Abstract
The formalism developed in Chap. 5 will be used in this chapter to determine the microscopic time evolution of an infinite quantum system from the macroscopic (classical) evolution. It is clear that such an unusual determination of microscopic dynamics is possible for a very special type of interactions only, and it might be highly equivocal. It is shown here that this is the case for a wide class of quantum mean-field theories.
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Notes
- 1.
For some history, general meaning and technical construction of dynamics (given by full and correctly solved microscopic evolutions—without any approximations) of “Quantum mean-field theories” see also [40], and for some of its applications look in [41].
- 2.
Note: For noncompact \(\mathrm{supp}\ E_\mathfrak {g}\), the integral is a limit of integrals over bounded subsets \(B\subset \mathfrak {g}^*\): \(\int \dots := \lim _{B\uparrow \mathfrak {g}^*}\int \omega _m(E_\mathfrak {g}(B)\varvec{f}(F_m))\,\mu _\omega (\mathrm{d}m).\)
- 3.
KMS is for Kubo, Martin and Schwinger.
- 4.
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Bóna, P. (2020). Dynamics of Quantum Mechanical Macroscopic Systems. In: Classical Systems in Quantum Mechanics. Springer, Cham. https://doi.org/10.1007/978-3-030-45070-0_6
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DOI: https://doi.org/10.1007/978-3-030-45070-0_6
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