Please help me understand this HO energy in He4 gas

[claymine]

TL;DR

The result of angular frequency deduced from Eq 1.8 is quite confusing to me. Can some one walk me through it please?

Thank you

 

[dRic2]

It seems to me the author used the relation $\omega^2 = \frac k m$ for the frequency of an harmonic oscillator, where -in this case- $k = \phi_p$ and $m = \frac 1 {\rho p^2}$.

 

[claymine]

It seems to me the author used the relation $\omega^2 = \frac k m$ for the frequency of an harmonic oscillator, where -in this case- $k = \phi_p$ and $m = \frac 1 {\rho p^2}$.

No, I don’t think so

 

[dRic2]

Why not ? It looks like the total energy of an HO... BTW I'm sorry but that's the only thing I could think of

 

[claymine]

Why not ? It looks like the total energy of an HO... BTW I'm sorry but that's the only thing I could think of

cuz in his notation (eq1.8) he has rho bar he forgot the divsion symbol. this is a book called qft in stat phys by A. Abrikosov btw. previously he mentioned in low temp He4 energy is proportional to momentum

 

[dRic2]

Sorry, I'm not following. If you compare that equation with $\frac 1 2 m \dot x ^2 + \frac 1 2 k x^2$ it is straightforward to obtain $\omega ^2 = \frac k m$

 

[claymine]

ah you are right my apologies for being pretentious, your way is a pretty elegant solution

 

[claymine]

Sorry, I'm not following. If you compare that equation with $\frac 1 2 m \dot x ^2 + \frac 1 2 k x^2$ it is straightforward to obtain $\omega ^2 = \frac k m$

thank you