Quantum Lindblad Equation
type: Item
instance of: mathematical expression
instance of: continuous-time expression
description: Markovian quantum master equation for the evolution of quantum mechanical density matrices (pure or mixed states). It generalizes the Schrödinger equation to open quantum systems; that is, systems in contacts with their surroundings. The resulting dynamics is no longer unitary, but still satisfies the property of being trace-preserving and completely positive for any initial condition.
in defining formula: H
in defining formula: L
in defining formula: γ > 0
in defining formula: ℏ
in defining formula: ρ
in defining formula: t
in defining formula: i
community: MathModDB
MaRDI profile type: MaRDI formula profile
defining formula: d d t ρ = − i ℏ [ H , ρ ] + <munderover> ∑ k = 1 N 2 − 1 </munderover> γ k ( L k ρ L k † − 1 2 [ L k † L k , ρ ] + )
contains: Detailed Balance Principle
contains: Quantum Hamiltonian (Electric Charge)
contains: Initial Quantum Density
contains: Quantum Hamiltonian (Electric Polarizability)
contains: Quantum Hamiltonian (Electric Dipole)
Wikidata QID: Q4476520
named after: Goeran Lindblad
related URL: Lindbladian
description: describes open system quantum dynamics including dissipation and/or decoherence
alternative label: Gorini–Kossakowski–Sudarshan–Lindblad Equation