What quantum mechanical concepts have been used in the "soft" sciences? At the smallest/simplest level (quantum mechanics), our models of physics becomes less deterministic and more probabilistic. This is also (very) generally what occurs in the most complex sciences (psychology, sociology, ecology, atmospheric sciences, ect.), where deterministic models do not predict behavior well. Despite the vast differences between these fields & quantum mechanics, have any quantum mechanical concepts, methods, or models been applied to such hyper-complex "soft" scientific fields?
I assume this would most likely occur in the form of certain statistical techniques or approaches that were developed by physicists and later utilized by scientists in these other fields.
If this is not the case, what fundamental differences prevent such cross application?
 A: Chaos is different from quantum mechanics. Neither is particularly apt to social sciences. Some people have attempted to do so. The result is often little better than "bad poetry."
The usual example of chaos is sometimes referred to as "the butterfly effect." This is the situation where a very small change in the inputs produces a large change in the output. Snooker is an example. A very tiny change in the angle the cue ball hits the target ball will, after some propagation of balls around the table, produce very large changes in motion of the balls. So the black goes in the hole or it does not, due to an extremely tiny change in initial hit of the cue ball.
Quantum mechanics is quite different to this. The initial conditions can be arbitrarily similar (similar enough to produce wave interference) and produce widely different output.  This is because of "wave-particle-duality." Particles do not have values until observed, upon which they produce a specific value. The photon moves through the diffraction grating and comes to some specific place on the photographic film. But the probability pattern builds up after large numbers of photons travel through the system, producing light and dark stripes.
Neither of these is appropriate to describe the situation in social sciences. Consider some such thing as trying to determine the effects of a particular childhood nutrition strategy on some such thing as school performance. At this level, the quantum mechanical effects are negligible. And a minor change in nutrition, say one gram more or less of carbs per year, is not going to produce any distinguishable result.
The situation here is uncertain because of issues far displaced from chaos or quantum. The challenges arise because it is massively difficult to isolate the input factors and determine them.
School performance, for example, could esily be expected to be influenced by many different inputs. Family patterns, income, culture, etc. etc. It would be a chore to even list them all, never mind determine them and extract the effect. Thus, supposing there is an effect due to nutrition, it may be required to extract the effect from the effect of large numbers of other input factors. Each of which may be known to a different degree of accuracy.
This school uses this set of textbooks and that another set. It already begins to be difficult to extract results. This school runs for 7 hours per day and that one 9. This one starts students at age 6 and that at age 5. And so on and so on. This one is in the innner city and that one is far out in rural areas. All of these could easily be expected to have some effect, though in advance it would be difficult to know exactly what.
And it is also massively difficult to be confident in the output factors. It may be that different school systems do things very differently and so performance is a major challenge to extract and compare. This school uses numerical grades and that letter grades is just a trivial example. This school uses standardized state-wide tests, this one uses surprise quizzes, and that one uses interviews of the students. This one does a lot of written work with written tests, and that one does a lot of hands-on work with group presentations. It is a challenge to extract the results and present them in a manner that fairly compares them. Sometimes even for the same school from one year to the next.
And, even when two schools use the same method of evaluating performance, it is not instantly obvious that this method is a good predictor of the academic future of a given student. Written tests, for example, can be well correlated on average. But the individual student is subject to a huge collection of factors that may mean he does not align with the results his tests would suggest.
None of these issues is in any way related to chaos or quantum mechanics. We expect that there is an effect (of nutrition in the example.) And we expect that it won't be chaotic in the sense that small input changes will produce huge output changes. Nor is there any sense in which the system exhibits wave-particle-duality.
These chalenges are related to the questions being about subjects that are not crisply defined, not easily divided into single-factor situations, and not easily presentable in simple numbers.
An additional issue with many social science questions is the difficulty of experimenting on humans. Indeed, such experiments have gigantic ethical hurdles. Suppose that a particular nutrition strategy did improve school performance. Then, to test this, we would have to assign (presumably in a double-blind manner) large numbers of students to follow the strategy, and other students to not follow it. That is, we would need to require children's nutrition to be controlled for experimental purposes. Which, presumably, means that those in the low performance strategy were pushed into low performance by the experiment. It is natural to conclude that such a test would be completely unacceptable ethically, since it will produce this result for every test subject except those lucky enough to be in the best strategy group.
Yet, such tests are required in order to determine the effects of certain things. So it requires volunteers. (Or it may already exist due to cultural norms in different sub-cultures.) And then it is necessary to sort out the effects of the self-sorting volunteers. (Or the additional complicating factors due to the sub-culture doing a variety of other things specific to it.)
To summarize: chaos and quantum mechanics are not the reasons that social sciences have challenges to producing clear answers. They have their own challenges that arise due to the nature of the questions asked and the persons involved.
