We consider a gas of fermions at zero temperature and low density, interacting via a microscopic two body potential which admits a bound state. The particles are confined to a domain with Dirichlet (i.e. zero) boundary conditions. Starting from the microscopic BCS theory, we derive an effective macroscopic Gross-Pitaevskii (GP) theory describing the condensate of fermion pairs. The GP theory also has Dirichlet boundary conditions. Along the way, we prove that the GP energy, defined with Dirichlet boundary conditions on a bounded Lipschitz domain, is continuous under interior and exterior approximations of that domain.We consider a gas of fermions at zero temperature and low density, interacting via a microscopic two body potential which admits a bound state. The particles are confined to a domain with Dirichlet (i.e. zero) boundary conditions. Starting from the microscopic BCS theory, we derive an effective macroscopic Gross-Pitaevskii (GP) theory describing the condensate of fermion pairs. The GP theory also has Dirichlet boundary conditions. Along the way, we prove that the GP energy, defined with Dirichlet boundary conditions on a bounded Lipschitz domain, is continuous under interior and exterior approximations of that domain.

arXiv:1608.01088Aug 3, 20160 citations

Pair condensation and bound states in fermionic systems

Armen Sedrakian, J. W. Clark

We study the finite temperature-density phase diagram of an attractive fermionic system that supports two-body (dimer) and three-body (trimer) bound states in free space. Using interactions characteristic for nuclear systems, we obtain the critical temperature ${T}_{c2}$ for the superfluid phase transition and the limiting temperature ${T}_{c3}$ for the extinction of trimers. The phase diagram features a Cooper-pair condensate in the high-density, low-temperature domain which, with decreasing density, crosses over to a Bose condensate of strongly bound dimers. The high-temperature, low-density domain is populated by trimers whose binding energy decreases toward the density-temperature domain occupied by the superfluid and vanishes at a critical temperature ${T}_{c3}>{T}_{c2}$ .We study the finite temperature-density phase diagram of an attractive fermionic system that supports two-body (dimer) and three-body (trimer) bound states in free space. Using interactions characteristic for nuclear systems, we obtain the critical temperature ${T}_{c2}$ for the superfluid phase transition and the limiting temperature ${T}_{c3}$ for the extinction of trimers. The phase diagram features a Cooper-pair condensate in the high-density, low-temperature domain which, with decreasing density, crosses over to a Bose condensate of strongly bound dimers. The high-temperature, low-density domain is populated by trimers whose binding energy decreases toward the density-temperature domain occupied by the superfluid and vanishes at a critical temperature ${T}_{c3}>{T}_{c2}$.

arXiv:nucl-th/0511076Physical Review CMar 16, 200639 citations

Fermion Condensation in Finite Systems

M. Ya. Amusia, Konstantin G. Popov, Vasily R. Shaginyan +1 more

Springer series in solid-state sciencesOct 25, 20141 citation

Quartet condensation of fermions

Aseem Talukdar

Bulletin of the American Physical SocietyMar 15, 20061 citation

{T}_{c2}

for the superfluid phase transition and the limiting temperature

{T}_{c3}

for the extinction of trimers. The phase diagram features a Cooper-pair condensate in the high-density, low-temperature domain which, with decreasing density, crosses over to a Bose condensate of strongly bound dimers. The high-temperature, low-density domain is populated by trimers whose binding energy decreases toward the density-temperature domain occupied by the superfluid and vanishes at a critical temperature

{T}_{c3}>{T}_{c2}