We study a single component Fermi gas near a p -wave resonance with the lowest order constrained variational (LOCV) method. We obtain the energy per particle for the ground state of the single component Fermi gas near a p -wave resonance with the LOCV method. We also calculate the compressibility of the single component Fermi gas near a p -wave resonance and it shows that in the strongly interacting BCS side, the system would lose its stability and collapse. The width of the unstable region is proportional to the Fermi energy which reflects the universality of the dilute Fermi gas. The two p -wave contacts are also obtained and their variation tendencies with the interaction strength are qualitatively in agreement with recent experimental results.We study a single component Fermi gas near a p -wave resonance with the lowest order constrained variational (LOCV) method. We obtain the energy per particle for the ground state of the single component Fermi gas near a p -wave resonance with the LOCV method. We also calculate the compressibility of the single component Fermi gas near a p -wave resonance and it shows that in the strongly interacting BCS side, the system would lose its stability and collapse. The width of the unstable region is proportional to the Fermi energy which reflects the universality of the dilute Fermi gas. The two p -wave contacts are also obtained and their variation tendencies with the interaction strength are qualitatively in agreement with recent experimental results.

arXiv:1710.06581Europhysics Letters (EPL)Jul 2, 20185 citations

Correlation energy of a weakly interacting Fermi gas

Niels Benedikter, Phan Thành Nam, Marcello Porta +2 more

Aug 30, 202123 citations

Three comments on the Fermi gas at unitarity in a harmonic trap

Dam Thanh Son

In this note we consider three issues related to the unitary Fermi gas in a harmonic trap. We present a short proof of a virial theorem, which states that the average energy of a particle system at unitarity in a harmonic trap is twice larger than the average potential energy. The theorem is valid for all systems with no intrinsic scale, at zero or finite temperature. We discuss the odd-even splitting in a unitarity Fermi gas in a harmonic trap. We show that at large number of particles N the odd-even splitting is proportional to N^{1/9}\hbarω, with an undetermined numerical constant. We also show that for odd N the lowest excitation energies are of order N^{-1/3}\hbarω.In this note we consider three issues related to the unitary Fermi gas in a harmonic trap. We present a short proof of a virial theorem, which states that the average energy of a particle system at unitarity in a harmonic trap is twice larger than the average potential energy. The theorem is valid for all systems with no intrinsic scale, at zero or finite temperature. We discuss the odd-even splitting in a unitarity Fermi gas in a harmonic trap. We show that at large number of particles N the odd-even splitting is proportional to N^{1/9}\hbarω, with an undetermined numerical constant. We also show that for odd N the lowest excitation energies are of order N^{-1/3}\hbarω.

arXiv:0707.1851Jul 12, 20074 citations

Thermodynamics of a Strongly-Interacting Fermi Gas

Joseph M. Kinast

APSMay 1, 20052 citations

Imperfect Fermi gas: Kinetic and interaction energies

Arkady A Shanenko

A uniform ground-state three-dimensional Fermi gas with short-range repulsive pairwise interaction is under consideration. Its kinetic and interaction energies are calculated up to the second order of the expansion in the gas parameter. Similar to recent results for an interacting Bose gas, the quantities in question are found to depend on the pairwise interaction through two characteristic lengths: the former, $a$ , is the $s$ -wave scattering length, and the latter, $b$ , is related to $a$ by $b=a\ensuremath{-}m(\ensuremath{\partial}a∕\ensuremath{\partial}m)$, where $m$ stands for the fermion mass. To control the results, we proceed in two independent ways. The first involves the Hellmann-Feynman theorem applied to derive the kinetic and interaction energies from the total-energy expansion in the gas parameter first found by Huang and Yang. The second way operates with in-medium pair wave functions and allows one to calculate the quantities of interest ``from scratch.'' The results of the present investigation, taken together with those of the recent consideration of a dilute Bose gas, make it possible to conclude that the pairwise interaction in a quantum gas has an essential and nontrivial effect on the kinetic energy, which is not the case for a classical many-particle system.A uniform ground-state three-dimensional Fermi gas with short-range repulsive pairwise interaction is under consideration. Its kinetic and interaction energies are calculated up to the second order of the expansion in the gas parameter. Similar to recent results for an interacting Bose gas, the quantities in question are found to depend on the pairwise interaction through two characteristic lengths: the former, $a$, is the $s$-wave scattering length, and the latter, $b$, is related to $a$ by $b=a\ensuremath{-}m(\ensuremath{\partial}a∕\ensuremath{\partial}m)$, where $m$ stands for the fermion mass. To control the results, we proceed in two independent ways. The first involves the Hellmann-Feynman theorem applied to derive the kinetic and interaction energies from the total-energy expansion in the gas parameter first found by Huang and Yang. The second way operates with in-medium pair wave functions and allows one to calculate the quantities of interest ``from scratch.'' The results of the present investigation, taken together with those of the recent consideration of a dilute Bose gas, make it possible to conclude that the pairwise interaction in a quantum gas has an essential and nontrivial effect on the kinetic energy, which is not the case for a classical many-particle system.

arXiv:cond-mat/0401218Physical Review ADec 21, 20040 citations

a

, is the

s

-wave scattering length, and the latter,

b

, is related to

a

by $b=a\ensuremath{-}m(\ensuremath{\partial}a∕\ensuremath{\partial}m)$, where

m

stands for the fermion mass. To control the results, we proceed in two independent ways. The first involves the Hellmann-Feynman theorem applied to derive the kinetic and interaction energies from the total-energy expansion in the gas parameter first found by Huang and Yang. The second way operates with in-medium pair wave functions and allows one to calculate the quantities of interest ``from scratch.'' The results of the present investigation, taken together with those of the recent consideration of a dilute Bose gas, make it possible to conclude that the pairwise interaction in a quantum gas has an essential and nontrivial effect on the kinetic energy, which is not the case for a classical many-particle system.