Reliability of the Ginzburg–Landau Theory in the BCS-BEC Crossover by Including Gaussian Fluctuations for 3D Attractive Fermions

We calculate the parameters of the Ginzburg–Landau (GL) equation of a three-dimensional attractive Fermi gas around the superfluid critical temperature. We compare different levels of approximation throughout the Bardeen–Cooper–Schrieffer (BCS) to the Bose–Einstein Condensate (BEC) regime. We show that the inclusion of Gaussian fluctuations strongly modifies the values of the Ginzburg–Landau parameters approaching the BEC regime of the crossover. We investigate the reliability of the Ginzburg–Landau theory, with fluctuations, studying the behavior of the coherence length and of the critical rotational frequencies throughout the BCS-BEC crossover. The effect of the Gaussian fluctuations gives qualitative correct trends of the considered physical quantities from the BCS regime up to the unitary limit of the BCS-BEC crossover. Approaching the BEC regime, the Ginzburg–Landau equation with the inclusion of Gaussian fluctuations turns out to be unreliable.

Reliability of the Ginzburg–Landau Theory in the BCS-BEC Crossover by Including Gaussian Fluctuations for 3D Attractive Fermions

We calculate the parameters of the Ginzburg–Landau (GL) equation of a three-dimensional attractive Fermi gas around the superfluid critical temperature. We compare different levels of approximation throughout the Bardeen–Cooper–Schrieffer (BCS) to the Bose–Einstein Condensate (BEC) regime. We show that the inclusion of Gaussian fluctuations strongly modifies the values of the Ginzburg–Landau parameters approaching the BEC regime of the crossover. We investigate the reliability of the Ginzburg–Landau theory, with fluctuations, studying the behavior of the coherence length and of the critical rotational frequencies throughout the BCS-BEC crossover. The effect of the Gaussian fluctuations gives qualitative correct trends of the considered physical quantities from the BCS regime up to the unitary limit of the BCS-BEC crossover. Approaching the BEC regime, the Ginzburg–Landau equation with the inclusion of Gaussian fluctuations turns out to be unreliable.

Efimov Physics and Connections to Nuclear Physics

Physical systems characterized by a shallow two-body bound or virtual state are governed at large distances by continuous scale invariance, which is broken into discrete scale invariance when three or more particles come into play. This symmetry induces a universal behavior for different systems that is independent of the details of the underlying interaction and rooted in the smallness of the ratio ℓ[Formula: see text] a B ≪ 1, where the length a B is associated with the binding energy of the two-body system [Formula: see text], and ℓ is the natural length given by the interaction range. Efimov physics refers to this universal behavior, which is often hidden by the onset of system-specific nonuniversal effects. In this review, we identify universal properties by providing an explicit link of physical systems to their unitary limit, in which a B → ∞, and we show that nuclear systems belong to this class of universality. Expected final online publication date for the Annual Review of Nuclear and Particle Science, Volume 71 is September 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Low-Density Neutron Matter and the Unitary Limit

We review the properties of neutron matter in the low-density regime. In particular, we revise its ground state energy and the superfluid neutron pairing gap and analyze their evolution from the weak to the strong coupling regime. The calculations of the energy and the pairing gap are performed, respectively, within the Brueckner–Hartree–Fock (BHF) approach of nuclear matter and the Bardeen–Cooper–Schrieffer (BCS) theory using the chiral nucleon-nucleon interaction of Entem and Machleidt at N3LO and the Argonne V18 phenomenological potential. Results for the energy are also shown for a simple Gaussian potential with a strength and range adjusted to reproduce the 1S0 neutron-neutron scattering length and effective range. Our results are compared with those of quantum Monte Carlo (QMC) calculations for neutron matter and cold atoms. The Tan contact parameter in neutron matter is also calculated, finding a reasonable agreement with experimental data from ultra-cold atoms only at very low densities. We find that low-density neutron matter exhibits a behavior close to that of a Fermi gas at the unitary limit, although, this limit is actually never reached. We also review the properties (energy, effective mass, and quasiparticle residue) of a spin-down neutron impurity immersed in a low-density free Fermi gas of spin-up neutrons already studied by the author in a recent work where it was shown that these properties are very close to those of an attractive Fermi polaron in the unitary limit.

Three-body correlations in nonlinear response of correlated quantum liquid

Understanding the properties of correlated quantum liquids is a fundamental issue of condensed matter physics. Even in such a correlated case, fascinatingly, we can tell that the equilibrium fluctuations of the system govern its linear response to an external field, relying on the fluctuation dissipation relations based on the two-body correlations. Going beyond, up to the three-body correlations, is of importance for van der Waals force [1], the three-body force in nuclei [2], the Efimov state [3, 4], the ring exchange interaction in solid 3He [5, 6], and frustrated spin systems [7]. In our work, we have used a quantum dot in the Kondo regime, which is a controllable realization of such a correlated quantum liquid [8–11]. Thanks to the quality of our sample, where the Kondo effect in the unitary limit was achieved, we could quantitatively measure the three-body correlations and their role in the non-equilibrium regime, in perfect agreement with recent results of the Fermi liquid theory [12– 15]. In particular, we have demonstrated its importance when time-reversal symmetry is broken, solving a long-standing puzzle of the Kondo systems under the magnetic field [13]. The demonstrated method to relate three-body correlation and non-equilibrium transport opens up a way for further investigation of the dynamics of quantum many-body systems.

Low-energy neutron scattering on light nuclei and $^{19}$B as a $^{17}$B-$n$-$n$ three-body system in the unitary limit

We consider the evolution of the neutron-nucleus scattering length for the lightest nuclei. We show that, when increasing the number of neutrons in the target nucleus, the strong Pauli repulsion is weakened and the balance with the attractive nucleon-nucleon interaction results into a resonant virtual state in ^{18}18B. We describe ^{19}19B in terms of a ^{17}17B-nn-nn three-body system where the two-body subsystems ^{17}17B-nn and nn-nn are unbound (virtual) states close to the unitary limit. The energy of ^{19}19B ground state is well reproduced and two low-lying resonances are predicted. Their eventual link with the Efimov physics is discussed. This model can be extended to describe the recently discovered resonant states in ^{20,21}20,21B.