The structure, regulation, and performance of pension funds in nine industrial countries

The author offers an overview of issues relating to the development of funded pension schemes in industrial countries. The analysis applies the economic theory of pension regulation to experience with the structure, regulation, and performance of funds in nine countries - Canada, Denmark, Germany, Japan, Netherlands, Sweden, Switzerland, the United Kingdom, and the United States - seeking to shed light on the finance of old age security in developing countries and the reform of pension funds in industrial countries. The main points of the analysis follow. Pension funds are either defined benefit or defined contribution. The individual bears more risk with defined contribution plans because the pension benefit depends on asset returns. Conceptually, defined benefit funds offer better employee retirement insurance. Private defined benefit pensions are generally available only through companies and typically include some restriction of labor mobility. Because of some shortcomings of fully or largely funded plans, especially for income redistribution, governments have chosen to maintain at least basic levels of pay-as-you-go social security. The scope of such unfunded social security schemes is the key determinant of the scale of private retirement savings. The extent to which pension funds are used as a vehicle for retirement saving depends on the regulatory regime. Tax advantages are the most important incentive, but a wide range of other regulatory choices also make pension funds more or less attractive to firms and employees. And some regulations, such as those affecting the portability of pensions, may have important consequences for economic efficiency. Though countries differ widely in their regulation of pension funds, some suggestions for good practice can still be made. Whether pension funds are a cost effective way of providing pensions depends on the real asset returns that can be attained, in relation to the growth of real wages. Ideally, there should be a gap of 2 to 3 percent between them. Portfolio distributions and fund management are the key determinants of returns to pension funds, subject to the returns available in the market. Prudent diversification in domestic and foreign markets and indexation of much of pension funds'portfolios both appear to be important. Pension funds affect capital markets in many ways. They influence market structure and demand for securities; stimulate innovation, allocative efficiency, and market development; and have a positive effect on overall saving. They may also have some deleterious effects, such as increases in volatility, short termism, and weakening of the control exerted by investors and creditors over firms. Prospects for pension funds in industrial countries vary with the maturity of existing funds and the generosity of social security benefits. In countries such as France, Germany, and Italy, growth in coming decades could be sizable. The key recommendations for countries that are just starting pension funds are for a mix of social security and private funds; for separate funding rather than book reserves; for defined benefit plans, subject to appropriate regulation; and for company-based pension funds.Pensions&Retirement Systems,Insurance&Risk Mitigation,Environmental Economics&Policies,Insurance Law,Banks&Banking Reform

Bosons in anisotropic traps: ground state and vortices

We solve the Gross-Pitaevskii equations for a dilute atomic gas in a magnetic trap, modeled by an anisotropic harmonic potential. We evaluate the wave function and the energy of the Bose Einstein condensate as a function of the particle number, both for positive and negative scattering length. The results for the transverse and vertical size of the cloud of atoms, as well as for the kinetic and potential energy per particle, are compared with the predictions of approximated models. We also compare the aspect ratio of the velocity distribution with first experimental estimates available for $^{87}$Rb. Vortex states are considered and the critical angular velocity for production of vortices is calculated. We show that the presence of vortices significantly increases the stability of the condensate in the case of attractive interactions.Comment: 22 pages, REVTEX, 8 figures available upon request or at http://anubis.science.unitn.it/~dalfovo/papers/papers.htm

Small-amplitude normal modes of a vortex in a trapped Bose-Einstein condensate

We consider a cylindrically symmetric trap containing a small Bose-Einstein condensate with a singly quantized vortex on the axis of symmetry. A time-dependent variational Lagrangian analysis yields the small-amplitude dynamics of the vortex and the condensate, directly determining the equations of motion of the coupled normal modes. As found previously from the Bogoliubov equations, there are two rigid dipole modes and one anomalous mode with a negative frequency when seen in the laboratory frame.Comment: 4 pages, no figures, Revte

Semiclassical Solution of the Quantum Hydrodynamic Equation for Trapped Bose-condensed Gas in the l=0 Case

