# Tag Info

9

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.

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. ...

5

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 ...

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

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

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

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

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 ...

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

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 ...

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

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, ...

2

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 ...

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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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I will answer your second question because it's the one with which I'm more familiar. The question we're answering is: "Why does current in a superconductor move with no resistance?" To understand this we should first understand why normal metals have nonzero resistivity. Imagine an electron in the metal and suppose it is traveling in some direction. If ...

1

A Google books search for "bulk modulus of liquid helium" turned up this result: Helium, edited by Paul Muljadi. On page 7, you will find the value of the bulk modulus as on the order 50 MPa. There is a reference linked to this value, but it is not part of the free preview, so I cannot tell you what it is.

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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 ...

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That's an interesting question, but I'm not sure whether you would get a similar slowing of gravity waves. Light waves are slowed because their associated electric field polarises the medium it's passing through, and the induced electric dipole interacts with the original light wave. Gravitational waves can't induce a dipole moment, but they can induce a ...

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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 ...

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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 ...

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