We have studied, in a fully non-perturbative calculation, a dilute system of spin 1/2 interacting fermions, characterized by an infinite scattering length at finite temperatures. Various thermodynamic properties and the condensate fraction were calculated and we have also determined the critical temperature for the superfluid-normal phase transition in this regime. The thermodynamic behavior appears as a rather surprising and unexpected mélange of fermionic and bosonic features. The thermal response of a spin 1/2 fermion at the BCS-BEC crossover should be classified as that of a new type of superfluid. The unitary regime is commonly referred to as the situation in which the scattering length a greatly exceeds the average inter-particle separation, thus n|a| 3 ≫ 1, where n is the particle number density [1,2]. It is widely accepted by theorists that at T = 0 these systems are superfluid and that in the unitary regime the coherence length is comparable in magnitude with the average interparticle separation. At T = 0 this problem has been considered by a number of authors [3] and the most accurate results so far have been reported in Refs. [4,5,6]. In 2002 it was shown experimentally that such systems are (meta)stable, and they have been studied extensively experimentally ever since [7,8].The typical theoretical treatment of such systems is based on the idea put forward by Eagles, Leggett and others [9], and used subsequently by most authors [10,11]. The form of the many-body wave function is as in the weak coupling BCS limit and is used for all values of the scattering length a. The particle number projected BCS wave function has the functional formwhere odd subscripts refer to spin-up particles and even subscripts to spin-down particles, A is the antisymmetrization operator, r 12 = |r 1 − r 2 | and φ(r) is either the Cooper pair wave function in the BCS limit, or the two-bound state wave function in the BEC limit. The main difficulty with this approach becomes evident when one tries to use this kind of wave function in the unitary regime, where n|a| 3 ≫ 1. In the extreme BEC limit, this wave function describes a state with all bosons (dimers) at rest, in the condensed state. The fraction of non-condensed bosons (dimers) is known to be small thenwhere n d = n/2 and a dd = 0.6a is the dimer-dimer scattering length [6,12]. When one approaches the unitary regime, the fraction of non-condensed bosons becomes of order one [13], which resembles qualitatively the situation in superfluid 4 He, and then a meanfield description (with or without fluctuations) becomes questionable. In order to calculate the thermal properties of a system of fermions in the unitary regime, we have placed them on a 3D-spatial lattice and used a path integral representation of the partition function. We start fromwhere β = 1/T = N τ τ andÔ is a quantity of interest. T stands for the temperature and µ for the chemical potential, andĤ andN are the Hamiltonian and the particle number operators respectively.Since the system under consideration is di...

We describe the fissioning dynamics of ^{240}Pu from a configuration in the proximity of the outer fission barrier to full scission and the formation of the fragments within an implementation of density functional theory extended to superfluid systems and real-time dynamics. The fission fragments emerge with properties similar to those determined experimentally, while the fission dynamics appears to be quite complex, with many excited shape and pairing modes. The evolution is found to be much slower than previously expected, and the ultimate role of the collective inertia is found to be negligible in this fully nonadiabatic treatment of nuclear dynamics, where all collective degrees of freedom (CDOF) are included (unlike adiabatic treatments with a small number of CDOF).

We introduce a natural and simple way to implement the regularization scheme of the Hartree-Fock-Bogoliubov equations with zero range pairing interaction. The renormalization scheme proves to be equivalent to a simple energy cutoff with a position dependent running coupling constant.

The Quantum Monte Carlo method for spin 1/2 fermions at finite temperature is formulated for dilute systems with an s-wave interaction. The motivation and the formalism are discussed along with descriptions of the algorithm and various numerical issues. We report on results for the energy, entropy and chemical potential as a function of temperature. We give upper bounds on the critical temperature Tc for the onset of superfluidity, obtained by studying the finite size scaling of the condensate fraction. All of these quantities were computed for couplings around the unitary regime in the range −0.5 ≤ (kF a) −1 ≤ 0.2, where a is the s-wave scattering length and kF is the Fermi momentum of a non-interacting gas at the same density. In all cases our data is consistent with normal Fermi gas behavior above a characteristic temperature T0 > Tc, which depends on the coupling and is obtained by studying the deviation of the caloric curve from that of a free Fermi gas. For Tc < T < T0 we find deviations from normal Fermi gas behavior that can be attributed to pairing effects. Low temperature results for the energy and the pairing gap are shown and compared with Green Function Monte Carlo results by other groups.

The first detailed comparison between ab initio calculations of finite fermionic superfluid systems, performed recently by Chang and Bertsch ͓Phys. Rev. A 76, 021603͑R͒ ͑2007͔͒ and by von Stecher, Grange, and Blume ͓e-print arXiv:0705.0671v1͔ and the extension of the density-functional theory superfluid local-density approximation ͑SLDA͒ is presented. It is shown that SLDA reproduces the total energies, number density distributions in inhomogeneous systems along with the energy of the normal state in homogeneous systems. Unlike the Kohn-Sham LDA, in SLDA the effective fermion mass differs from the bare fermion mass and the spectrum of elementary excitations is also reproduced.