Landau levels on a torus

Landau levels have represented a very rich field of research, which has gained widespread attention after their application to quantum Hall effect. In a particular gauge, the holomorphic gauge, they give a physical implementation of Bargmann's Hilbert space of entire functions. They have also been recognized as a natural bridge between Feynman's path integral and Geometric Quantization. We discuss here some mathematical subtleties involved in the formulation of the problem when one tries to study quantum mechanics on a finite strip of sides L_1, L_2 with a uniform magnetic field and periodic boundary conditions. There is an apparent paradox here: infinitesimal translations should be associated to canonical operators [p_x,p_y] \propto i\hslash B, and, at the same time, live in a Landau level of finite dimension B L_1L_2/(hc/e), which is impossible from Wintner's theorem. The paper shows the way out of this conundrum.Comment: 10 pages, two color eps-file

The Publicity of Thought

An influential tradition holds that thoughts are public: different thinkers share many of their thoughts, and the same applies to a single subject at different times. This ‘publicity principle’ has recently come under attack. Arguments by Mark Crimmins, Richard Heck and Brian Loar seem to show that publicity is inconsistent with the widely accepted principle that someone who is ignorant or mistaken about certain identity facts will have distinct thoughts about the relevant object—for instance, the astronomer who does not know that Hesperus is Phosphorus will have two distinct thoughts Hesperus is bright and Phosphorus is bright. In this paper, I argue that publicity can be defended if we adopt a relational account on which thoughts are individuated by their mutual relations. I then go on to develop a specific relational theory—the ‘linking account’—and contrast it with other relational views

Testing Williamson’s theory on transaction-specific governance structures: Evidence from electricity markets

Long term contracts increase the hazard of ex post maladaptation, creating demand for processes that enable adaptation over the course of long-term exchange. Enabling adaptation, however, may diminish the effectiveness of the long-term contracts, designed as prima facie hold-up remedies. Following Joskow (1987), we attempt to empirically capture the positive relationship between physical asset specificity and the duration of long-term contracts between California electricity generators. In addition, following Masten and Crocker (1985), we try to measure the effect of legal provisions on contract duration and interpret them as efficient instruments for providing flexibility in long-term relationships. The more important the investment in relationship-specific assets, the longer the contractual duration. However, parties mitigate long-term contract inflexibility, based on ex ante bargained terms and conditions, with provisions that allow for contingent adaptation. Our empirical results provide support for the hypothesised relationships under different model specifications and alternative estimation techniques.electricity long-term contracts, idiosyncratic relations, asset specificity, efficient adaptation

The Numerical Sausage

The renormalization group equation describing the evolution of the metric of the non linear sigma models poses some nice mathematical problems involving functional analysis, differential geometry and numerical analysis. We describe the techniques which allow a numerical study of the solutions in the case of a two-dimensional target space (deformation of the $O(3)\; \sigma$--model. Our analysis shows that the so-called sausages define an attracting manifold in the U(1) symmetric case, at one-loop level. The paper describes i) the known analytical solutions, ii) the spectral method which realizes the numerical integrator and allows to estimate the spectrum of zero--modes, iii) the solution of variational equations around the solutions, and finally iv) the algorithms which reconstruct the surface as embedded in $R^3$.Comment: 15 pages, uuencoded postscript fil

High energy gravitational scattering: a numerical study

The S-matrix in gravitational high energy scattering is computed from the region of large impact parameters b down to the regime where classical gravitational collapse is expected to occur. By solving the equation of an effective action introduced by Amati, Ciafaloni and Veneziano we find that the perturbative expansion around the leading eikonal result diverges at a critical value signalling the onset of a new regime. We then discuss the main features of our explicitly unitary S-matrix down to the Schwarzschild's radius R=2G s^(1/2), where it diverges at a critical value b ~ 2.22 R of the impact parameter. The nature of the singularity is studied with particular attention to the scaling behaviour of various observables at the transition. The numerical approach is validated by reproducing the known exact solution in the axially symmetric case to high accuracy.Comment: 11 pages, 6 figure

Old master paintings, export veto and price formation: an empirical study

In this paper, we focus on the institutional setting where Old Masters'Paintings (OMP) markets transactions are carried. We develop a preliminary attempt to embody legal provisions in econometric, hedonic pricing models. We consider a particular regulation applicable only in Italy, the "export veto" for art objects that are particularly relevant for the national cultural patrimony. We proxy such legal provision in order to include it in the statistical analysis and to check whether it affects the OMP price differentials between pre-auction estimated price and post-auction hammer price. Preliminary results show that the price differential is affected by the legal variable, therefore suggesting that the country's institutional framework plays an important role in price dynamics

A numerical simulation of pre-big bang cosmology

We analyse numerically the onset of pre-big bang inflation in an inhomogeneous, spherically symmetric Universe. Adding a small dilatonic perturbation to a trivial (Milne) background, we find that suitable regions of space undergo dilaton-driven inflation and quickly become spatially flat ($\Omega \to 1$). Numerical calculations are pushed close enough to the big bang singularity to allow cross checks against previously proposed analytic asymptotic solutions.Comment: 19 pages, revtex, matlab code available at http://www.fis.unipr.it/~onofr