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Historically, the terms gas, liquid and (crystalline) solid meant, respectively: weak/no interactions between particles, strong interactions but statistical translation/orientation invariance, and finally breaking of translation/orientation invariance. Applied to more spin systems, a liquid would have translational invariance, but some global order --- i.e. ...

Usually "quantum liquid" refers to the ground state of a Hamiltonian that do not break translation symmetry of the Hamiltonian. (In a sense, "quantum gas" = "quantum liquid".) "Quantum spin liquid" refers to the ground state of a spin Hamiltonian that do not break spin-rotation and translation symmetries of the Hamiltonian.

No. Densities are far too low for liquids to form and survive for more than a tiny fraction of a second. Furthermore, in the interstellar medium, temperatures are too high - in most of the diffuse interstellar medium, the temperature is around 80 K. Even the densest, coldest spots, molecular cores, are not even close to the densities and temperatures needed; ...

Superfluid Helium-4 has a very well studied excitation structure -- at very low momenta, there is a low energy excitation, the phonon, that corresponds to a periodic density fluctuation in the superfluid with well defined wave-number and an energy $E = c \hbar k$ (c being the speed of sound in the superfluid). Though others might quibble with me over ...

I believe the term is "critical velocity". For liquid He-4, the dispersion relation can be found here: Elementary excitations of superfluid 4He The critical velocity is usually the lowest slope which intersects with the dispersion relation, since then at that speed one can create excitations that will damp the motion. Notice that for He-4 in particular, ...

I'd like to add a few things to Spencer Nelson's answer. There are two concepts to which your question might actually be referring, since "no longer obey the standard laws of physics" is vague, and I wanted to clarify. Supercooled fluids- These are fluids that are slowly and gently cooled to below the temperature at which they normally turn to solids. ...

You refer to the Landau criterion for superfluidity (there is a separate question whether this is really the best way to think about superfluids, and whether the Landau criterion is necessary and/or sufficient). In a superfluid the low energy excitations are phonons, the dispersion relation is linear $E_p\sim c p$, and the critical velocity is non-zero. In ...

You can have superfluids that are not BECs and BECs that are not superfluid. Let me quote a text, "Bose-Einstein Condensation in Dilute Gases", Pethick & Smith, 2nd edition (2008), chapter 10: Historically, the connection between superfluidity and the existence of a condensate, a macroscopically occupied quantum state, dates back to Fritz ...

gas = particles are so little packed that they can easily move. liquid = particles are fairly dense packed but can move over long distances. solid = particles are so densely packed that they are confined to small vibrations araound an equilibrium position (site), and larger moves (site changes) are quite rare. In many cases, the sites form a periodic ...

You can gain some intuition from looking at the density distribution function in momentum space which for the $|BCS\rangle$ is given by $n_k=v^{2}_k$. In the BCS limit one finds approximately the filled Fermi sphere, while in the BEC limit $n_k\sim 1/(1+[ka]^2)^2$ which is proportional to the square of the Fourier transform of the dimer wave function. For ...

A superleak is the same as an ordinary leak (namely a hole in a container) but it has a microscopic size. Therefore no regular fluid can escape the container through this hole because its viscosity is too high. A regular fluid will rather just sit over the hole. However, In liquid Helium-II, below the transition temperature (also called the $\lambda$ point, ...

When the superfluid helium leaks out of the container, that's not tunnelling. A few drops of superfluid helium contain many many atoms and for all of them to tunnel through would be extremely improbably as to pretty much not happen. So what makes the helium flow out? If you notice carefully, the container is not a normal glass mug, but it's bottom is made ...

Fermi-Dirac and Bose-Einstein condensates do indeed share many of the striking features of superfluids like liquid helium, though as wikipedia will tell you the concepts overlap but are not identical. My favourite superfluid aspect of atom clouds is the formation of quantized vortices when they are spun: the angular momentum will go into creating many ...

I recently started reading this book: http://www.amazon.com/BCS-BEC-Crossover-Unitary-Lecture-Physics/dp/3642219772 So far I like the organization and pace. But judging by the table of contents it appears to be very detailed and thorough. It is, however, a monograph. But the style is pretty close to a textbook. Plus it has around 150 references at the end ...

Because water is liquid at much too high a temperature. Helium is only superfluid near absolute zero. To have a superfluid, you need the quantum wavelength of the atoms given the environmental decoherence to be longer than the separation between the atoms, so they can coherently come together.