How often do particles regain quantum coherence after decoherence? Quantum decoherence is "well known" process. It is simply defined as a loss of quantum coherence. It is often used as a partial explanation for "collapse of the wave funtion" (wave funtion is collapsed because the particle interacts with environment, other particle or "is observed", ... in other words it is loss of information to environment).
Some smart people claim, decoherence is not sufficient cause for wave function to collapse (https://arxiv.org/abs/quant-ph/0112095), so there is most probably something more...
Back to the question. How can particle regain it's wave function? Or more precisely:

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*How can particle regain quantum coherence?

*How often it happens in nature?

*What is the distribution of coherent and decoherent particles in Universe (or on earth) ?

*What is the underpinning mechanism in regaining coherence (in simple math terms)?

*Do we have some experiments that do this?

*Can particle regain coherence "spontaneously"?

PS: Sorry for all questions that are stupid (;
 A: Decoherence is the phenomenon where a superposition of two quantum states becomes an incoherent mixture of those states, because the two states get entangled with the environment differently. That is, we go from the state
$$\left(|\psi_1\rangle + |\psi_2 \rangle \right) |\text{environment} \rangle$$
to the state
$$|\psi_1, \text{environment } 1 \rangle + |\psi_2, \text{environment } 2 \rangle$$
and since the environment states are different, this is functionally equivalent to just having either $|\psi_1 \rangle$ or $|\psi_2 \rangle$ with some probability, but not a superposition of the two. I'm putting this background here because some of your questions just don't make sense:

  
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*What is the distribution of coherent and decoherent particles in Universe (or on earth) ?
  
*Can particle regain coherence "spontaneously"?
  

That doesn't make sense. A particle is not coherent or decoherent, only different pieces of a quantum superposition of states can be coherent or decoherent with respect to each other. 

  
*
  
*How can particle regain quantum coherence?
  
*How often it happens in nature? 
  

Decoherence is a thermodynamic process where the original system gets entangled with the environment, which is assumed to be large and complicated. Having this process spontaneously reverse itself is not impossible, but unlikely in the same sense that having an egg spontaneously uncook itself is.
