Kubo–Martin–Schwinger condition

E590893

criterion in quantum field theory criterion in quantum statistical mechanics equilibrium condition mathematical condition in physics

The Kubo–Martin–Schwinger condition is a fundamental criterion in quantum statistical mechanics and quantum field theory that characterizes thermal equilibrium states through specific analyticity and periodicity properties of correlation functions.

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Observed surface forms (1)

Surface form	Occurrences
Kubo–Martin–Schwinger equilibrium condition	1

Statements (48)

Predicate	Object
instanceOf	criterion in quantum field theory ⓘ criterion in quantum statistical mechanics ⓘ equilibrium condition ⓘ mathematical condition in physics ⓘ
alsoKnownAs	KMS condition NERFINISHED ⓘ
appliesTo	C*-algebraic dynamical systems ⓘ algebraic quantum field theory ⓘ quantum field theory ⓘ quantum statistical mechanics ⓘ
assumes	one-parameter automorphism group α_t ⓘ
characterizes	thermal equilibrium states ⓘ
connectedTo	fluctuation–dissipation theorem NERFINISHED ⓘ linear response theory ⓘ
definesPropertyOf	Gibbs equilibrium states ⓘ states on C*-algebras ⓘ
expresses	β-periodicity of correlation functions in imaginary time ⓘ
formalizedBy	C*-algebra theory in the 1960s ⓘ
formalizedIn	operator algebra framework ⓘ
generalizes	classical detailed balance condition ⓘ
hasDomain	equilibrium quantum states ⓘ
hasRange	constraints on correlation functions ⓘ
historicallyIntroducedIn	1950s ⓘ
implies	detailed balance in quantum systems ⓘ time-translation invariance of the state ⓘ
involvesParameter	inverse temperature β ⓘ
mathematicallyExpressedAs	φ(A α_{iβ}(B)) = φ(BA) for all A,B in the algebra ⓘ
namedAfter	Julian Schwinger NERFINISHED ⓘ Paul C. Martin NERFINISHED ⓘ Ryogo Kubo NERFINISHED ⓘ
relatedTo	Gibbs ensemble NERFINISHED ⓘ Matsubara formalism NERFINISHED ⓘ Tomita–Takesaki modular theory NERFINISHED ⓘ canonical ensemble ⓘ imaginary-time formalism ⓘ modular automorphism group ⓘ thermal Green’s functions ⓘ
usedFor	characterizing thermal states in infinite systems ⓘ constructing thermal quantum field theories ⓘ defining equilibrium without Hamiltonian spectrum assumptions ⓘ defining thermal correlation functions ⓘ
usedIn	Hawking radiation analysis ⓘ Unruh effect analysis ⓘ algebraic approach to quantum statistical mechanics ⓘ thermal quantum field theory on curved spacetime ⓘ
usesConcept	analyticity ⓘ correlation functions ⓘ periodicity in imaginary time ⓘ time-translation automorphism group ⓘ

Referenced by (3)

Full triples — surface form annotated when it differs from this entity's canonical label.

Unruh effect → usesConcept → Kubo–Martin–Schwinger condition ⓘ

Ryogo Kubo → knownFor → Kubo–Martin–Schwinger condition ⓘ

Ryogo Kubo → notableConcept → Kubo–Martin–Schwinger condition ⓘ

this entity surface form: Kubo–Martin–Schwinger equilibrium condition