2
$\begingroup$

In every discussion of SC and SF that I read (e.g. Simons), the SC Hamiltonian (BCS) has a $\epsilon_k - \mu$ in the kinetic part of the Hamiltonian, while the SF Hamiltonian has just a $\epsilon_k + g$ term, where the $g$ stems from the interaction.

Is there an intuitive reason or is it only tradition?

$\endgroup$
  • 1
    $\begingroup$ It's certainly because the superfluid (SF) is made of bosons, isn't it ? $\endgroup$ – FraSchelle Apr 18 '15 at 11:39
1
$\begingroup$

You are considering a system of fermions (SC hamiltonian) and a system of bosons (weakly interacting BEC). In order for the density to be finite, fermions must have a positive chemical potential $\mu>0$. On the other hand, the chemical potential of a system of bosons is less or equal to the energy of the lowest-energy state. In a non-interacting system this means that $\mu\leq 0$. The condensation occurs exactly when the chemical potential hits the energy of the lowest-energy state from below.

If you consider a Bose-Einstein condensate of weakly interacting particles on the Gross-Pitaevskii equation level (low temperature), you will find that $$\mu = g n,$$ where $g$ is the T-matrix describing the interactions and $n$ is the density of particles. But this is just an artefact of the fact that all the energies are shifted by a mean-field interaction energy, namely, $g n$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.