# Tag Info

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A fermion is any particle, elementary or composite, that obeys Fermi-Dirac (as opposed to Bose-Einstein) statistics relating to how identical particles behave when you swap two of them. Due to an important but complicated result, this is taken to amount to having half-integer spin. A lepton is one type of elementary particle with spin 1/2. The only leptons ...

11

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.

9

A fermion is any particle characterized by Fermi–Dirac statistics and obeying the Pauli exclusion principle. So for example quarks are fermions, as are Helium-3 atoms. A fermion does not have to be an elementary particle. I'm not even sure that it has to be spin $\tfrac{1}{2}$, though I can't think of any fermions that aren't. A lepton is a spin ...

8

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. ...

8

There are no consequences concerning the quantization of the charge or the existence of real magnetic monopoles. The connection with the monopoles is only formal. What the experimentalists study is the (superfluid) velocity field $v$ and the corresponding vorticity $\Omega=\nabla \times v$ in the gas and the spin orientation of the atoms (the system is ...

7

The superfluid phonons have the linear dispersion $\omega=ck$, and the low-energy effective theory is Lorentz invariant. So the superfluid is an example of emergent Lorentz symmetry. The statement: The velocity of sound in the superfluid is the same for all inertial observers, regardless of their relative motion to the superfluid is valid if the clock and ...

7

Viscosity is necessary in order for the wing to generate lift. Without the change in circulation caused by flow separation from the trailing edge, there will be no lift. In an inviscid fluid there will be no separation, and hence no lift. A similar flow pattern can be observed in viscous fluids when the Reynolds number is extremely low (Re<<1), and you ...

5

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; ...

4

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 ...

4

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 ...

4

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, ...

4

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 ...

4

It's nothing else than Landau's 1941 two-fluid model of superfluids (similar to helium-4) that won him the 1962 Nobel prize in physics. Landau, L. D., The Theory of Superfluidity of Helium II, J. Phys. 5, 71 (1941) At temperatures near absolute zero, the fluids are composed of two components, the normal fluid we know from room temperatures (and whose ...

4

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 ...

4

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 ...

4

The Standard Model includes 12 elementary known as fermions that respect the Pauli exclusion principle. They include six quarks (up, down, charm, strange, top, bottom), and six leptons (electron, electron neutrino, muon, muon neutrino, tau, tau neutrino) (ref) All leptons are fermions, but not all fermions are leptons.

3

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, ...

3

The $L\cdot\Omega$ term comes directly from the change of frame of reference, especially from the transformation from the static frame of reference to the rotating frame of reference. Let $\mathcal{R}\equiv(x,y,z)$ the initial static frame, and $\widetilde{\mathcal{R}}\equiv(x',y',z')$ the rotating frame at a constant velocity ...

3

The fountain is sealed off with a plug that blocks the normal fluid (and lets the superfluid pass). The plug is heated, which is the source of energy that powers the fountain.

3

Superfluids come in several types. The most theoretically accessible case are superfluids that are Bose-Einstein condensates, just like in the case of superconductors. However, the bosons that get condensed in superconductors are Cooper pairs (of electrons). It's the whole atoms, including nuclei (e.g. helium-4), that get Bose-Einstein condensed in the ...

3

You cannot have a total vorticity with periodic boundary conditions, since if you take a path around all of your vortices, it will have a non-zero circulation. But you have periodic bc, so you can continuously deform that path to a point, and a point has zero circulation. Mirror images are not quite the same as in electrostatics. We want periodic boundary ...

3

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. ...

2

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 ...

2

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 ...

2

Both of them are super-interesting to study:-) Superfluid is a low-temperature state of a quantum many-body system of electrically neutral particles (e.g. atoms). Superfluids have some amazing properties. For example, there is no dissipation (i.e. friction) and the flow is irrotational (up to quantum vortices). Theoretically it is described by a macroscopic ...

2

The one-body density matrix is defined by $\rho(r,r')=\langle \hat\psi^\dagger (r) \hat\psi (r')\rangle$. ODLRO is equivalent to say that $\lim_{|r-r'|\to \infty} \rho(r,r') \neq 0$ and in the case of (bosonic) superfluids this corresponds to $\lim_{|r-r'|\to \infty} \rho(r,r')=\langle \hat\psi^\dagger (r) \rangle\langle\hat\psi (r')\rangle$. You can ...

2

A microscopic theory of superfluidity of Helium-4 was developed by Bogoliubov around 1947 (please see a short review and a reference in, e.g., http://www.lptl.jussieu.fr/files/Dupuis09a.pdf (PRL 102, 190401 (2009)). It is a bit difficult to summarize the theory here.

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The Mott transition in the Bose-Hubbard model is a quantum phase transition. From the point of view of field theory, that does not change much compare to standard (finite-temperature) phase transitions. The main difference is that you now have to take into account the quantum fluctuations which correspond to the "imaginary time" direction in addition to the ...

2

Maybe it would be useful to clear up a little bit the all thing : First of all, Bose-Einstein Condensation does not necessarily implies superfluidity: Bose-Einstein condensation (BEC) is characterized by a macroscopic occupation of a many-particle state $\Phi$ which correspond to the product of individual particle groud-states with zero-momentum ...

2

Yes, it will float. Floating is based on buoyancy. Which is not related to surface properties like friction of either the object or the fluid. The pressure causing the force keeping the object to keep floating is the hydrostatic pressure, also unrelated to surface properties; So it's about the pressure gradient you mention in the question. Interestingly, ...

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