In this paper the quantum hydrodynamic equation describing the collective, low energy excitations of a dilute atomic Bose gas in a given trapping potential is investigated with the JWKB semiclassical method. In the case of spherically symmetric harmonic confining potential a good agreement is shown between the semiclassical and the exact energy eigenvalues as well as wave functions. It is also demonstrated that for larger quantum numbers the calculation of the semiclassical wave function is numerically more stable than the exact polynomial with large alternating coefficients.Comment: 12 pages, 7 figure

Condensate Heating by Atomic Losses

Atomic Bose-Einstein condensate is heated by atomic losses. Predicted depletion ranges from 1% for a uniform 3D condensate to around 10% for a quasi-1D condensate in a harmonic trap.Comment: 4 pages in RevTex, 1 eps figur

Second-order corrections to mean field evolution for weakly interacting Bosons. I

Inspired by the works of Rodnianski and Schlein and Wu, we derive a new nonlinear Schr\"odinger equation that describes a second-order correction to the usual tensor product (mean-field) approximation for the Hamiltonian evolution of a many-particle system in Bose-Einstein condensation. We show that our new equation, if it has solutions with appropriate smoothness and decay properties, implies a new Fock space estimate. We also show that for an interaction potential $v(x)= \epsilon \chi(x) |x|^{-1}$, where $\epsilon$ is sufficiently small and $\chi \in C_0^{\infty}$, our program can be easily implemented locally in time. We leave global in time issues, more singular potentials and sophisticated estimates for a subsequent part (part II) of this paper

Exciting, Cooling And Vortex Trapping In A Bose-Condensed Gas

A straight forward numerical technique, based on the Gross-Pitaevskii equation, is used to generate a self-consistent description of thermally-excited states of a dilute boson gas. The process of evaporative cooling is then modelled by following the time evolution of the system using the same equation. It is shown that the subsequent rethermalisation of the thermally-excited state produces a cooler coherent condensate. Other results presented show that trapping vortex states with the ground state may be possible in a two-dimensional experimental environment.Comment: 9 pages, 7 figures. It's worth the wait! To be published in Physical Review A, 1st February 199

Quantum Depletion of an Excited Condensate

We analyze greying of the dark soliton in a Bose-Einstein condensate in the limit of weak interaction between atoms. The condensate initially prepared in the excited dark soliton state is loosing atoms because of spontaneous quantum depletion. These atoms are depleted from the soliton state into single particle states with nonzero density in the notch of the soliton. As a result the image of the soliton is losing contrast. This quantum depletion mechanism is efficient even at zero temperature when a thermal cloud is absent.Comment: 4 pages; version to appear in Phys.Rev.A; change in the title plus a number of small changes in the tex

Bose-Einstein condensation with magnetic dipole-dipole forces

Ground-state solutions in a dilute gas interacting via contact and magnetic dipole-dipole forces are investigated. To the best of our knowledge, it is the first example of studies of the Bose-Einstein condensation in a system with realistic long-range interactions. We find that for the magnetic moment of e.g. chromium and a typical value of the scattering length all solutions are stable and only differ in size from condensates without long-range interactions. By lowering the value of the scattering length we find a region of unstable solutions. In the neighborhood of this region the ground state wavefunctions show internal structures not seen before in condensates. Finally, we find an analytic estimate for the characteristic length appearing in these solutions.Comment: final version, 4 pages, 4 figure

Free expansion of Bose-Einstein condensates with quantized vortices

The expansion of Bose-Einstein condensates with quantized vortices is studied by solving numerically the time-dependent Gross-Pitaevskii equation at zero temperature. For a condensate initially trapped in a spherical harmonic potential, we confirm previous results obtained by means of variational methods showing that, after releasing the trap, the vortex core expands faster than the radius of the atomic cloud. This could make the detection of vortices feasible, by observing the depletion of the density along the axis of rotation. We find that this effect is significantly enhanced in the case of anisotropic disc-shaped traps. The results obtained as a function of the anisotropy of the initial configuration are compared with the analytic solution for a noninteracting gas in 3D as well as with the scaling law predicted for an interacting gas in 2D.Comment: 5 pages, 6 postscript figure