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- W1978548059 abstract "We consider the integro-differential equation for the classical trajectory of an oscillator coupled to another one. On the quantum level the elimination of the coordinate A of the “unvisible” oscillator leads to an effective path integral (X, Ξ, μ) for the associated imaginary time stochastic process t ϵ, (-∞,∞) x(t). We prove reflection positivity of the measure dμ ≈ F · dξ, where dξ governes the free oscillator x and F is the counterpart of Feynman's influence functional. Finally, realizing the Hamiltonian semigroup exp(-tH), t ≧ 0, in the physical Hilbert space ℋ = L2(X, Γ, μ), where Γ ⊆ Ξ+, we try to understand what is memory.Uber ein Quantensystem mit GedachtnisWir untersuchen die Integro-Differentialgleichung fur die klassische Trajektorie eines Oszillators, welcher an einen zweiten gekoppelt ist. Was passiert in der Quantenmechanik, wenn man die Koordinate des „unsichtbaren” Oszillators eliminiert? In imaginarer Zeit erhalten wir ein effektives Funktionalintegral (X, Ξ, μ) fur den assoziierten stochastischen Prozes t ϵ (-∞,∞) x(t). Formal gilt dμ ≈ F · dξ. Hierbei beschreibt das Mas dξ die Dynamik des freien Oszillators „x” und F entspricht dem Feynmanschen Einflusfunktional. Wir zeigen, das dμ reflexionspositiv ist und realisieren die Halbgruppe exp(-tH), t ≧ 0, in ℋ = L2(X, Ξ+, μ). Dabei versuchen wir zu verstehen, wie in der Quantentheorie Gedachtnis entsteht." @default.
- W1978548059 created "2016-06-24" @default.
- W1978548059 creator A5063855552 @default.
- W1978548059 date "1989-01-01" @default.
- W1978548059 modified "2023-09-27" @default.
- W1978548059 title "On a Quantum System with Memory" @default.
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- W1978548059 doi "https://doi.org/10.1002/andp.19895010107" @default.
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