First , we consider strong field index enhancement
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Some strong laws of large numbers for markov chain fields indexed by a special nonhomogeneous tree
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In this paper we have predicted two kinds of new quantum coherence effects . one is the strong - field index enhancement via selective population trapping of dressed states and the other is the preservation of the coherent population trapping ( cpt ) is by quantum interference of incoherent pump processes
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Secondly , definitions of a extended bethe tree , bethe tree and cayley tree are introduced . further , the even - odd markov chain fields and markov chain fields indexed by a extended bethe tree , bethe tree and cayley tree are defined . subsequently the strong limit theorems proved above are applied to the study of all kinds of even - odd markov chain fields and markov chain fields defined above , which both extend the conclusions in [ 30 ] and [ 39 ] and prove a class of strong limit theorems for the even - odd markov chain fields and markov chain fields . as corollaries , we obtain some strong limit theorems for the frequencies of occurrence of states and ordered couples of states for the even - odd markov chain fields and markov chain fields . lastly , some coarse estimates are gained about the state occurrence frequencies for all kinds of even - odd markov chain fields and markov chain fields defined in the paper
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