Two-State Systems

The first part of this week's installment of Nelson got me thinking about some of the two-state or two level models which we see in physics...

The first is of course the two-state chemical reaction, where the states are initial and final conformations, as discussed in the text.

Another good one is the double-well system, where we literally have two potential wells that overlap (so there is an unstable equilibrium somewhere between them). The stereocilia that we looked at last week had this property. It turns out that quite a lot of systems have it too.

One class of examples is the artificial double well, used in optical tweezing and atom trapping. The idea is that light is used to create a spatially-dependent potential energy, so that particles are drawn toward the region of maximum intensity (for molecules this occurs if the light is below resonant frequency) or repelled from it (as happens if the light frequency is above resonance). The particles jump from trap to trap because of thermal agitation, or, if cold enough, purely because of quantum tunneling (which makes these systems a little different from their classical cousins). We can see weird effects due to this: periodic transfer of the population between the wells (`Rabi regime'), or if interactions are strong enough we get macroscopic quantum self-trapping, where the population of one well is maintained above that of the other even with no asymmetry of the actual applied potential (the internal interaction potential becomes strongly asymmetric since it depends on the number density squared).

In non-biological systems we tend to see more in the way of extended collections of wells, as in a solid chunk of material. Here the potential is periodic (essentially), which accounts for the conduction and heat capacity properties of some solids.

From a more biophysical standpoint we have the (strongly asymmetric) double wells associated with free energies of things such as protein folding and the dephosphorylation of ATP.

Does anyone have any others to add? I'm sure that there are plenty I have missed!