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9

Let me make quite clear that the recent experiment does NOT imply the detection of a true magnetic monopole. Somehow, in all the excitement, the word "synthetic" was dropped rather quickly from the phrase "synthetic magnetic field". A synthetic magnetic field is a physical quantity that obeys the same equations as a magnetic field, typically realized in ...


4

After reading this paper, I wracked my brain trying to come up with the perfect analogy. Suffice it to say I failed, so here is my less than ideal answer. The monopole created and referred to in this article is not a true Dirac monopole. It is no more a real monopole than a thermal vacuum testing chamber is outer space. That is, it is an artificially ...


3

Hints to the sought-for formula (16) for $\hat{H}$: Use integration by parts in ${\bf r}$-space to remove derivatives from the Dirac delta distributions, cf. comment by user ACuriousMind. Work on the problem from both ends (15) and (16). Use Leibniz rule $$\tag{*}\nabla^2 (fg)~=~ g\nabla^2 f + f \nabla^2 g+ 2 \nabla f\cdot\nabla g,$$ so that $\nabla$ only ...


3

There are different ways to define this phase. In mean-field (low temperature, weak interaction regime), the many-body wave function $\psi(x_1, x_2,...)=\prod_i \Phi(x_i)$ where $\Phi(x)$ is sometimes called the macroscopic wavefunction (because all the bosons are in the same state described by $\Phi$). In the simplest case (homogeneous system), one can ...


2

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.


2

The defining feature of a Bose condensate is that the one-body density matrix $$ \rho^{(1)}(\mathbf{r},\mathbf{r}^{\prime}) = \langle \Psi^{\dagger}(\mathbf{r})\Psi(\mathbf{r}^{\prime})\rangle,$$ has at least one eigenvalue that is macroscopically large, i.e. it is of order $N$, with $N$ the number of particles in the system. Here, $\Psi(\mathbf{r})$ is ...


2

Your equation (1) describes approximately the centre-of-mass (COM) coordinates of every atom = (some nucleons + some electrons) system. Of course there are many other degrees of freedom that are not taken into account in this description. But those degrees of freedom can always be ignored unless they become correlated with the centre-of-mass coordinates. ...


2

I recently updated the wikipedia article on statistical ensembles which might be relevant. Basically, in classical physics the probability distribution for the state of a system is written as an integral over position and momentum as in your equation. It turns out to be necessary to choose an arbitrary unit of action (energy times time) in order to define ...


1

In principle, it is very simple and straightforward. The problem is to map out the region where the integer filling state is the ground state. Suppose you have $L$ sites. Take $N=L$ particles, find its ground state energy, which is denoted as $E_g(L)$. Note that here the Hamiltonian does not contain the $\mu $ term. Do it again for $N=L+1$, the ground ...


1

It feels like you are going to fast in your way to think. The difference between the chemical potential and the ground state energy is clear : 1.The ground-state energy of your system is here $\epsilon_\textbf{k}=0$ correponding to the ground-state $|\textbf{k=0}\rangle$, which is macroscopically occupied in a BEC (i.e. $N\sim N_0$). 2.The chemical ...


1

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

It is not a monopole, is just an artifact. Note that any addition of dipolar contributions of magnetic field (spin, coils, magnets…) must be dipolar or of a higher order magnetic field, in no case it could be monopolar. It is to say, there is not possible to construct a monopolar field as a superposition of dipolar (or higher order) contributions. The ...


1

You call the condensate 'scalar' when the atoms are spin-0. When instead atoms have a non trivial spin you talk about 'spinor condensates'.


1

In the specific case of slowing light with a Bose-Einstein condensate there will be a limit because the slowing of the light is due to an interaction of the light with the BEC to form a polariton. If you put too much energy in you'll destroy the BEC and it will stop slowing the light. Offhand I don't know what the limit is, but it will be a very small amount ...


1

Bose-Einstein condensation is based on the indistinguishability and wave nature of particles, which are both basic concept of quantum mechanics. If you want to define Bose-Einstein condensation in one sentence, you can say it is the occupation of the lowest quantum state of the external potential by a large fraction of bosons forming the system. Particles ...


1

It depends what you call "one state". With only one species, the Fock state basis is of the form $|n_1,n_2,n_3\rangle$ which gives the number of particle on the sites $1$, $2$, $3$. This is one state of the system (even though it is not a eigenstate). In the case with two species, one can trivially generalize the notation, with a basis ...


1

Never worked with BEC but for ordinary matter it works like this: The incoming field makes the electrons oscillate with the same phase and frequency as the driving field (superposition state). If this state emits radiation before any kind of dephasing (usually takes femto/picoseconds) the outgoing field will be a copy of the incoming field.


1

Feshbach resonance is important to BEC because it allows the adjustment of the interaction between atoms. At low energy regime, the BEC dynamics can be described by the mean field Gross–Pitaevskii equation: $$i \hbar \frac{\partial \psi}{\partial t} = -\frac{\hbar^2}{2m}\nabla^2 \psi + V\psi + \frac{4\pi \hbar^2 a_s}{m}|\psi|^2 \psi \tag{1}$$ The $\psi$ is ...


1

It's been done to some extent by Fujio Shimizu and Jun-ichi Fujita. Also, MIT has a well-known lab dedicated to this type of research headed by Dr. Ketterle .



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