Bose-Einstein Condensation in Dependence of the Mean Energy Density

The infinite volume limit of the thermodynamic functions of an ideal Bose gas with respect to a grand-canonical equilibrium is taken such that the mean energy density is fixed. Above the critical mean energy density the macroscopically occupied ground state contributes to the mean entropy density while the mean density of the particle number has an infrared divergence. A thermodynamic stability result is derived; for a photon gas it means that, if condensation can be achieved, the condensed state should persist in the presence of a black perturbation

Scalar Potentials for Vector Fields and an Application to Quantum Electrodynamics

For an arbitrary vector field F: xϵR^3 ↦ F(x)ϵR^3, the representation F = ∇Φ + L_ψ + ∇˰L_χ is proved where Φ, ψ, χ are scalar potentials. Using this decomposition in the Maxwell equations disentangles the longitudinal and transversal degrees of freedom of the electromagnetic field. As a result the electromagnetic field can be quantized restriction free

Bose-Einstein Condensation of Free Photons

A grand-canonical description of a photon gas implies Bose-Einstein condensation above Planck’s mean photon number density of black body radiation. For a finite reflecting cavity approximately all excess photons would occupy the Dirichlet ground state thereby forming a monochromatic radio wave

Gender behavior in betting markets

We extend gender research on risk behavior to betting markets. Our data set consists of all 5,136,660 bets in New Zealand from 2006 to 2009 and allows assigning each bet to individ-ual bettors. Women are much more prone to the favorite-longshot bias and suffer higher losses. Usually, betting on longshots is associated with higher variance of return, but we find that bet sizes are disproportionally decreasing in odds. Hence, the average risk when betting on longshots is in fact lower. This observation reconciles our findings with gender research on risk preferences and leads to new insights on the favorite-longshot bias

Collision Detection and Administration Methods for Many Particles with Different Sizes

This paper deals with the calculation of the motion and the adminis-tration of the contacts for systems with many colliding bodies of round shape and possibly large size-differences. Both two dimensional (2D) and three dimensional (3D) cases are investigated, while the efficiency of the employed algorithms is compared. For the integration of the equations of motion, standard methods are used, but to reduce the effort for collision detection, more sophisticated administration algorithms for the neighbor-hood search are prosented. Especially for large systems with many parti-cles and a wide, polydisperse size distribution, this is a challenge. Three methods, the Verlet-Neighbor List (VL), the Linked Cell (LC) method, and the Linked Linear List (LLL), are discussed and compared for 2D and 3D. Only LLL performs well for strongly different particle sizes