Physics:Quantum Master equation - Revision history

WikiHarold: Restore missing Quantum reference definitions

2026-05-24T00:31:15Z

Restore missing Quantum reference definitions

← Older revision		Revision as of 00:31, 24 May 2026
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	=== Markovian approximation ===		=== Markovian approximation ===

	A common simplification assumes that the environment has no memory, so the dynamics are approximately local in time.<ref name="MIT_OCW" />		A common simplification assumes that the environment has no memory, so the dynamics are approximately local in time.<ref name="MIT_OCW">{{cite web \|url=https://ocw.mit.edu/courses/22-51-quantum-theory-of-radiation-interactions-fall-2012/resources/mit22_51f12_ch8/ \|title=22.51 Course Notes, Chapter 8: Open Quantum Systems \|website=MIT OpenCourseWare \|access-date=2026-04-12}}</ref>

	== The Lindblad form ==		== The Lindblad form ==
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	{{#invoke:PhysicsQC\|tocHeadingAndList\|Physics:Quantum basics/See also}}		{{#invoke:PhysicsQC\|tocHeadingAndList\|Physics:Quantum basics/See also}}

	=References=		= References =
	{{reflist\|3}}		{{reflist\|3}}

Maintenance script: Normalize quantum page header order

2026-05-22T11:33:15Z

Normalize quantum page header order

← Older revision		Revision as of 11:33, 22 May 2026
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	{{Quantum book backlink\|Open quantum systems}}		{{Quantum book backlink\|Open quantum systems}}
	{{Quantum article nav\|previous=Physics:Quantum Open systems\|previous label=Open systems\|next=Physics:Quantum Lindblad equation\|next label=Lindblad equation}}		{{Quantum article nav\|previous=Physics:Quantum Open systems\|previous label=Open systems\|next=Physics:Quantum Lindblad equation\|next label=Lindblad equation}}

	<div style="display:flex; gap:24px; align-items:flex-start; max-width:1200px;">		<div style="display:flex; gap:24px; align-items:flex-start; max-width:1200px;">

Maintenance script: Clean Book label remnants and backlink spacing

2026-05-22T11:11:33Z

Clean Book label remnants and backlink spacing

← Older revision		Revision as of 11:11, 22 May 2026
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	{{Short description\|Quantum Collection topic on Quantum Master equation}}		{{Short description\|Quantum Collection topic on Quantum Master equation}}

	{{Quantum book backlink\|Open quantum systems}}		{{Quantum book backlink\|Open quantum systems}}
	{{Quantum article nav\|previous=Physics:Quantum Open systems\|previous label=Open systems\|next=Physics:Quantum Lindblad equation\|next label=Lindblad equation}}		{{Quantum article nav\|previous=Physics:Quantum Open systems\|previous label=Open systems\|next=Physics:Quantum Lindblad equation\|next label=Lindblad equation}}

Maintenance script: Remove hidden BOM characters and direct Book label after Short description

2026-05-22T11:03:46Z

Remove hidden BOM characters and direct Book label after Short description

← Older revision		Revision as of 11:03, 22 May 2026
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	{{Short description\|Quantum Collection topic on Quantum Master equation}}~~Book I~~		{{Short description\|Quantum Collection topic on Quantum Master equation}}

	{{Quantum book backlink\|Open quantum systems}}		{{Quantum book backlink\|Open quantum systems}}

Maintenance script: Clean Short description prefix and add Book I label

2026-05-22T10:48:49Z

Clean Short description prefix and add Book I label

← Older revision		Revision as of 10:48, 22 May 2026
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	~~~~{{Short description\|Quantum Collection topic on Quantum Master equation}}		{{Short description\|Quantum Collection topic on Quantum Master equation}}Book I

	{{Quantum book backlink\|Open quantum systems}}		{{Quantum book backlink\|Open quantum systems}}

Maintenance script: Apply Quantum previous-next navigation

2026-05-20T12:25:40Z

Apply Quantum previous-next navigation

← Older revision		Revision as of 12:25, 20 May 2026
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	{{Short description\|Quantum Collection topic on Quantum Master equation}}		{{Short description\|Quantum Collection topic on Quantum Master equation}}

	{{Quantum book backlink\|Open quantum systems}}		{{Quantum book backlink\|Open quantum systems}}
			{{Quantum article nav\|previous=Physics:Quantum Open systems\|previous label=Open systems\|next=Physics:Quantum Lindblad equation\|next label=Lindblad equation}}

	<div style="display:flex; gap:24px; align-items:flex-start; max-width:1200px;">		<div style="display:flex; gap:24px; align-items:flex-start; max-width:1200px;">

Maintenance script: Improve Book I intro quality

2026-05-20T09:04:38Z

Improve Book I intro quality

← Older revision		Revision as of 09:04, 20 May 2026
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	{{Short description\|Quantum Collection topic on Quantum Master equation}}		{{Short description\|Quantum Collection topic on Quantum Master equation}}

