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Register a new userAcoustic attenuation rate in the Fermi-Bose model with a finite-range fermion-fermion interaction
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We study the acoustic attenuation rate in the Fermi-Bose model describing a mixtures of bosonic and fermionic atom gases. We demonstrate the dramatic change of the acoustic attenuation rate as the fermionic component is evolved through the BEC-BCS crossover, in the context of a mean-field model applied to a finite-range fermion-fermion interaction at zero temperature, such as discussed previously by M.M. Parish et al. [Phys. Rev. B 71, 064513 (2005)] and B. Mihaila et al. [Phys. Rev. Lett. 95, 090402 (2005)]. The shape of the acoustic attenuation rate as a function of the boson energy represents a signature for superfluidity in the fermionic component.
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Dilute gas Bose-Einstein condensates (BECs), currently used to cool fermionic atoms in atom traps, can also probe the superfluidity of these fermions. The damping rate of BEC-acoustic excitations (phonon modes), measured in the middle of the trap as a function of the phonon momentum, yields an unambiguous signature of BCS-like superfluidity, provides a measurement of the superfluid gap parameter and gives an estimate of the size of the Cooper-pairs in the BEC-BCS crossover regime. We also predict kinks in the momentum dependence of the damping rate which can reveal detailed information about the fermion quasi-particle dispersion relation.
The fermion sign problem is studied in the path integral formalism. The standard picture of Fermi liquids is first critically analyzed, pointing out some of its rather peculiar properties. The insightful work of Ceperley in constructing fermionic path integrals in terms of constrained world-lines is then reviewed. In this representation, the minus signs associated with Fermi-Dirac statistics are self consistently translated into a geometrical constraint structure (the {em nodal hypersurface}) acting on an effective bosonic dynamics. As an illustrative example we use this formalism to study 1+1-dimensional systems, where statistics are irrelevant, and hence the sign problem can be circumvented. In this low-dimensional example, the structure of the nodal constraints leads to a lucid picture of the entropic interaction essential to one-dimensional physics. Working with the path integral in momentum space, we then show that the Fermi gas can be understood by analogy to a Mott insulator in a harmonic trap. Going back to real space, we discuss the topological properties of the nodal cells, and suggest a new holographic conjecture relating Fermi liquids in higher dimensions to soft-core bosons in one dimension. We also discuss some possible connections between mixed Bose/Fermi systems and supersymmetry.
It is well known that bosons on an optical lattice undergo a second-order superfluid-insulator transition (SIT) when the lattice potential increases. In this paper we study SIT when fermions coexist with the bosons. We find that the critical properties of particle-hole symmetric SIT with dynamical exponent z=1 is modified when fermions are present; it either becomes a fluctuation-driven first order transition or a different second-order transition. On the other hand the more generic particle-hole asymmetric (with z=2) SIT is stable against coupling with fermions. We also discuss pairing interaction between fermions mediated by quantum critical fluctuations near SIT.
We investigate the possibility of spatially homogeneous and inhomogeneous chiral fermion-antifermion condensation and superconducting fermion-fermion pairing in the (1+1)-dimensional model by Chodos {it et al.} [ Phys. Rev. D 61, 045011 (2000)] generalized to continuous chiral invariance. The consideration is performed at nonzero values of temperature $T$, electric charge chemical potential $mu$ and chiral charge chemical potential $mu_5$. It is shown that at $G_1<G_2$, where $G_1$ and $G_2$ are the coupling constants in the fermion-antifermion and fermion-fermion channels, the $(mu,mu_5)$-phase structure of the model is in a one-to-one correspondence with the phase structure at $G_1>G_2$ (called duality correspondence). Under the duality transformation the (inhomogeneous) chiral symmetry breaking (CSB) phase is mapped into the (inhomogeneous) superconducting (SC) phase and vice versa. If $G_1=G_2$, then the phase structure of the model is self-dual. Nevertheless, the degeneracy between the CSB and SC phases is possible in this case only when there is a spatial inhomogeneity of condensates.
We apply the exponential operator method to derive the propagator for a fermion immersed within a rigidly rotating environment with cylindrical geometry. Given that the rotation axis provides a preferred direction, Lorentz symmetry is lost and the general solution is not translationally invariant in the radial coordinate. However, under the approximation that the fermion is completely dragged by the vortical motion, valid for large angular velocities, translation invariance is recovered. The propagator can then be written in momentum space. The result is suited to be used applying ordinary Feynman rules for perturbative calculations in momentum space.
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