Quantum Hydrodynamics

All the talk lately seems to be focused on the Brookhaven RHIC quark-gluon results, which is fine, but not exactly "new", is it? OK then, let's talk a little about the Physics, since yes Virginia, there actually are other fields of study in Physics other than Superstrings, and Jacobson/Verlinde.

So, out near the tip of Long Island (New York State) where the wind is so vicious few choose to live there lies a wonderful collider called the RHIC, which basically makes train wrecks out of gold ions and notes the wonderful results. One of these results is a very brief glimpse of what the early Universe may have looked like right after the (alleged) Big Bang, when the babyverse was so hot that atomic nuclei could not form, and the whole babyverse consisted essentially of a quark-gluon plasma exhibiting thick fluidic properties. A quark-gluon "soup", if you will.


So that's what they do in Brookhaven Lab essentially, they make soup out of gold. :-)


There are several noted websites that go into the details far deeper than here. Plato (the blogger) at his Dialogos of Eide weblog here turned me on to Sean Carroll's explanation of the issue at Cosmic Variance, here, which makes for excellent reading.


All talk of "fluids", be they gas, liquid, or plasma, reminds me of my college Fluid Dynamics courses, which then remind me of that LAST unsolved problem in Newtonian (Classical) Physics, which is Navier-Stokes.


Briefly and from Wiki:

The Navier–Stokes equations dictate not position but rather velocity. A solution of the Navier–Stokes equations is called a velocity field or flow field, which is a description of the velocity of the fluid at a given point in space and time. Once the velocity field is solved for, other quantities of interest (such as flow rate or drag force) may be found. This is different from what one normally sees in classical mechanics, where solutions are typically trajectories of position of a particle or deflection of a continuum. Studying velocity instead of position makes more sense for a fluid, however for visualization purposes one can compute various trajectories.

The Navier–Stokes equations are also of great interest in a purely mathematical sense. Somewhat surprisingly, given their wide range of practical uses, mathematicians have not yet proven that in three dimensions solutions always exist (existence), or that if they do exist, then they do not contain any singularity (or infinity or discontinuity) (smoothness). These are called the Navier–Stokes existence and smoothness problems. The Clay Mathematics Institute has called this one of the seven most important open problems in mathematics and has offered a US$1,000,000 prize (approx. €0.68M or £0.62M as of December 2009^[update]) for a solution or a counter-example^[1].

... and furthermore, since I find myself attracted to all things non-linear, seeing as how we live in a non-linear universe ...

The Navier–Stokes equations are nonlinear partial differential equations in almost every real situation. In some cases, such as one-dimensional flow and Stokes flow (or creeping flow), the equations can be simplified to linear equations. The nonlinearity makes most problems difficult or impossible to solve and is the main contributor to the turbulence that the equations model.

The nonlinearity is due to convective acceleration (due to the change in velocity with position). Hence, any convective flow, whether turbulent or not, will involve nonlinearity, an example of convective but laminar (nonturbulent) flow would be the passage of a viscous fluid (for example, oil) through a small converging nozzle. Such flows, whether exactly solvable or not, can often be thoroughly studied and understood.

Thanks, Wiki. Well, that's all fine and well, but there seems to be a certain lesser known field that may be more suitable, or alternatively suitable, for the problems at hand: Quantum Hydrodynamics. Again, from Wiki:

Quantum hydrodynamics (QHD) is most generally the study of hydrodynamic systems which demonstrate behavior implicit in quantum subsystems (usually quantum tunneling). They arise in semiclassical mechanics in the study of semiconductor devices, in which case being derived from the Wigner-Boltzmann equation. In quantum chemistry they arise as solutions to chemical kinetic systems, in which case they are derived from the Schrodinger equation by way of Bohmian mechanics or Madelung equations.

An important system of study in quantum hydrodynamics is that of superfluidity. Some other topics of interest in quantum hydrodynamics are quantum turbulence, quantized vortices, first, second and third sound, and quantum solvents. The quantum hydrodynamic equation is an equation in Bohmian mechanics, which, it turns out, has a mathematical relationship to classical fluid dynamics (see Madelung equations). This is a rich theoretical field. (emphasis mine)

Some common experimental applications of these studies are in liquid helium (He-3 and He-4), and of the interior of neutron stars and the quark-gluon plasma. Many famous scientists have worked in quantum hydrodynamics, including Richard Feynman, Lev Landau, and Pyotr L. Kapitsa.

References

• Robert Wyatt, Quantum Dynamics with Trajectories: Introduction to Quantum Hydrodynamics (Springer, 2005)

Bohmian mechanics? WTF? (=Why, that's Funny!). I thought papers on Bohmian mechanics were best suited to line the birdcage with! You mean it's in play again?!


Awesome.