Gravitational self-localization for spherical masses

In this work, I consider the center-of-mass wave function for a homogenous sphere under the influence of the self-interaction due to Newtonian gravity. I solve for the ground state numerically and calculate the average radius as a measure of its size. For small masses, M≲10−17 kg, the radial size is independent of density, and the ground state extends beyond the extent of the sphere. For masses larger than this, the ground state is contained within the sphere and to a good approximation given by the solution for an effective radial harmonic-oscillator potential. This work thus determines the limits of applicability of the point-mass Newton Schrödinger equations for spherical masses. In addition, I calculate the fringe visibility for matter-wave interferometry and find that in the low-mass case, interferometry can in principle be performed, whereas for the latter case, it becomes impossible. Based on this, I discuss this transition as a possible boundary for the quantum-classical crossover, independent of the usually evoked environmental decoherence. The two regimes meet at sphere sizes R≈10−7 m, and the density of the material causes only minor variations in this value.

Essays on firm dynamics in the Swedish wholesale trade sector

This thesis consists of a summary and five self-contained papers addressing dynamics of firms in the Swedish wholesale trade sector. Paper [1] focuses upon determinants of new firm formation in the Swedish wholesale trade sector, using two definitions of firms’ relevant markets, markets defined as administrative areas, and markets based on a cost minimizing behavior of retailers. The paper shows that new entering firms tend to avoid regions with already high concentration of other firms in the same branch of wholesaling, while right-of-the-center local government and quality of the infrastructure have positive impacts upon entry of new firms. The signs of the estimated coefficients remain the same regardless which definition of relevant market is used, while the size of the coefficients is generally higher once relevant markets delineated on the cost-minimizing assumption of retailers are used. Paper [2] analyses determinant of firm relocation, distinguishing between the role of the factors in in-migration municipalities and out-migration municipalities. The results of the analysis indicate that firm-specific factors, such as profits, age and size of the firm are negatively related to the firm’s decision to relocate. Furthermore, firms seems to be avoiding municipalities with already high concentration of firms operating in the same industrial branch of wholesaling and also to be more reluctant to leave municipalities governed by right-of-the- center parties. Lastly, firms seem to avoid moving to municipalities characterized with high population density. Paper [3] addresses determinants of firm growth, adopting OLS and a quantile regression technique. The results of this paper indicate that very little of the firm growth can be explained by the firm-, industry- and region-specific factors, controlled for in the estimated models. Instead, the firm growth seems to be driven by internal characteristics of firms, factors difficult to capture in conventional statistics. This result supports Penrose’s (1959) suggestion that internal resources such as firm culture, brand loyalty, entrepreneurial skills, and so on, are important determinants of firm growth rates. Paper [4] formulates a forecasting model for firm entry into local markets and tests this model using data from the Swedish wholesale industry. The empirical analysis is based on directly estimating the profit function of wholesale firms and identification of low- and high-return local markets. The results indicate that 19 of 30 estimated models have more net entry in high-return municipalities, but the estimated parameters is only statistically significant at conventional level in one of our estimated models, and then with unexpected negative sign. Paper [5] studies effects of firm relocation on firm profits of relocating firms, employing a difference-in-difference propensity score matching. Using propensity score matching, the pre-relocalization differences between relocating and non-relocating firms are balanced, while the difference-in-difference estimator controls for all time-invariant unobserved heterogeneity among firms. The results suggest that firms that relocate increase their profits significantly, in comparison to what the profits would be had the firms not relocated. This effect is estimated to vary between 3 to 11 percentage points, depending on the length of the analyzed period.