Sunday, February 21, 2010

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) 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


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.

6 comments:

Plato said...

Under the heading of Superfluids I can show where I've been and then the rest is up to you.


MIT physicists create new form of matter by Lori Valigra, Special to MIT News Office June 22, 2005

"In superfluids, as well as in superconductors, particles move in lockstep. They form one big quantum-mechanical wave," explained Ketterle. Such a movement allows superconductors to carry electrical currents without resistance.

To cool it, brings the "same process," as to the condition extended to the QGP? This is the point I am trying to make. If they are aligned?


I mean given the environment what features within it would seem apparent to the nature of viscosity to have it perform certain functions that we might loose energy besides all that has been account for in the LHC?

Plato said...

There is a special class of fluids that are called superfluids. Superfluids have the property that they can flow through narrow channels without viscosity. However, more fundamental than the absence of dissipation is the behavior of superfluids under rotation. In contrast to the example of a glass of water above, the rotation in superfluids is always inhomogeneous (figure). The fluid circulates around quantized vortex lines. The vortex lines are shown as yellow in the figure, and the circulating flow around them is indicated by arrows. There is no vorticity outside of the lines because the velocity near each line is larger than further away. (In mathematical terms curl v = 0, where v(r) is the velocity field.)

Steven Colyer said...

I have identified four fields (so far) where Quantum Mechanics makes itself manifest in the Macroscopic world. Only the first is done at room temperature, although the really exciting stuff in lasers is done at very low temperatures close to absolute zero (which is where the work of the other three is done):

1) Lasers
2) Superconductivity
3) Superfluidity
4) Quantum Hall effect

I'm drawn to that last one, QHE. It's relatively new, so it's cutting edge and exciting, and has so far received 2 Nobel Prizes in Physics.

Superconductivity has won more Nobel Prizes in Physics than any other branch of Physics.

Superstrings Theory, by way of comparison, has won exactly zero.

Plato said...

Hi Steven,

Stefan of Backreaction has some more info on this. Use google search function there as one would not like to "search escape:)" but more info to show this correspondence in thinking.

Did it begin there?:)

Superconductivity, at room temperature is very important as well?:)

Room-temperature superconductivity. It's the holy grail of solid-state physics. A means of conducting electricity without any losses whatsoever at temperatures hundreds of degrees higher than what is required of today's "warm superconductors" - the copper perovskites. So, is this even possible? Can science achieve what seems an unattainably lofty goal?

It is in the elements of super fluidity that a correlation has been drawn by me.

I gave a link for that. As well, the understanding that when you go back to the very beginning of the universe in terms of measure(not just Steven Weinberg's first three minutes), you have to find places that are represented cosmologically as well. Not just recognize them in your experiments. That correlation has to take place or why do you do experiments?

So what feasible means shall you use to go as far back in time that we have just reiterated?

What "building blocks" shall you use?

Some are afraid of where supersymmetry will take them, as they have to go back to the very measure in the microseconds.

Ultimately, where does this exist?

Best,

Steven Colyer said...

What "building blocks" shall you use?

That is the BEST question I have heard asked in a long, long time, and I can't thank you enough for that. Here is my second answer. (my first is I don't know ... so I'm speculating ... just like so many frigging others ... :-) )

What "building blocks" shall you use?

My answer, in a possibly pathetic application of Aristotelian "Logic", is ...

1) Everything "emerges" except the building blocks.

2) ONE building block is unacceptable, because it would not be "acted" upon, so such a Universe would be static, meaning "time" would not emerge. Occam then asks us to look at one number up from "one", that is to say : two building blocks.

3) Each of the then TWO building blocks, based on the simple "law" (if that's what it is) would then NOT be able to be "time-dependent," since "time" will have to emerge from the two building blocks.

4) By process of elimination, all time-dependent "building blocks" will then have to be eliminated. This includes Momentum, momentum-dependent Force, Charge, Spin, and Energy. What is left?

5) Two things are left, as far as I can tell: a specific-quantity Rest Mass, and Geometry.

Rest Mass of a specific quantity, and Geometry, with the conundrum that the specific Rest Mass was greater than the specific Geometry can handle.

And because the Geometry can't handle it, the Geometry has no choice other than to "expand", and from that, everything emerged.

Does that make sense? Maybe not, I can't think of everything.

But only ONE theory of Physics (that I have so far explored), as far as I currently understand them, would have no problem with what I just said. It's not a theory I liked when I first heard of it (indeed, it shocked me), but it's also a theory that, try as I might (and I have tried very hard), I can find no fault with.

The theory is Fecund Universes, by Lee Smolin.

Steven Colyer said...

I have since purchased Wyatt's book and am reading and enjoying it.

I will add the book to the top of the article now. Lots of good stuff ahead in better understanding electrical current, and tons of other stuff.