An efficient method for the Quantum Monte Carlo evaluation of the static density-response function of a many-electron system

In a recent Letter we introduced Hellmann-Feynman operator sampling in diffusion Monte Carlo calculations. Here we derive, by evaluating the second derivative of the total energy, an efficient method for the calculation of the static density-response function of a many-electron system. Our analysis of the effect of the nodes suggests that correlation is described correctly and we find that the effect of the nodes can be dealt with

Two-fluid model for a rotating trapped Fermi gas in the BCS phase

We investigate the dynamical properties of a superfluid gas of trapped fermionic atoms in the BCS phase. As a simple example we consider the reaction of the gas to a slow rotation of the trap. It is shown that the currents generated by the rotation can be understood within a two-fluid model similar to the one used in the theory of superconductors, but with a position dependent ratio of normal and superfluid densities. The rather general result of this paper is that already at very low temperatures, far below the critical one, an important normal-fluid component appears in the outer regions of the gas. This renders the experimental observation of superfluidity effects more difficult and indicates that reliable theoretical predictions concerning other dynamical properties, like the frequencies of collective modes, can only be made by taking into account temperature effects.Comment: 6 pages, 4 figure

Kelvin mode of a vortex in a nonuniform Bose-Einstein condensate

In a uniform fluid, a quantized vortex line with circulation h/M can support long-wavelength helical traveling waves proportional to e^{i(kz-\omega_k t)} with the well-known Kelvin dispersion relation \omega_k \approx (\hbar k^2/2M) \ln(1/|k|\xi), where \xi is the vortex-core radius. This result is extended to include the effect of a nonuniform harmonic trap potential, using a quantum generalization of the Biot-Savart law that determines the local velocity V of each element of the vortex line. The normal-mode eigenfunctions form an orthogonal Sturm-Liouville set. Although the line's curvature dominates the dynamics, the transverse and axial trapping potential also affect the normal modes of a straight vortex on the symmetry axis of an axisymmetric Thomas-Fermi condensate. The leading effect of the nonuniform condensate density is to increase the amplitude along the axis away from the trap center. Near the ends, however, a boundary layer forms to satisfy the natural Sturm-Liouville boundary conditions. For a given applied frequency, the next-order correction renormalizes the local wavenumber k(z) upward near the trap center, and k(z) then increases still more toward the ends.Comment: 9 pages, 1 figur

Neutrino Superfluidity

It is shown that Dirac-type neutrinos display BCS superfluidity for any nonzero mass. The Cooper pairs are formed by attractive scalar Higgs boson exchange between left- and right-handed neutrinos; in the standard SU(2)xU(1) theory, right-handed neutrinos do not couple to any other boson. The value of the gap, the critical temperature, and the Pippard coherence length are calculated for arbitrary values of the neutrino mass and chemical potential. Although such a superfluid could conceivably exist, detecting it would be a major challenge.Comment: This is the version published in PR

Fermionic superfluidity with positive scattering length

Superfluidity in an ultracold Fermi gas is usually associated with either a negative scattering length, or the presence of a two-body bound state. We show that none of these ingredients is necessary to achieve superfluidity. Using a narrow Feshbach resonance with strong repulsive background interactions, the effective interactions can be repulsive for small energies and attractive for energies around the Fermi energy, similar to the effective interactions between electrons in a metallic superconductor. This can result in BCS-type superfluidity while the scattering length is positive.Comment: 6 pages, 3 figures; v2: added references and details energy-dependent interactio

Medical applications of nasa-developed science and technology quarterly progress report no. 2, 30 apr. - 31 jul. 1965

Medical applications of aerospace science and technolog

Quantum logic as superbraids of entangled qubit world lines

Presented is a topological representation of quantum logic that views entangled qubit spacetime histories (or qubit world lines) as a generalized braid, referred to as a superbraid. The crossing of world lines is purely quantum in nature, most conveniently expressed analytically with ladder-operator-based quantum gates. At a crossing, independent world lines can become entangled. Complicated superbraids are systematically reduced by recursively applying novel quantum skein relations. If the superbraid is closed (e.g. representing quantum circuits with closed-loop feedback, quantum lattice gas algorithms, loop or vacuum diagrams in quantum field theory), then one can decompose the resulting superlink into an entangled superposition of classical links. In turn, for each member link, one can compute a link invariant, e.g. the Jones polynomial. Thus, a superlink possesses a unique link invariant expressed as an entangled superposition of classical link invariants.Comment: 4 page

Correlation potentials for molecular bond dissociation within the self-consistent random phase approximation

Self-consistent correlation potentials for H$_2$ and LiH for various inter-atomic separations are obtained within the random phase approximation (RPA) of density functional theory. The RPA correlation potential shows a peak at the bond midpoint, which is an exact feature of the true correlation potential, but lacks another exact feature: the step important to preserve integer charge on the atomic fragments in the dissociation limit. An analysis of the RPA energy functional in terms of fractional charge is given which confirms these observations. We find that the RPA misses the derivative discontinuity at odd integer particle numbers but explicitly eliminates the fractional spin error in the exact-exchange functional. The latter finding explains the accurate total energy in the dissociation limit.Comment: 9 pages, 10 figure

Flow equation approach to the linear response theory of superconductors

We apply the flow equation method for studying the current-current response function of electron systems with the pairing instability. To illustrate the specific scheme in which the flow equation procedure determines the two-particle Green's functions we reproduce the standard response kernel of the BCS superconductor. We next generalize this non-perturbative treatment considering the pairing field fluctuations. Our study indicates that the residual diamagnetic behavior detected above the transition temperature in the cuprate superconductors can originate from the noncondensed preformed pairs.Comment: 12 pages, 4 figure

Competition between final-state and pairing-gap effects in the radio-frequency spectra of ultracold Fermi atoms

The radio-frequency spectra of ultracold Fermi atoms are calculated by including final-state interactions affecting the excited level of the transition, and compared with the experimental data. A competition is revealed between pairing-gap effects which tend to push the oscillator strength toward high frequencies away from threshold, and final-state effects which tend instead to pull the oscillator strength toward threshold. As a result of this competition, the position of the peak of the spectra cannot be simply related to the value of the pairing gap, whose extraction thus requires support from theoretical calculations.Comment: 4 pages, 3 figures, final version published in Phys. Rev. Let