,4, Gianluca Stefanucci3,4

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We developed a new theory for open quantum systems, unifying dissipation, correlations, and driving. This approach enables accurate simulations of quantum materials, revealing enhanced quasiparticle stability and lifetimes.

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Area of Science:

  • Quantum physics
  • Condensed matter theory
  • Many-body perturbation theory

Background:

  • Open quantum systems are challenging due to dissipation, correlations, and external driving.
  • Existing theories struggle to treat these factors simultaneously and on equal footing.
  • Accurate modeling of quantum materials requires a unified theoretical framework.

Purpose of the Study:

  • To present a unified many-body perturbation theory for open quantum systems.
  • To incorporate dissipation, correlations, and external driving within a single formalism.
  • To enable first-principles modeling of complex quantum materials.

Main Methods:

  • Utilizing a Keldysh-Lindblad formalism.
  • Introducing a diagrammatic treatment with new Feynman rules for dissipative interactions.
  • Preserving Keldysh and anti-Hermitian symmetries for Kadanoff-Baym equations.
  • Deriving dissipative second Born and GW approximations.

Main Results:

  • Developed a compact and systematically improvable diagrammatic approach.
  • Maintained the structure of Kadanoff-Baym equations for direct application of numerical methods.
  • Demonstrated efficient simulation of relaxation and decoherence dynamics.
  • Observed dissipation-induced correlations leading to quasiparticle stabilization and extended lifetimes in the driven Haldane model.

Conclusions:

  • The presented framework offers a general route for first-principles modeling of correlated, driven, and dissipative quantum materials.
  • The theory successfully unifies key aspects of open quantum systems, paving the way for new discoveries.
  • The method allows for accurate prediction of quantum material properties under realistic conditions.