In this paper a theoretical study of a possible phase transition in dilute 3 He-He(II) mixtures is presented using the Galitskii-Migdal-Feynman formalism.The effective scattering length is calculated from the Galitskii-Migdal-Feynman T -matrix, which is essentially the effective scattering amplitude dependent on the medium.It is found that at very low 3 He concentrations the s-wave effective scattering length for 3 He-He(II) varies discontinuously from positive to negative values at some critical concentration.This indicates a crossover from a regime with dimers to another with the Cooper pairs.The binding energy of the weakly-bound dimers 3 He2 is computed.The effective p-wave scattering lengths are calculated and compared to the effective s-wave scattering lengths at low and high concentrations.It is found that p-scattering has an important effect on the instability of these mixtures at concentrations x > 1%.Finally, the transport coefficients are computed and compared to the theoretical predictions of Fu and Pethick and the experimental results of König and Pobell.
In this paper a theoretical study of a possible phase transition in dilute 3 He-He(II) mixtures is presented using the Galitskii-Migdal-Feynman formalism.The effective scattering length is calculated from the Galitskii-Migdal-Feynman T -matrix, which is essentially the effective scattering amplitude dependent on the medium.It is found that at very low 3 He concentrations the s-wave effective scattering length for 3 He-He(II) varies discontinuously from positive to negative values at some critical concentration.This indicates a crossover from a regime with dimers to another with the Cooper pairs.The binding energy of the weakly-bound dimers 3 He2 is computed.The effective p-wave scattering lengths are calculated and compared to the effective s-wave scattering lengths at low and high concentrations.It is found that p-scattering has an important effect on the instability of these mixtures at concentrations x > 1%.Finally, the transport coefficients are computed and compared to the theoretical predictions of Fu and Pethick and the experimental results of König and Pobell.
We have studied the ground state properties of two-dimensional 3 He -4 He mixtures at zero temperature. 3 He atoms with opposite spins form loosely bound dimers in free space and in low concentration mixtures with 4 He . The binding energy of the dimer ranges from milli-Kelvins near the saturation density to micro-Kelvins at the solidification density. The radius of such a weakly bound dimer is tens of Ångstöms. We also calculate the phase diagram of the mixture. The maximum solubility of 3 He ≈7% is determined by comparing chemical potentials in the pure and mixed fluids. The upper stability limit of the super-saturated mixture is obtained from the second derivative of the enthalpy. It becomes negative at the concentration 10-15% depending of the pressure, indicating a softening of the concentration-fluctuation mode. We also find an indication of the phase transition from the dimerized to atomic mixture.
In this paper the Galitskii–Migdal–Feynman (GMF) formalism is applied to spin-polarized 3 He–HeII mixtures with special emphasis on the effect of the magnetic field on hole–hole scattering. For comparison purposes, the relative phase shifts for S- and P-waves, in both GMF and Brueckner–Bethe–Goldstone (BBG) formalisms, are calculated and analysed. Also, the corresponding scattering lengths are evaluated. In polarized mixtures, the S-wave pairing decreases because of the flip of one spin in the pair; whereas the magnetic field has no effect on P-wave pairing.
The problem of the evolution from BCS theory with cooperative Cooper pairing to the formation and condensation of composite bosons has attracted considerable attention for the past several decades. It has gained renewed impetus in the mid-eighties with the discovery of the high-Tc superconductors, which have a coherence length comparable to the interparticle spacing. More recently, this subject has spurred a great deal of research activity in connection with experiments involving dilute atomic gases of fermionic atoms. The initial objective of this work will be to use functional integral techniques to analyze the low-temperature BCS-to-BEC evolution of d-wave superconductors within the saddle point (mean field) approximation for a continuum model. Then, the same mathematical formalism will be applied to the problem of the BCS-to-BEC evolution of fully spin-polarized p-wave Fermi gases in two dimensions. We find that a quantum phase transition occurs for both systems as they are driven from the BCS-like regime of weakly interacting fermionic pairs to the opposite BEC-like regime of strongly interacting bosonic molecules. This is in contrast to the smooth crossover predicted and observed in systems that exhibit s-wave pairing symmetry. We calculate several spectroscopic and thermodynamic properties that signal the occurrence of this phase transition, and suggest some possible experimental realizations. Finally, fluctuations about the saddle point solution are included in the calculations, and the effects of such correction are analyzed in the low (T~0) and high (T~Tc) temperature limits. We conclude that, at high temperatures, the bosonic degrees of freedom that arise from two-particle bound states become essential to describe the strong coupling limit,\nas the saddle point approximation alone becomes unreliable.
We consider dimerization of 3He in a dilute solution of 3He in superfluid 4He filling straight narrow channels that can be found in nanoscale porous media. Dimer formation is facilitated by the restricted geometry and occurs despite the fact that in bulk fluid the interparticle interaction is too weak to lead to a bound state. Dimerization results in the effective ``bosonization'' of the system: a Bose quantum fluid of (3He)2 arises in place of the 3He Fermi component. At high temperatures, when the 3He impurity quasiparticles form a Maxwell-Boltzmann gas, a drastic change in the thermodynamics occurs due to the presence of dimers. The specific heat and magnetic susceptibility of the 3He component, which we calculate at arbitrary degrees of dimerization, show a marked deviation from behavior expected of an undimerized 3He component. We show that the binding energy---which depends on the channel width---is expected to be sufficiently high to make experimental observation feasible. The presence of (3He)2 dimers gives rise to an extra absorption mechanism for first sound propagating through the superfluid 4He, due to resonant absorption and decay of dimers in the acoustic field. We have calculated the absorption coefficient. Several experiments suggest themselves, utilizing, perhaps, K-L zeolites or carbon nanotubes. If the dimers themselves turn out to be attractive, then quadrumers may appear: it may even be the case that a single 3He polymer will form over the entire length of the channel.
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 Tc. 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, as, 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 as which contains information about the interaction potential. At the unitary point however, since as diverges, all the properties of the system are described by a single length scale k −1
Abstract The thermophysical properties of spin-polarized atomic tritum (T↓) are calculated in the temperature range 0.01 K–10 K using the Galitskii–Migdal–Feynman (GMF) formalism. The calculations are performed using Silvera and Born–Oppenheimer triplet-state potentials. It is concluded that T↓ may form a liquid at very low temperatures. At low T , the effective s-wave scattering length a 0 < 0, which corresponds to a very weak attractive interaction. There is no bound state for the T↓ dimer, but the negative a 0 indicates that it is only slightly short of binding. The transport properties of T↓ increase with increasing temperature. This behavior shows that T↓ remains as a gas in this T -range. The transport properties of 3 He and 4 He are included for comparison purposes. The difference in the transport properties of T↓ and 3 He is due to the fact that T↓ atoms obey Bose statistics while 3 He atoms obey Fermi statistics, whereas the difference with the 4 He (Boson) is due to the mass difference between T↓ and 4 He.