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0

This is just a quick stab, and it might show my ignorance more than anything else. Since you are working with a two, level spin system i'm actually giessting $m,n=\pm\frac{1}{2}$ . You can then explicitly write your density matrix as  \rho\left(t\right)=\begin{pmatrix}\rho_{\frac{1}{2},\frac{1}{2}} & \rho_{-\frac{1}{2},\frac{1}{2}}e^{-i\omega t}e^{-\...

1

The transition is due to the interaction of your small system that you want to experiment on with the environment (including the measurement apparatus). If the interaction is brief and the environment part of the system macroscopic, then what you see is the transition from the initial total wave function $\psi(t_0) = \psi_{\mathrm{in}} = \psi_{\mathrm{in,sys}... 0 If two particles are entangled and then separated, will affecting one of them affect the other? If the state space for particle$i$is$H_i$and$U$is a unitary operator acting on$H_1$, then$U$acts on$H_1\otimes H_2$(that is, the state space of the entangled pair) as$U\otimes 1\$. If affecting one particle affects the other, then how is it not ...

3

By an incoherent state (relatively to a basis, and it must be specified), they simply mean a mixed state described by a diagonal density matrix (in this basis). The word "coherence" refers to the usual thing in the discussion of "decoherence" (indeed, it has no simple relationship with the coherent states of harmonic oscillators). Coherence is the ...

2

The first part of the sentence is right, given some assumptions, the rest is not. The most precise description of every physical system is in terms of a very general superposition of a priori possible states. There is never any collapse. But the rest isn't true. An off-diagonal element of the density matrix doesn't correspond to any single state. It ...

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