Physics:Quantum BBGKY hierarchy - Revision history

WikiHarold: Restore missing Quantum reference definitions

2026-05-24T00:31:02Z

Restore missing Quantum reference definitions

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	Each equation for <math>\rho_s</math> depends on <math>\rho_{s+1}</math>, producing a chain of coupled equations.<ref name="Bonitz"/>		Each equation for <math>\rho_s</math> depends on <math>\rho_{s+1}</math>, producing a chain of coupled equations.<ref name="Bonitz">{{cite book \|last=Bonitz \|first=Michael \|title=Quantum Kinetic Theory \|publisher=Teubner \|year=1998 \|isbn=9783519002540}}</ref>

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

Maintenance script: Normalize quantum page header order

2026-05-22T11:33:49Z

Normalize quantum page header order

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2026-05-22T11:12:07Z

Clean Book label remnants and backlink spacing

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	{{Quantum book backlink\|Statistical mechanics and kinetic theory}}		{{Quantum book backlink\|Statistical mechanics and kinetic theory}}
	{{Quantum article nav\|previous=Physics:Quantum Boltzmann equation\|previous label=Boltzmann equation\|next=Physics:Quantum Relaxation and thermalization\|next label=Relaxation and thermalization}}		{{Quantum article nav\|previous=Physics:Quantum Boltzmann equation\|previous label=Boltzmann equation\|next=Physics:Quantum Relaxation and thermalization\|next label=Relaxation and thermalization}}

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2026-05-22T11:04:20Z

Remove hidden BOM characters and direct Book label after Short description

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	{{Quantum book backlink\|Statistical mechanics and kinetic theory}}		{{Quantum book backlink\|Statistical mechanics and kinetic theory}}

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

2026-05-22T10:49:22Z

Clean Short description prefix and add Book I label

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Maintenance script: Apply Quantum previous-next navigation

2026-05-20T12:26:37Z

Apply Quantum previous-next navigation

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	{{Quantum book backlink\|Statistical mechanics and kinetic theory}}		{{Quantum book backlink\|Statistical mechanics and kinetic theory}}
			{{Quantum article nav\|previous=Physics:Quantum Boltzmann equation\|previous label=Boltzmann equation\|next=Physics:Quantum Relaxation and thermalization\|next label=Relaxation and thermalization}}

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Maintenance script: Improve Book I intro quality

2026-05-20T09:05:26Z

Improve Book I intro quality

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	'''BBGKY hierarchy''' ~~is a Book I topic in the Quantum Collection. Quantum~~ BBGKY hierarchy (Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy) is a system of coupled equations describing the time evolution of reduced density operators in a many-body quantum system. It provides a rigorous connection between the exact quantum Liouville equation and kinetic equations such as the quantum Boltzmann equation. The hierarchy describes how correlations propagate between particles and is fundamental in statistical mechanics and quantum kinetic theory. Quantum BBGKY hierarchy (Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy) is a system of coupled equations describing the time evolution of reduced density operators in a many-body quantum system. It provides a rigorous connection between the exact quantum Liouville equation and kinetic equations such as the quantum Boltzmann equation.		'''BBGKY hierarchy''' quantum BBGKY hierarchy (Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy) is a system of coupled equations describing the time evolution of reduced density operators in a many-body quantum system. It provides a rigorous connection between the exact quantum Liouville equation and kinetic equations such as the quantum Boltzmann equation. The hierarchy describes how correlations propagate between particles and is fundamental in statistical mechanics and quantum kinetic theory. Quantum BBGKY hierarchy (Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy) is a system of coupled equations describing the time evolution of reduced density operators in a many-body quantum system. It provides a rigorous connection between the exact quantum Liouville equation and kinetic equations such as the quantum Boltzmann equation. where the trace is taken over the remaining degrees of freedom.
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Maintenance script: Clean Book I red links, intro, and image slots

