Quantum Lindblad Equation (Q6534317): Difference between revisions

Revision as of 14:07, 24 February 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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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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Identifiers

Wikidata QID

Q4476520

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@@ aliases / en / 0 / aliases / en / 0 @@
+Gorini–Kossakowski–Sudarshan–Lindblad Equation
@@ Property / defining formula @@
- $\frac{d}{d t} ρ = - \frac{i}{ℏ} [H, ρ] + \sum_{i = 1}^{N^{2} - 1} γ_{i} (L_{i} ρ L_{i}^{†} - \frac{1}{2} [L_{i}^{†} L_{i}, ρ]_{+})$ 
\frac{\mathrm d}{\mathrm{d}t}\rho=-\frac{\mathrm i}\hbar[H,\rho]+\sum _{i=1}^{N^2-1}\gamma_i\left(L_i\rho L_i^\dagger-\frac12[L_i^\dagger L_i,\rho]_+\right)
-Normal rank
@@ Property / in defining formula @@
+ $i$ 
\mathrm{i}
@@ Property / in defining formula: $i$ / rank @@
+Normal rank
@@ Property / in defining formula: $i$ / qualifier @@
+symbol represents: imaginary unit
@@ Property / defining formula @@
+ $\frac{d}{d t} ρ = - \frac{i}{ℏ} [H, ρ] + \sum_{k = 1}^{N^{2} - 1} γ_{k} (L_{k} ρ L_{k}^{†} - \frac{1}{2} [L_{k}^{†} L_{k}, ρ]_{+})$ 
\frac{\mathrm d}{\mathrm{d}t}\rho=-\frac{\mathrm i}\hbar[H,\rho]+\sum _{k=1}^{N^2-1}\gamma_k\left(L_k\rho L_k^\dagger-\frac12[L_k^\dagger L_k,\rho]_+\right)
+Normal rank
@@ Property / contains @@
+Detailed Balance Principle
@@ Property / contains: Detailed Balance Principle / rank @@
+Normal rank
@@ Property / contains @@
+Quantum Hamiltonian (Electric Charge)
@@ Property / contains: Quantum Hamiltonian (Electric Charge) / rank @@
+Normal rank
@@ Property / Wikidata QID @@
+Q4476520
@@ Property / Wikidata QID: Q4476520 / rank @@
+Normal rank

Quantum Lindblad Equation (Q6534317): Difference between revisions

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

$i$

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

Revision as of 14:07, 24 February 2025

Statements

Identifiers

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Mathematics(0 entries)

Quantum Lindblad Equation (Q6534317): Difference between revisions

ddtρ=−iℏ[H,ρ]+∑i=1N2−1γi(LiρLi†−12[Li†Li,ρ]+)

i

ddtρ=−iℏ[H,ρ]+∑k=1N2−1γk(LkρLk†−12[Lk†Lk,ρ]+)

Revision as of 14:07, 24 February 2025

Statements

Identifiers

Sitelinks

Mathematics(0 entries)

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

$i$

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