Quantum Lindblad Equation (Q6534317): Difference between revisions

Latest revision as of 10:19, 29 July 2025

describes open system quantum dynamics including dissipation and/or decoherence

Gorini–Kossakowski–Sudarshan–Lindblad Equation

Language	Label	Description	Also known as
English	Quantum Lindblad Equation	describes open system quantum dynamics including dissipation and/or decoherence	Gorini–Kossakowski–Sudarshan–Lindblad Equation

Statements

instance of

mathematical expression

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continuous-time expression

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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.

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in defining formula

H

symbol represents

Quantum Hamiltonian Operator

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L

symbol represents

Quantum Jump Operator

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γ > 0

symbol represents

Quantum Damping Rate

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ℏ

symbol represents

Planck Constant

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ρ

symbol represents

Quantum Density Operator

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t

symbol represents

Time

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i

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MaRDI formula profile

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defining formula

\frac{d}{d t} ρ = - \frac{i}{ℏ} [H, ρ] + \sum_{k = 1}^{N^{2} - 1} γ_{k} (L_{k} ρ L_{k}^{†} - \frac{1}{2} [L_{k}^{†} L_{k}, ρ]_{+})

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contains

Detailed Balance Principle

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Quantum Hamiltonian (Electric Charge)

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Initial Quantum Density

object has role

initial condition

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Quantum Hamiltonian (Electric Polarizability)

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Quantum Hamiltonian (Electric Dipole)

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named after

Goeran Lindblad

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Identifiers

Wikidata QID

Q4476520

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Sitelinks

Mathematics(1 entry)

mardi Formula:6534317

@@ Property / description / Property / 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
+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.
@@ Property / in defining formula: $i$ / qualifier @@
+symbol represents: imaginary unit
@@ Property / in defining formula: $i$ / qualifier @@
-symbol represents: imaginary unit
@@ Property / instance of @@
+continuous-time expression
@@ Property / instance of: continuous-time expression / rank @@
+Normal rank
@@ Property / contains @@
+Quantum Hamiltonian (Electric Polarizability)
@@ Property / contains: Quantum Hamiltonian (Electric Polarizability) / rank @@
+Normal rank
@@ Property / contains @@
+Quantum Hamiltonian (Electric Dipole)
@@ Property / contains: Quantum Hamiltonian (Electric Dipole) / rank @@
+Normal rank
@@ Property / named after @@
+Goeran Lindblad
@@ Property / named after: Goeran Lindblad / rank @@
+Normal rank
@@ Property / related URL @@
+https://en.wikipedia.org/wiki/Lindbladian
@@ Property / related URL: https://en.wikipedia.org/wiki/Lindbladian / rank @@
+Normal rank
@@ links / mardi / name / links / mardi / name @@
+Formula:6534317