We study the system of a dilute gas of fermions in 3-dimensions, with attractive interactions tuned to the unitarity point, using the non-perturbative Restricted Path Integral Monte Carlo (R-PIMC) method. The pairing and superfluid properties of this system are calculated at finite temperature. The total energy at very low temperature from our results agrees closely with that of previous ground-state Quantum Monte Carlo calculations. We identify the temperature T * ≈ 0.70ǫF below which pairing correlations develop, and estimate the critical temperature for the superfluid transition Tc ≈ 0.25ǫF from a finite size scaling analysis of the superfluid density. PACS numbers:The recent experiments, starting with generating a degenerate gas of cold atoms [3], the use of Feshbach resonance to tune the effective interaction between the fermions [4,5], the measurements of the gap to identify a pairing scale [6] and the measurements of vortices [7] to identify the superfluid state, have all given an impetus to the study of superfluidity in the BCS-BEC crossover regime.The nature of superconductivity or superfluidity in a many-particle system with an increasing pairing attraction was shown [1, 2] to interpolate smoothly between the BCS regime for weak attraction between the fermions, and the Bose-Einstein condensation (BEC) regime for strong coupling. In the weak coupling regime, the Cooper pair size is much larger than the interparticle spacing, and the simultaneous pairing and condensation of fermions is well described by the BCS theory. In the strong coupling regime, fermions form strongly bound bosonic molecules at a pairing temperature scale T * that is considerably higher than the BEC temperature T c .In a two species system of fermions with an attractive interaction between them, the unitary point is defined by the divergence of the zero energy s-channel scattering length, a s , for two particles in free space. The unitary point is interesting since it describes a strongly correlated system with universal properties [8]. In general, there are two length scales that define the system: the interparticle spacing ∝ n −1/3 , and the scattering length a s which contains information about the interaction potential. At the unitary point however, since a s diverges, all the properties of the system are described by a single length scale k −1 F or energy scale ǫ F where k F = (3π 2h3 n) 1/3 is the Fermi momentum of the corresponding non-interacting system.At the unitarity point there is no small parameter, therefore well controlled numerical methods are needed to calculate the properties of the system. Here we present the first calculation of the superfluid density and other pairing correlations as a function of temperature at the unitary point in a continuum model of a two component fermion gas with attractive pairwise interaction between the species. Our main results are: (i) an accurate determination of the temperature dependent internal energy which makes it a viable tool for thermometry for cold atoms; (ii) determination o...

We present an overview of the effects of detailed-balance violating perturbations on the universal static and dynamic scaling behavior near a critical point. It is demonstrated that the standard critical dynamics universality classes are generally quite robust: In systems with non-conserved order parameter, detailed balance is effectively restored at criticality. This also holds for models with conserved order parameter, and isotropic non-equilibrium perturbations. Genuinely novel features are found only for models with conserved order parameter and spatially anisotropic noise correlations.PACS numbers: 05.40.+j, 64.60.Ak, 64.60.Ht.One of the major goals in theoretical non-equilibrium physics has been the identification and classification of universality classes for the long-wavelength, long-time scaling behavior both near continuous dynamical phase transitions, and for systems displaying generic scale invariance. Indeed, through investigations of certain specific models, a number of prototypical non-equilibrium universality classes have been identified. A complementary approach is to study the influence of non-equilibrium perturbations on the known universality classes for equilibrium dynamical critical phenomena [5]. Equilibrium critical dynamics is concerned with the relaxational and reversible kinetics near a thermodynamic critical point at temperature T c , as generically described by the Landau-Ginzburg-Wilson (LGW) model for an n-component order parameter vector field S in d space dimensions [6]. In addition to the two independent static critical exponents, e.g. the correlation length exponent ν defined via ξ ∝ |τ | −ν (τ = T − T c ) and Fisher's exponent η for the algebraic decay of the two-point correlation function at criticality (T = T c ),, the order parameter relaxation is governed by a dynamic exponent z that describes critical slowing down: The characteristic time scale diverges as t ch ∝ |τ | −zν upon approaching the transition. This allows for time scale separation and thus a formulation of critical dynamics in terms of non-linear Langevin equations: The relevant 'slow' modes consist of the order parameter and all conserved quantities to which it is statically or dynamically coupled. All remaining 'fast' degrees of freedom are captured through an effective Gaussian white noise. Different values for z ensue depending on whether the order parameter is a conserved quantity or not, and on the additional conserved quantities present. The diffusive relaxation of the latter near criticality can either be characterized by the same exponent z as for the order parameter ('strong' dynamic scaling), or be given by different power laws ('weak' scaling) [5].In order to ensure relaxation towards thermal equilibrium at long times, as given by a Gibbs distribution, one has to carefully implement detailed-balance conditions. In the language of non-linear Langevin equations, these are (i) the Einstein relation between the relaxation constants and the noise strengths, and (ii) the condition that the probability cur...

We investigate the critical dynamics of the n-component relaxational models C and D, which incorporate the coupling of a nonconserved and conserved order parameter S, respectively, to the conserved energy density rho, under nonequilibrium conditions by means of the dynamical renormalization group. Detailed balance violations can be implemented isotropically by allowing for different effective temperatures for the heat baths coupling to the slow modes. In the case of model D with conserved order parameter, the energy density fluctuations can be integrated out, leaving no trace of the nonequilibrium perturbations in the asymptotic regime. For model C with scalar order parameter, in equilibrium governed by strong dynamic scaling (z(S)=z(rho)), we find no genuine nonequilibrium fixed point either. The nonequilibrium critical dynamics of model C with n=1 thus follows the behavior of other systems with nonconserved order parameter wherein detailed balance becomes effectively restored at the phase transition. For n> or =4, the energy density generally decouples from the order parameter. However, for n=2 and n=3, in the weak dynamic scaling regime (z(S)< or =z(rho)) entire lines of genuine nonequilibrium model C fixed points emerge to one-loop order, which are characterized by continuously varying static and dynamic critical exponents. Similarly, the nonequilibrium model C with spatially anisotropic noise and n<4 allows for continuously varying exponents, yet with strong dynamic scaling. Subjecting model D to anisotropic nonequilibrium perturbations leads to genuinely different critical behavior with softening only in subsectors of momentum space and correspondingly anisotropic scaling exponents. Similar to the two-temperature model B (randomly driven diffusive systems) the effective theory at criticality can be cast into an equilibrium model D dynamics, albeit incorporating long-range interactions of the uniaxial dipolar or ferroelastic type.