Physics:Quantum Berry phase - Revision history

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	[[File:Quantum_berry_phase_yellow.png\|~~thumb\|right\|320px~~\|Berry phase as geometric phase accumulated around a closed path.]]		\|text='''Quantum Berry phase''' is a geometric phase acquired by a quantum state when the parameters of a system are changed slowly around a closed path. Unlike an ordinary dynamical phase, which depends on energy and elapsed time, the Berry phase depends on the geometry of the path traced in parameter space.<ref>{{cite web \|url=https://en.wikipedia.org/wiki/Berry_phase \|title=Berry phase \|publisher=Wikipedia \|access-date=20 May 2026}}</ref>

	'''Quantum Berry phase''' is a geometric phase acquired by a quantum state when the parameters of a system are changed slowly around a closed path. Unlike an ordinary dynamical phase, which depends on energy and elapsed time, the Berry phase depends on the geometry of the path traced in parameter space.<ref>{{cite web \|url=https://en.wikipedia.org/wiki/Berry_phase \|title=Berry phase \|publisher=Wikipedia \|access-date=20 May 2026}}</ref>

	The idea was introduced by Michael Berry in 1984 and quickly became a unifying concept across [[Physics:Quantum mechanics\|quantum mechanics]], condensed matter physics, optics, molecular physics, and quantum information. It shows that the history of a quantum state can leave a measurable phase imprint even when the system returns to its original physical configuration.		The idea was introduced by Michael Berry in 1984 and quickly became a unifying concept across [[Physics:Quantum mechanics\|quantum mechanics]], condensed matter physics, optics, molecular physics, and quantum information. It shows that the history of a quantum state can leave a measurable phase imprint even when the system returns to its original physical configuration.
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	== Geometric phase ==		== Geometric phase ==

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	~~<div style="display~~:~~flex; gap:24px; align-items:flex-start; max-width:1280px; clear:both;">~~		[[File:Quantum_berry_phase_yellow.png\|thumb\|right\|320px\|Berry phase as geometric phase accumulated around a closed path.]]
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	'''Quantum Berry phase''' is a geometric phase acquired by a quantum state when the parameters of a system are changed slowly around a closed path. Unlike an ordinary dynamical phase, which depends on energy and elapsed time, the Berry phase depends on the geometry of the path traced in parameter space.<ref>{{cite web \|url=https://en.wikipedia.org/wiki/Berry_phase \|title=Berry phase \|publisher=Wikipedia \|access-date=20 May 2026}}</ref>		'''Quantum Berry phase''' is a geometric phase acquired by a quantum state when the parameters of a system are changed slowly around a closed path. Unlike an ordinary dynamical phase, which depends on energy and elapsed time, the Berry phase depends on the geometry of the path traced in parameter space.<ref>{{cite web \|url=https://en.wikipedia.org/wiki/Berry_phase \|title=Berry phase \|publisher=Wikipedia \|access-date=20 May 2026}}</ref>

	The idea was introduced by Michael Berry in 1984 and quickly became a unifying concept across [[Physics:Quantum mechanics\|quantum mechanics]], condensed matter physics, optics, molecular physics, and quantum information. It shows that the history of a quantum state can leave a measurable phase imprint even when the system returns to its original physical configuration.		The idea was introduced by Michael Berry in 1984 and quickly became a unifying concept across [[Physics:Quantum mechanics\|quantum mechanics]], condensed matter physics, optics, molecular physics, and quantum information. It shows that the history of a quantum state can leave a measurable phase imprint even when the system returns to its original physical configuration.
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	== Geometric phase ==		== Geometric phase ==

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	{{Short description\|Geometric phase acquired by a quantum state during cyclic evolution}}		{{Short description\|Geometric phase acquired by a quantum state during cyclic evolution}}
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	{{Quantum article nav\|previous=Physics:Quantum Adiabatic theorem\|previous label=Adiabatic theorem\|next=Physics:Quantum Aharonov-Bohm effect\|next label=Aharonov-Bohm effect}}		{{Quantum article nav\|previous=Physics:Quantum Adiabatic theorem\|previous label=Adiabatic theorem\|next=Physics:Quantum Aharonov-Bohm effect\|next label=Aharonov-Bohm effect}}

