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Quantum-Electrodynamical Density-Functional Theory Exemplified by the Quantum Rabi Model.

Vebjørn H Bakkestuen1, Vegard Falmår1, Maryam Lotfigolian1

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|February 19, 2025
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Summary
This summary is machine-generated.

This study demonstrates key features of density-functional theory (DFT) in quantum electrodynamics (QEDFT) using the quantum Rabi and Dicke models. Researchers derived analytical expressions and an adiabatic connection for studying DFT properties without approximations.

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Area of Science:

  • Quantum electrodynamics
  • Condensed matter physics
  • Quantum optics

Background:

  • Density-functional theory (DFT) is a powerful quantum mechanical method.
  • Quantum electrodynamics (QED) describes interactions between light and matter.
  • Combining DFT with QED (QEDFT) offers new avenues for studying quantum systems.

Purpose of the Study:

  • To demonstrate key features of DFT within a minimalistic quantum electrodynamics framework.
  • To enable the study of elementary properties of quantum-electrodynamical density-functional theory (QEDFT).
  • To analyze the quantum Rabi and Dicke models using QEDFT.

Main Methods:

  • Utilizing the quantum Rabi model (two-level system coupled to a single photon mode).
  • Discussing the Dicke model (multiple two-level systems coupled to a single photon mode).
  • Deriving analytical expressions for the constrained-search functional and exchange-correlation potential.

Main Results:

  • Demonstrated key features of DFT in a minimalistic QED implementation.
  • Provided analytical expressions for the constrained-search functional and exchange-correlation potential.
  • Derived an almost explicit form for the adiabatic connection, bounded analytically and numerically.

Conclusions:

  • The study successfully applies DFT principles to quantum electrodynamical systems.
  • Key features of DFT can be investigated within QEDFT without approximations.
  • The derived expressions and adiabatic connection offer a foundation for future QEDFT research.