2026-05-20T08:17:09Z

Clean Book I red links, intro, and image slots

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	'''~~Quantum~~ BBGKY hierarchy''' (Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy) is a system of coupled equations describing the time evolution of reduced density operators in a many-body quantum system.~~<ref name="Bogoliubov">{{cite book \|last=Bogoliubov \|first=N. N. \|title=Problems of Dynamical Theory in Statistical Physics \|publisher=North-Holland \|year=1962 \|isbn=9780444863881}}</ref>~~ It provides a rigorous connection between the exact ~~[[Physics:Quantum Liouville equation\|~~quantum Liouville equation]] and kinetic equations such as the ~~[[Physics:Quantum Boltzmann equation\|~~quantum Boltzmann equation]].~~<ref name="Bonitz">{{cite book \|last=Bonitz \|first=Michael \|title=Quantum Kinetic Theory \|publisher=Teubner \|year=1998 \|isbn=9783519002540}}</ref>~~		'''BBGKY hierarchy''' is a Book I topic in the Quantum Collection. Quantum BBGKY hierarchy (Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy) is a system of coupled equations describing the time evolution of reduced density operators in a many-body quantum system. It provides a rigorous connection between the exact quantum Liouville equation and kinetic equations such as the quantum Boltzmann equation. The hierarchy describes how correlations propagate between particles and is fundamental in statistical mechanics and quantum kinetic theory. Quantum BBGKY hierarchy (Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy) is a system of coupled equations describing the time evolution of reduced density operators in a many-body quantum system. It provides a rigorous connection between the exact quantum Liouville equation and kinetic equations such as the quantum Boltzmann equation.

	The hierarchy describes how correlations propagate between particles and is fundamental in ~~[[Physics:Statistical mechanics\|~~statistical mechanics]] and ~~[[Physics:Quantum Kinetic theory\|~~quantum kinetic theory]].~~<ref name="Balescu">{{cite book \|last=Balescu \|first=Radu \|title=Statistical Mechanics~~ of ~~Charged Particles \|publisher=Wiley \|year=1963 \|isbn=9780471060161}}</ref>~~
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Maintenance script: Normalize Book I Quantum page structure

2026-05-19T22:50:47Z

Normalize Book I Quantum page structure

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	[[Category:Statistical mechanics]]		[[Category:Statistical mechanics]]

	{{Sourceattribution\|Quantum BBGKY hierarchy\|1}}		{{Author\|Harold Foppele}}

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Harold: Arrange page top as TOC lead image columns

2026-05-17T14:02:30Z

Arrange page top as TOC lead image columns

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 {{Quantum book backlink|Statistical mechanics and kinetic theory}}
 '''Quantum BBGKY hierarchy''' (Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy) is a system of coupled equations describing the time evolution of reduced density operators in a many-body quantum system.<ref name="Bogoliubov">{{cite book |last=Bogoliubov |first=N. N. |title=Problems of Dynamical Theory in Statistical Physics |publisher=North-Holland |year=1962 |isbn=9780444863881}}</ref> It provides a rigorous connection between the exact [[Physics:Quantum Liouville equation|quantum Liouville equation]] and kinetic equations such as the [[Physics:Quantum Boltzmann equation|quantum Boltzmann equation]].<ref name="Bonitz">{{cite book |last=Bonitz |first=Michael |title=Quantum Kinetic Theory |publisher=Teubner |year=1998 |isbn=9783519002540}}</ref>
 The hierarchy describes how correlations propagate between particles and is fundamental in [[Physics:Statistical mechanics|statistical mechanics]] and [[Physics:Quantum Kinetic theory|quantum kinetic theory]].<ref name="Balescu">{{cite book |last=Balescu |first=Radu |title=Statistical Mechanics of Charged Particles |publisher=Wiley |year=1963 |isbn=9780471060161}}</ref>
-[[File:BBGKY hierarchy.jpg|400px|thumb|Schematic representation of the BBGKY hierarchy linking reduced density operators in many-body quantum systems.]]
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 ==Reduced density operators==
 For an <math>N</math>-particle system with density operator <math>\rho_N</math>, the reduced <math>s</math>-particle density operator is defined by