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Hierarchical equations of motion — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Hierarchical_equations_of_motion
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-07T13:44:47.304Z
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Hierarchical equations of motion — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Hierarchical_equations_of_motion (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_ef39deb152ef (Metraipolis archive dc_ef39deb152ef, sha256 a052734998cb2feca498a0761e136cba74be01c7e3bee64c4df373b149575e62)

BibTeX

@misc{dcef39deb152ef,
  title = {Hierarchical equations of motion — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Hierarchical_equations_of_motion},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_ef39deb152ef; sha256 a052734998cb2feca498a0761e136cba74be01c7e3bee64c4df373b149575e62},
  year = {2026}
}

Archived text

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

The hierarchical equations of motion (HEOM) technique derived by Yoshitaka Tanimura and Ryogo Kubo in 1989, is a non-perturbative approach developed to study the evolution of a density matrix ρ ( t ) {\displaystyle \rho (t)} of quantum dissipative systems. The method can treat system-bath interaction non-perturbatively as well as non-Markovian noise correlation times without the hindrance of the typical assumptions that conventional Redfield (master) equations suffer from such as the Born, Markovian and rotating-wave approximations. HEOM is applicable even at low temperatures where quantum effects are not negligible. The hierarchical equation of motion for a system in a harmonic Markovian bath is ∂ ∂ t ρ ^ n = − ( i ℏ H ^ A × + n γ ) ρ ^ n − i ℏ V ^ × ρ ^ n + 1 + i n ℏ Θ ^ ρ ^ n − 1 {\displaystyle {\frac {\partial }{\partial t}}{\hat {\rho }}_{n}=-\left({\frac {i}{\hbar }}{\hat {H}}_{A}^{\times }+n\gamma \right){\hat {\rho }}_{n}-{i \over \hbar }{\hat {V}}^{\times }{\hat {\rho }}_{n+1}+{in \over \hbar }{\hat {\Theta }}{\hat {\rho }}_{n-1}} where the superscript × {\displaystyle ^{\times }} denoting a commutator and the temperature-dependent super-operator Θ ^ {\displaystyle {\hat {\Theta }}} are defined below. The parameter γ {\displaystyle \gamma } is the frequency width of the Drude spectral function J ( ω ) {\displaystyle J(\omega )} (see below).

Tema degli esploratori: fisica e astronomia (deposito sistematico; categoria «Quantum mechanics»).
Fonte: Wikipedia in inglese, voce «Hierarchical equations of motion» — https://en.wikipedia.org/wiki/Hierarchical_equations_of_motion
Wikidata Q28458353 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q28458353
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Hierarchical_equations_of_motion?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 1332371134, consultata il 2026-10-07T13:17:39.341Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: da4b8bc61611e6fc6a6a9a7408b97991eef26d0def231a60d234b5c43987a56a