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- W2032863776 abstract "The members Hω=p2+Vω(x) of ergodic families of random operators, defined in ℋ=L2(Rd), are considered as acting in fibers in a direct integral decomposition of 𝒦=L2(Ω,P(dω);ℋ), (Ω,P) being the underlying probability space. Such a formulation may turn out to be useful in providing a rigorous background for theoretical physical methods employed in treating random systems. As an example a rigorous definition of the mass operator Σ(z) is presented and the formulation of transport equations in a functional analytic setting is briefly indicated. In case there is translational invariance in the probability law the operator H is shown to be unitarily equivalent to an operator Ĥ, which can be decomposed, Ĥ→Ĥ(k), in a way that diagonalizes p. Thus problems about averaged time evolution can be formulated entirely in terms of Ĥ(k) in L2(Ω,P)." @default.
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- W2032863776 date "1994-01-01" @default.
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- W2032863776 title "Random time evolution and direct integrals: Constants of the motion and the mass operator" @default.
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- W2032863776 doi "https://doi.org/10.1063/1.530781" @default.
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