	{{Quantum book backlink\|Open quantum systems}}		{{Quantum book backlink\|Open quantum systems}}
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	<div style="flex:1; line-height:1.45; color:#006b45; column-count:2; column-gap:32px; column-rule:1px solid #b8d8c8;">		<div style="flex:1; line-height:1.45; color:#006b45; column-count:2; column-gap:32px; column-rule:1px solid #b8d8c8;">
	'''Master equation''' ~~is a Book I topic in the Quantum Collection. The quantum master equation describes the time evolution of the density operator \rho of an open quantum system interacting with an environment. Unlike~~ closed systems, whose dynamics are governed by the Schrödinger equation, open systems exhibit dissipation and decoherence. Master equations provide a framework for studying irreversible processes, quantum noise, and relaxation phenomena~~. The quantum master equation describes the time evolution of the density operator \rho of an open quantum system interacting with an environment~~. Unlike closed systems, whose dynamics are governed by the Schrödinger equation, open systems exhibit dissipation and decoherence. Master equations provide a framework for studying irreversible processes, quantum noise, and relaxation phenomena.		'''Master equation''' unlike closed systems, whose dynamics are governed by the Schrödinger equation, open systems exhibit dissipation and decoherence. Master equations provide a framework for studying irreversible processes, quantum noise, and relaxation phenomena. Unlike closed systems, whose dynamics are governed by the Schrödinger equation, open systems exhibit dissipation and decoherence. Master equations provide a framework for studying irreversible processes, quantum noise, and relaxation phenomena. For a closed system, this reduces to the von Neumann equation: The system state is obtained by tracing out the environment: This leads to effective non-unitary evolution for the system. A common simplification assumes that the environment has no memory, so the dynamics are approximately local in time.
	</div>		</div>

Maintenance script: Clean Book I red links, intro, and image slots

2026-05-20T08:15:56Z

Clean Book I red links, intro, and image slots

← Older revision		Revision as of 08:15, 20 May 2026
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	{{Short description\|Quantum Collection topic on Quantum Master equation}}		{{Short description\|Quantum Collection topic on Quantum Master equation}}

	{{Quantum book backlink\|Open quantum systems}}		{{Quantum book backlink\|Open quantum systems}}
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	<div style="flex:1; line-height:1.45; color:#006b45; column-count:2; column-gap:32px; column-rule:1px solid #b8d8c8;">		<div style="flex:1; line-height:1.45; color:#006b45; column-count:2; column-gap:32px; column-rule:1px solid #b8d8c8;">
	~~The~~ '''~~quantum master~~ equation''' describes the time evolution of the density operator ~~<math>~~\rho~~</math>~~ of an open quantum system interacting with an environment. Unlike closed systems, whose dynamics are governed by the Schrödinger equation, open systems exhibit dissipation and decoherence.~~<ref name="MIT_OCW">{{cite web \|url=https://ocw~~.~~mit.edu/courses/22-51-~~quantum~~-theory-~~of~~-radiation-interactions-fall-2012/resources/mit22_51f12_ch8/ \|title=22~~.~~51 Course Notes~~, ~~Chapter 8: Open Quantum Systems \|website=MIT OpenCourseWare \|access-date=2026-04-12}}</ref>~~		'''Master equation''' is a Book I topic in the Quantum Collection. The quantum master equation describes the time evolution of the density operator \rho of an open quantum system interacting with an environment. Unlike closed systems, whose dynamics are governed by the Schrödinger equation, open systems exhibit dissipation and decoherence. Master equations provide a framework for studying irreversible processes, quantum noise, and relaxation phenomena. The quantum master equation describes the time evolution of the density operator \rho of an open quantum system interacting with an environment. Unlike closed systems, whose dynamics are governed by the Schrödinger equation, open systems exhibit dissipation and decoherence. Master equations provide a framework for studying irreversible processes, quantum noise, and relaxation phenomena.

	Master equations provide a framework for studying irreversible processes, quantum noise, and relaxation phenomena.
	</div>		</div>

Maintenance script: Normalize Book I Quantum page structure

2026-05-19T22:50:09Z

Normalize Book I Quantum page structure

← Older revision		Revision as of 22:50, 19 May 2026
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	{{Author\|Harold Foppele}}		{{Author\|Harold Foppele}}

	{{Sourceattribution\|Quantum Master equation\|1}}		{{Sourceattribution\|Physics:Quantum Master equation\|1}}

Harold: Normalize remaining Quantum body heading levels

2026-05-17T22:11:01Z

Normalize remaining Quantum body heading levels

← Older revision		Revision as of 22:11, 17 May 2026
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	* relaxation time		* relaxation time

	=Non-Markovian dynamics=		== Non-Markovian dynamics ==

	=== Memory effects ===		=== Memory effects ===

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	Appears in strongly coupled and structured environments.<ref name="Breuer2016" />		Appears in strongly coupled and structured environments.<ref name="Breuer2016" />

	=Applications=		== Applications ==

	Used in:		Used in:

← Older revision		Revision as of 11:11, 22 May 2026
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	{{Short description\|Quantum Collection topic on Quantum Master equation}}		{{Short description\|Quantum Collection topic on Quantum Master equation}}

	{{Quantum book backlink\|Open quantum systems}}		{{Quantum book backlink\|Open quantum systems}}
	{{Quantum article nav\|previous=Physics:Quantum Open systems\|previous label=Open systems\|next=Physics:Quantum Lindblad equation\|next label=Lindblad equation}}		{{Quantum article nav\|previous=Physics:Quantum Open systems\|previous label=Open systems\|next=Physics:Quantum Lindblad equation\|next label=Lindblad equation}}