Kinetic energy functional for Fermi vapors in spherical harmonic confinement

Two equations are constructed which reflect, for fermions moving independently in a spherical harmonic potential, a differential virial theorem and a relation between the turning points of kinetic energy and particle densities. These equations are used to derive a differential equation for the particle density and a non-local kinetic energy functional.Comment: 8 pages, 2 figure

Collective excitation frequencies of Bosons in a parabolic potential with interparticle harmonic interactions

The fact that the ground-state first-order density matrix for Bosons in a parabolic potential with interparticle harmonic interactions is known in exact form is here exploited to study collective excitations in the weak-coupling regime. Oscillations about the ground-state density are treated analytically by a linearized equation of motion which includes a kinetic energy contribution. We show that the dipole mode has the frequency of the bare trap, in accord with the Kohn theorem, and derive explicit expressions for the frequencies of the higher-multipole modes in terms of a frequency renormalized by the interactions.Comment: 6 pages, no figures, accepted for publication on Physics Letters

The chemical potential for the inhomogeneous electron liquid in terms of its kinetic and potential parts with special consideration of the surface pote ntial step and BCS-BEC crossover

The chemical potential $\mu$ of a many-body system is valuable since it carries fingerprints of phase changes. Here, we summarize results for $\mu$ for a thre e-dimensional electron liquid in terms of average kinetic and potential energie s per particle. The difference between $\mu$ and the energy per particle is fou nd to be exactly the electrostatic potential step at the surface. We also prese nt calculations for an integrable one-dimensional many-body system with delta f unction interactions, exhibiting a BCS-BEC crossover. It is shown that in the B CS regime the chemical potential can be expressed solely in terms of the ground -state energy per particle. A brief discussion is also included of the strong c oupling BEC limit.Comment: 4 pages 3 figure

Proposed lower bound for the shear viscosity to entropy density ratio in some dense liquids

Starting from relativistic quantum field theories, Kovtun et al. (2005) have quite recently proposed a lower bound eta/s >= hbar /(4 pi kB), where eta is the shear viscosity and s the volume density of entropy for dense liquids. If their proposal can eventually be proved, then this would provide key theoretical underpinning to earlier semiempirical proposals on the relation between a transport coefficient eta and a thermodynamic quantity s. Here, we examine largely experimental data on some dense liquids, the insulators nitrogen, water, and ammonia, plus the alkali metals, where the shear viscosity eta(T) for the four heaviest alkalis is known to scale onto an `almost universal' curve, following the work of Tankeshwar and March a decade ago. So far, all known results for both insulating and metallic dense liquids correctly exceed the lower bound prediction of Kovtun et al.Comment: to appear in Phys. Lett.

Molecules in clusters: the case of planar LiBeBCNOF built from a triangular form LiOB and a linear four-center species FBeCN

Krueger some years ago proposed a cluster LiBeBCNOF, now called periodane. His ground-state isomer proposal has recently been refined by Bera et al. using DFT. Here, we take the approach of molecules in such a cluster as starting point. We first study therefore the triangular molecule LiOB by coupled cluster theory (CCSD) and thereby specify accurately its equilibrium geometry in free space. The second fragment we consider is FBeCN, but treated now by restricted Hartree-Fock (RHF) theory. This four-center species is found to be linear, and the bond lengths are obtained from both RHF and CCSD calculations. Finally, we bring these two entities together and find that while LiOB remains largely intact, FBeCN becomes bent by the interaction with LiOB. Hartree-Fock and CCSD theories then predict precisely the same lowest isomer found by Bera et al. solely on the basis of DFT.Comment: to appear in Phys. Lett.

Stretched chemical bonds in Si6H6: A transition from ring currents to localized pi-electrons?

Motivated by solid-state studies on the cleavage force in Si, and the consequent stretching of chemical bonds, we here study bond stretching in the, as yet unsynthesized, free space molecule Si6H6. We address the question as to whether substantial bond stretching (but constrained to uniform scaling on all bonds) can result in a transition from ring current behaviour, characteristic say of benzene at its equilibrium geometry, to localized pi-electrons on Si atoms. Some calculations are also recorded on dissociation into 6 SiH radicals. While the main studies have been carried out by unrestricted Hartree-Fock (HF) theory, the influence of electron correlation has been examined using two forms of density functional theory. Planar Si6H6 treated by HF is bound to be unstable, not all vibrational frequencies being real. Some buckling is then allowed, which results in real frequencies and stability. Evidence is then provided that the non-planar structure, as the Si-Si distance is increased, exhibits pi-electron localization in the range 1.2-1.5 times the equilibrium distance

Similarity and contrasts between thermodynamic properties at the critical point of liquid alkali metals and of electron-hole droplets

The recent experimental study by means of time-resolved luminescence measurements of an electron-hole liquid (EHL) in diamond by Shimano et al. [Phys. Rev. Lett. 88 (2002) 057404] prompts us to compare and contrast critical temperature T_c and critical density n_c relations in liquid alkali metals with those in electron-hole liquids. The conclusion drawn is that these systems have similarities with regard to critical properties. In both cases the critical temperature is related to the cube root of the critical density. The existence of this relation is traced to Coulomb interactions and to systematic trends in the dielectric constant of the electron-hole systems. Finally a brief comparison between the alkalis and EHLs of the critical values for the compressibility ratio Z_c is also given

Temperature dependence of density profiles for a cloud of non-interacting fermions moving inside a harmonic trap in one dimension

We extend to finite temperature a Green's function method that was previously proposed to evaluate ground-state properties of mesoscopic clouds of non-interacting fermions moving under harmonic confinement in one dimension. By calculations of the particle and kinetic energy density profiles we illustrate the role of thermal excitations in smoothing out the quantum shell structure of the cloud and in spreading the particle spill-out from quantum tunnel at the edges. We also discuss the approach of the exact density profiles to the predictions of a semiclassical model often used in the theory of confined atomic gases at finite temperature.Comment: 7 pages, 4 figure

Linear response function around a localized impurity in a superconductor

Imaging the effects of an impurity like Zn in high-Tc superconductors [Nature 61 (2000) 746] has rekindled interest in defect problems in the superconducting phase. This has prompted us here to re-examine the early work of March and Murray [Phys. Rev. 120 (1960) 830] on the linear response function in an initially translationally invariant Fermi gas. In particular, we present corresponding results for a superconductor at zero temperature, both in the s- and in the d-wave case, and mention their direct physical relevance in the case when the impurity potential is highly localized

A non trivial extension of the two-dimensional Ising model: the d-dimensional "molecular" model

A recently proposed molecular model is discussed as a non-trivial extension of the Ising model. For d=2 the two models are shown to be equivalent, while for d>2 the molecular model describes a peculiar second order transition from an isotropic high temperature phase to a low-dimensional anisotropic low temperature state. The general mean field analysis is compared with the results achieved by a variational Migdal-Kadanoff real space renormalization group method and by standard Monte Carlo sampling for d=3. By finite size scaling the critical exponent has been found to be 0.44\pm 0.02 thus establishing that the molecular model does not belong to the universality class of the Ising model for d>2.Comment: 25 pages, 5 figure