Recent content by muscaria

It depends on what kind of superfluid you have in mind, but for typical ones which I assume you have in mind (described by the Gross-Pitaevskii equation) you also have space-time symmetry transformations, instead of the field transformations you have already mentioned (U1 gauge symmetry). For...

This is not strictly the case. For instance, the Lagrangian of a charged particle in an EM field takes the form ##L=\frac{1}{2}mv^2+q\textbf{v}\cdot\textbf{A}-q\phi##. I think the point is not about it being related strictly to kinetic and potential energies, but rather simply to the fact that...

There is a classical analogy you can draw. It is an analogy which one shouldn't take too literally, but it still gives some insight. I remember seeing this video series a good while ago and enjoying it (it covers the analogy): I can't remember if it mentions what it happening quantum...

I think what is important is that they are pulse-like (short-lived) impulse fields which "tilt"/bring the spins out of equilibrium. Again I am no specialist in this (so maybe someone else can add to this), but I believe there are a number of different relaxation-type times which can be used to...

Not at all. Just that the OP seemed to be suggesting that the plane could rotate and I was asking him why he thought that may be so - I was trying to get him to appreciate that if the change in time of one field was proportional to the curl of the other, the plane could not rotate. Hence, the...

From the point of view of classical mechanics, any calculations and "necessary discretisation" are imposed by you, independent of how things operate. In other words, you are simply choosing a scale to calculate things - where you effectively have infinite resolution and can zoom in as much as...

In addition to Vanadium's post. Why would the plane rotate though? Note that the change in time of one field (E say) is related to the curl of the other (B) and vice versa.

Fair enough.. Apologies to the OP if that was confusing.

Have you ever heard of Fermat's principle of shortest time? Least action principle?

A Vacuum state is the lowest energy configuration (ground state) of a field. The field is "always" there, so to speak. Light is an excitation of the EM field. Consider the following analogy of a sound wave propagating through a fluid: the lowest energy configuration of the fluid would typically...

Thanks for this! I didn't know the name "front velocity". I guess "velocity of wave propagation" depends on what we mean, right? E.g. If a density perturbation was introduced in a condensate say (through some localised potential), then the velocity of "node creation" would be the front velocity...

Why are you bringing the velocity of light into the picture? The pilot wave is just the wavefunction and evolves in time accordingly (Schrodinger Equation), is this clear?

I am assuming you mean ##y=A_2e^{i(2\pi f t+\Phi)}e^{i\phi}##, right? If so, yes this is correct, you would multiply your original function through by ##\frac{A_2}{A_1}e^{i\phi}##. I am not sure how Matlab deals with complex numbers, but if you are to multiply a complex function by...

Typically, ##\Delta## is not a variation but an ##\textit{actual}## difference, e.g. ##\Delta f= f(x_2)-f(x_1)##. Lagrange introduced a special symbol for the process of variation, which he called ##\delta##. Although variation is an infinitesimal change in a similar manner to the ##d## in...

Energy is defined in general as follows for the case I think you have in mind. We can split the Lagrangian ##L(q,\dot{q})=T(q,\dot{q})-U(q,\dot{q})## into a quadratic part (kinetic) and whatever remains, as $$L=\frac{1}{2}\sum_{ij}c_{ij}\dot{q}_i\dot{q}_j-U(q,\dot{q}).$$ ##U## is the generalised...