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In many articles I read the term "crossover phenomena" and a lot of methodology discussed according to it, with little or no description about what is meant by it. Sometimes there is a connection to networks, matrices, and then to other structures of elements. Can someone describe the concept of the phenomena?

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I've heard this, or similar terminology, in a broad array of sciences. Can you be more specific about what context you are talking about? –  Colin K Apr 19 '11 at 16:36
Do You read that in physics articles? I know it from nearly any field of science and arts. en.wikipedia.org/wiki/Crossover –  Georg Apr 19 '11 at 16:36

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up vote 3 down vote accepted

"Crossover" is a general term describing a situation when a system can go from being in one phase to being in another phase as a certain parameter is changed.

The best example of a "crossover" phenomenon I can think of is the BEC-BCS crossover which occurs in cold Fermi gases. There one can tune the scattering length $a$ for pairwise interactions to go from being positive to negative. For $a < 0$ bound states can form and we get a BCS state (Bardeen-Cooper-Schrieffer) due to formation of Cooper pairs. As $a$ is tuned to go from being negative to positive the system "crosses over" from being a BCS to a BEC (Bose-Einstein Condensate).

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I've also heard it used in the context of anything that ahs any conceptual similarity to cross-correlation. In the sense that if you correlate two signals, each of which have a double-peak shape, you will get a large central peak, and two "cross-over" peaks on either side in your correlation output. I've seen it used this way to describe absorption lines in saturated absorption spectroscopy as well. –  Colin K Apr 19 '11 at 17:16

It is fashionable jargon, suitable for Humpty-Dumpty:

When I use a word, it means just what I choose it to mean — neither more nor less.

Gluzman and Yukalov describe it as being like a function in an interval where, although the behaviour of the function is qualitatively different in the vicinity of the different boundaries of the interval, the function is continuous and there is no identifiable phase transition point.

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