The Random Phase Approximation for Interacting Fermi Gases in the Mean-Field Regime
Martin Ravn Christiansen, Christian Hainzl, Phan Thành Nam
Abstract
Abstract We present a general approach to justify the random phase approximation for the homogeneous Fermi gas in three dimensions in the mean-field scaling regime. We consider a system of N fermions on a torus, interacting via a two-body repulsive potential proportional to $N^{-\frac {1}{3}}$ . In the limit $N\rightarrow \infty $ , we derive the exact leading order of the correlation energy and the bosonic elementary excitations of the system, which are consistent with the prediction of the random phase approximation in the physics literature.
Topics & Concepts
PhysicsScalingFermionTorusFermi gasRandom phase approximationMean field theoryFermi Gamma-ray Space TelescopeLimit (mathematics)HomogeneousStatistical physicsOrder (exchange)Energy (signal processing)Quantum mechanicsMathematical physicsMathematicsMathematical analysisGeometryElectronEconomicsFinanceCold Atom Physics and Bose-Einstein CondensatesTheoretical and Computational PhysicsQuantum, superfluid, helium dynamics