	~~[[File~~:~~Quantum_berry_phase_yellow~~.~~png\|thumb\|280px\|Berry phase as geometric phase accumulated around a closed path.]]~~		<div style="display:flex; gap:24px; align-items:flex-start; max-width:1280px; clear:both;">
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	'''Quantum Berry phase''' is a geometric phase acquired by a quantum state when the parameters of a system are changed slowly around a closed path. Unlike an ordinary dynamical phase, which depends on energy and elapsed time, the Berry phase depends on the geometry of the path traced in parameter space.<ref>{{cite web \|url=https://en.wikipedia.org/wiki/Berry_phase \|title=Berry phase \|publisher=Wikipedia \|access-date=20 May 2026}}</ref>		'''Quantum Berry phase''' is a geometric phase acquired by a quantum state when the parameters of a system are changed slowly around a closed path. Unlike an ordinary dynamical phase, which depends on energy and elapsed time, the Berry phase depends on the geometry of the path traced in parameter space.<ref>{{cite web \|url=https://en.wikipedia.org/wiki/Berry_phase \|title=Berry phase \|publisher=Wikipedia \|access-date=20 May 2026}}</ref>

	The idea was introduced by Michael Berry in 1984 and quickly became a unifying concept across [[Physics:Quantum mechanics\|quantum mechanics]], condensed matter physics, optics, molecular physics, and quantum information. It shows that the history of a quantum state can leave a measurable phase imprint even when the system returns to its original physical configuration.		The idea was introduced by Michael Berry in 1984 and quickly became a unifying concept across [[Physics:Quantum mechanics\|quantum mechanics]], condensed matter physics, optics, molecular physics, and quantum information. It shows that the history of a quantum state can leave a measurable phase imprint even when the system returns to its original physical configuration.
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			[[File:Quantum_berry_phase_yellow.png\|thumb\|360px\|Berry phase as geometric phase accumulated around a closed path.]]
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	== Geometric phase ==		== Geometric phase ==

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			{{Quantum article nav\|previous=Physics:Quantum Adiabatic theorem\|previous label=Adiabatic theorem\|next=Physics:Quantum Aharonov-Bohm effect\|next label=Aharonov-Bohm effect}}

	[[File:Quantum_berry_phase_yellow.png\|thumb\|280px\|Berry phase as geometric phase accumulated around a closed path.]]		[[File:Quantum_berry_phase_yellow.png\|thumb\|280px\|Berry phase as geometric phase accumulated around a closed path.]]

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{{Short description|Geometric phase acquired by a quantum state during cyclic evolution}}
{{Quantum book backlink|Quantum dynamics and evolution}}

[[File:Quantum_berry_phase_yellow.png|thumb|280px|Berry phase as geometric phase accumulated around a closed path.]]

'''Quantum Berry phase''' is a geometric phase acquired by a quantum state when the parameters of a system are changed slowly around a closed path. Unlike an ordinary dynamical phase, which depends on energy and elapsed time, the Berry phase depends on the geometry of the path traced in parameter space.<ref>{{cite web |url=https://en.wikipedia.org/wiki/Berry_phase |title=Berry phase |publisher=Wikipedia |access-date=20 May 2026}}</ref>

The idea was introduced by Michael Berry in 1984 and quickly became a unifying concept across [[Physics:Quantum mechanics|quantum mechanics]], condensed matter physics, optics, molecular physics, and quantum information. It shows that the history of a quantum state can leave a measurable phase imprint even when the system returns to its original physical configuration.

== Geometric phase ==
In an adiabatic cycle, a quantum system remains in an instantaneous eigenstate while its Hamiltonian changes slowly. When the parameters return to their starting values, the state may acquire a phase determined by the curvature of the path in parameter space.

This phase can affect interference experiments and observable quantities. It is therefore not merely a mathematical convention, but part of the measurable structure of quantum evolution.

== Uses ==
Berry phase appears in the Aharonov-Bohm effect, molecular conical intersections, polarization optics, topological phases of matter, and the quantum Hall effect. In modern materials it helps describe band topology and robust edge behavior.

The concept is closely related to gauge structure, parallel transport, and the topology of quantum states.

== See also ==
* [[Physics:Quantum Time evolution]]
* [[Physics:Quantum Adiabatic theorem]]
* [[Physics:Quantum Aharonov-Bohm effect]]
* [[Physics:Quantum Topological phases of matter]]

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

{{Author|Harold Foppele}}

{{Sourceattribution|Physics:Quantum Berry phase|1}}