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Redfield equation — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Redfield_equation
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-07T21:33:04.505Z
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Redfield equation — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Redfield_equation (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_befeef4bc154 (Metraipolis archive dc_befeef4bc154, sha256 77b4bee6fb7c198952ccd15a6fd3e6f61983f1907c78042af3472eaf1911cea1)

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@misc{dcbefeef4bc154,
  title = {Redfield equation — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Redfield_equation},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_befeef4bc154; sha256 77b4bee6fb7c198952ccd15a6fd3e6f61983f1907c78042af3472eaf1911cea1},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Redfield_equation. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In quantum mechanics, the Redfield equation is a Markovian master equation that describes the time evolution of the reduced density matrix ρ of a strongly coupled quantum system that is weakly coupled to an environment. The equation is named after Alfred G. Redfield, who first applied it, doing so for nuclear magnetic resonance spectroscopy. It is also known as the Redfield relaxation theory. There is a close connection to the Lindblad master equation. If a so-called secular approximation is performed, where only certain resonant interactions with the environment are retained, every Redfield equation transforms into a master equation of Lindblad type. Redfield equations are trace-preserving and correctly produce a thermalized state for asymptotic propagation. However, in contrast to Lindblad equations, Redfield equations do not guarantee a positive time evolution of the density matrix. That is, it is possible to get negative populations during the time evolution. The Redfield equation approaches the correct dynamics for sufficiently weak coupling to the environment. The general form of the Redfield equation is ∂ ∂ t ρ ( t ) = − i ℏ [ H , ρ ( t ) ] − 1 ℏ 2 ∑ m [ S m , ( Λ m ρ ( t ) − ρ ( t ) Λ m † ) ] {\displaystyle {\frac {\partial }{\partial t}}\rho (t)=-{\frac {i}{\hbar }}[H,\rho (t)]-{\frac {1}{\hbar ^{2}}}\sum _{m}[S_{m},(\Lambda _{m}\rho (t)-\rho (t)\Lambda _{m}^{\dagger })]} where H {\displaystyle H} is the hermitian Hamiltonian, and the S m , Λ m {\displaystyle S_{m},\Lambda _{m}} are operators that describe the coupling to the environment, and [ A , B ] = A B − B A {\displaystyle [A,B]=AB-BA} is the commutation bracket. The explicit form is given in the derivation below.

Tema degli esploratori: fisica e astronomia (deposito sistematico; categoria «Quantum mechanics»).
Fonte: Wikipedia in inglese, voce «Redfield equation» — https://en.wikipedia.org/wiki/Redfield_equation
Wikidata Q25312728 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q25312728
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Redfield_equation?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1352352175, consultata il 2026-10-07T21:02:39.946Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: 05b5b8a31b9dde52579405179c3de7ba7002c01008ef2ead81e5262413675360