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0141578053
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note
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A familiar example is a thermal bath: when characterized only by its temperature, one ignores its dynamical response to the system in question.
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35
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0141578052
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note
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A familiar example is given by Zwanzig in his discussion of the projection operator approach: one can write down two differential equations for two interacting subsystems which make up the total system, but if one decides to focus only on one of these subsystems, its dynamics is governed by an integro-differential equation with nonlocal kernels, signifying memory effects. Note that the Markov approximation underlies many common treatments of quantum systems, such as the Fermi Golden Rule, the Wigner-Weisskopf form, the Pauli master equation, to name a few. It clamps down on the dynamical interactions which may result in the violation of the consistency requirement described above, and hence could yield inadequate or erroneous results pertaining to issues of quantum coherence and entanglement in certain circumstances, such as under strong interaction, at low temperature, or for a supra-Ohmic environment.
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