Speaker
Description
It was recently shown that the BCS formalism leads to several solutions for the energy gap and the equilibrium quasiparticle distribution (D. V. Anghel, Physica A 464, 74, 2016; ibid. Physica A 2019). While this became quite obvious when the attraction band (which is the single-particle energy interval in which the pairing interaction is manifested) is asymmetric with respect to the chemical potential of the system (that is, the center of the attraction band $\mu$ is different from the chemical potential $\mu_R$), I will show here that there are two solutions, with different energy gaps and quasiparticle populations even when $\mu = \mu_R$. One of the solution leads to the well-known BCS results, with an energy gap denoted here by $\Delta_1(\mu_R-\mu = 0, T)$ (where $T$ is the temperature), whereas the second one leads to an energy gap $\Delta_2(\mu_R-\mu = 0, T) \le \Delta_1(\mu_R-\mu = 0, T)$, for any $T$ below the critical temperature -- the critical temperature is the same for both solutions. In the second solution, the quasiparticle population is different from zero even at $T=0$ and it was shown before (D. V. Anghel, Phyica A, 2019) that $\Delta_2(\mu_R-\mu = 0, T=0) = \Delta_1(\mu_R-\mu = 0, T=0)/3$.
