We consider 3D and 2D fully (100%) polarized resonance superfluid Fermi-gas with p-wave pairing in the regime of BCS-BEC crossover. For low temperatures T « T cp ( T cp is a p-wave critical temperature) we evaluate the contribution of the superfluid fermionic quasiparticles and bosonic collective waves (phonons) in the specific heat ( C v ) and the normal density (ρ n ) in the BCS-regime for the chemical potential μ > 0, in BEC-regime for μ < 0 and in the interesting intermediate regime for μ → 0. We discuss an experimental possibility to observe a chiral anomaly (which leads to mass-current non-conservation at T = 0) in 3D A1-phase in ballistic regime as well as a topological term with a charge Q = 1 in the 2D fully polarized axial phase in BCS-regime.
We consider 3D and 2D fully (100%) polarized resonance superfluid Fermi-gas with p-wave pairing in the regime of BCS-BEC crossover. For low temperatures T « T cp ( T cp is a p-wave critical temperature) we evaluate the contribution of the superfluid fermionic quasiparticles and bosonic collective waves (phonons) in the specific heat ( C v ) and the normal density (ρ n ) in the BCS-regime for the chemical potential μ > 0, in BEC-regime for μ < 0 and in the interesting intermediate regime for μ → 0. We discuss an experimental possibility to observe a chiral anomaly (which leads to mass-current non-conservation at T = 0) in 3D A1-phase in ballistic regime as well as a topological term with a charge Q = 1 in the 2D fully polarized axial phase in BCS-regime.
The 2D resonant Fermi gas with p -wave pairing is considered n the BCS-BEC regime. For the 2D analog of the superfluid A1 phase, the Leggett equations [1] for superfluid gap Δ and chemical potential μ are analytically solved at T = 0 and the spectrum of the collective excitations (acoustic waves) is analyzed in the BCS regime (μ > 0), where the triplet Cooper pairs emerge; in the BEC regime (μ < 0), where the triplet local pairs (molecules) emerge; and in the transition region, where μ → 0. At low temperatures, the contribution of the superfluid Fermi quasiparticles of the resonant gas to heat capacity C v and the density of normal component ρ n is also calculated. At μ = 0, the fermionic contribution to ρ n and C v are represented as power functions of temperature (ρ n ∼ T 3 and C v ∼ T 2 ). However, similar power contributions to these quantities are related to phonons (bosonic acoustic oscillations). The possibility of the experimental observation of the nontrivial topological term with the charge Q = 1 in the BCS regime of the 2D A1 phase is briefly discussed.
We solve the Leggett equations for BCS-BEC crossover of the resonance p-wave superfluid. We calculate sound velocity, specific heat and the normal density for the BCS domain (μ>0), the BEC domain (μ<0), and for the interesting interpolation point (μ=0) in the 100%-polarized A1 phase in 3D. We are especially interested in the quasiparticle contribution coming from the zeros of the superfluid gap in the A1 phase. We discuss the spectrum of orbital waves and the superfluid hydrodynamics at temperature T→0. In this context we elucidate the difficult problem of the chiral anomaly and mass-current nonconcervation appearing in the BCS domain. We present the different approaches taken to solve this problem. To clarify this problem experimentally we propose an experiment for measurement of the anomalous current in the superfluid A1 phase in the presence of aerogel for He3 and in the presence of Josephson tunneling structures for ultracold gases in magnetic traps.
We solve the Leggett equations for BCS-BEC crossover in the 3D resonance p-wave superfluid with the symmetry of A1-phase. We calculate sound velocity, normal density and specific heat for the BCS-domain (μ>0), BEC-domain (μ<0) as well as close to important point μ=0 in 100% polarized case. We find the indications of quantum phase-transition close to the point μ(T=0)=0. Deep in BCS and BEC-domains the crossover ideas of Leggett and Nozieres, Schmitt-Rink work pretty well. We discuss the spectrum of orbital waves, the paradox of intrinsic angular momentum and complicated problem of chiral anomaly in BCS A1-phase at T=0. We present two different approaches to a chiral anomaly: one based on supersymmetric hydrodynamics, another one on the formal analogy with Dirac equation in quantum electrodynamics (QED theory). We evaluate the damping of nodal fermions due to different decay processes in superclean case at T=0 and find that we are in a ballistic regime ω τ≫1. We propose to use aerogel or nonmagnetic impurities to reach hydrodynamic regime ω τ≪1 at T=0. We discuss the concept of spectral flow and exact cancellations between time-derivatives of anomalous and quasiparticle currents in the equation for the conservation of total linear momentum. We propose to derive and solve a kinetic equation for nodal quasiparticles both in the hydrodynamic and in the ballistic regimes to demonstrate this cancellation explicitly. We briefly discuss the role of the other residual interactions different from damping and invite experimentalists to measure the spectrum and damping of orbital waves in A-phase of 3He at low temperatures.
We solve the Leggett equations for the BCS-BEC crossover in a three dimensional resonance p -wave superfluid with the symmetry of the A 1 phase. We calculate the sound velocity, the normal density, and the specific heat for the BCS domain (μ > 0), for the BEC domain (μ < 0), and close to the important point μ = 0 in the 100% polarized case. We find the indications of a quantum phase transition close to the point μ( T = 0) = 0. Deep in the BCS and BEC domains, the crossover ideas of Leggett, Nozieres, and Schmitt-Rink work quite well. We discuss the spectrum of orbital waves, the paradox of intrinsic angular momentum and the complicated problem of chiral anomaly in the BCS A 1 phase at T = 0. We present two different approaches to the chiral anomaly, based on supersymmetric hydrodynamics and on the formal analogy with the Dirac equation in quantum electrodynamics. We evaluate the damping of nodal fermions due to different decay processes in the superclean case at T = 0 and find that a ballistic regime ωτ ≫ 1 occurs. We propose to use aerogel or nonmagnetic impurities to reach the hydrodynamic regime ωτ ≪ 1 at T = 0. We discuss the concept of the spectral flow and exact cancelations between time derivatives of anomalous and quasiparticle currents in the equation for the total linear momentum conservation. We propose to derive and solve the kinetic equation for the nodal quasiparticles in both the hydrodynamic and ballistic regimes to demonstrate this cancelation explicitly. We briefly discuss the role of the other residual interactions different from damping and invite experimentalists to measure the spectrum and damping of orbital waves in the A phase of 3 He at low temperatures.
This thesis presents theoretical work in s- and p-wave resonantly paired Fermi gases at zero temperature. In the BEC regime of the wide-resonance s-wave BCS-BEC crossover, the chemical potential, speed of sound, condensate depletion, and ground state energy are computed. The quantities are calculated in a low density approximation. The bosonic scattering length is computed diagrammatically to be approximately 0.60a with a the fermionic scattering length, confirming a well-known result. The perturbative approach breaks down in the intermediate BCS-BEC crossover regime which is not investigated. Quantum corrections are computed in the low density expansion, and the mass-imbalanced two-species Fermi gas is investigated. For identical fermions, it is discussed how p-wave Feshbach resonances naturally fall into two classes of "weak" and "strong", depending on the short-distance physics. It is shown how bound fermionic trimers appear in the strongly-resonant superfluid. The appearance of the trimer under the strengthening of the resonance is investigated, and the lifetime of p-wave diatomic molecules due to collisional relaxation into trimers is estimated.