Phase space interference and the WKB approximation for squeezed number states

Squeezed number states for a single mode Hamiltonian are investigated from two complementary points of view. Firstly the more relevant features of their photon distribution are discussed using the WKB wave functions. In particular the oscillations of the distribution and the parity behavior are derived and compared with the exact results. The accuracy is verified and it is shown that for high photon number it fails to reproduce the true distribution. This is contrasted with the fact that for moderate squeezing the WKB approximation gives the analytical justification to the interpretation of the oscillations as the result of the interference of areas with definite phases in phase space. It is shown with a computation at high squeezing using a modified prescription for the phase space representation which is based on Wigner-Cohen distributions that the failure of the WKB approximation does not invalidate the area overlap picture.Comment: 9 pages, 4 figure

ENVIRONMENTAL PROTECTION WITH POLICIES FOR SALE

This paper generalizes the Grossman-Helpman political economy model to characterize the structure of environmental and industry protection for a small open economy when domestic and/or trade policies are the outcome of a noncooperative common agency game between sector-specific producer lobbies and the government. For a consumption externality, the political equilibrium results if domestic and trade policies are available, are production-enhancing protection of organized industries, but the same environmental protection as Pigouvian taxes. Subsidies to organized industries counterbalance environmental taxes when there is a production externality, and it is ambiguous whether domestic or trade policy alone leads to more environmental protection. In addition, this paper demonstrates that the original Grossman-Helpman results arise as a special case that rests on the assumption that only trade policies are available to the government.Environmental Economics and Policy,

Patterns in Wigner-Weyl approach

We present a family of methods, which can describe behaviour of quantum ensembles and demonstrate the creation of nontrivial (meta) stable states (patterns), localized, chaotic, entangled or decoherent from basic localized modes in collective models arising from the quantum hierarchy of Wigner-von Neumann-Moyal equations.Comment: LaTeX2e, w-art.cls, w-thm.sty, w-pamm.clo, 3 pages, 2 figures, presented at GAMM Meeting, 2006, Berlin, German

Designer de Sitter Spacetimes

Recent observations in cosmology indicate an accelerating expansion of the universe postulated to arise from some form of dark energy, the paradigm being positive cosmological constant. De Sitter spacetime is the well-known isotropic solution to the Einstein equations with cosmological constant. However, as discussed here, it is not the most general, locally isotropic solution. One can construct an infinite family of such solutions, designer de Sitter spacetimes, which are everywhere locally isometric to a region of de Sitter spacetime. However, the global dynamics of these designer cosmologies is very different than that of de Sitter spacetime itself. The construction and dynamics of these designer de Sitter spacetimes is detailed along with some comments about their implications for the structure of our universe.Comment: 6 pages, no figure, correction of sign in eq.

Conformal Mapping and Bound States in Bent Waveguides

Is it possible to trap a quantum particle in an open geometry? In this work we deal with the boundary value problem of the stationary Schroedinger (or Helmholtz) equation within a waveguide with straight segments and a rectangular bending. The problem can be reduced to a one dimensional matrix Schroedinger equation using two descriptions: oblique modes and conformal coordinates. We use a corner-corrected WKB formalism to find the energies of the one dimensional problem. It is shown that the presence of bound states is an effect due to the boundary alone, with no classical counterpart for this geometry. The conformal description proves to be simpler, as the coupling of transversal modes is not essential in this case.Comment: 16 pages, 10 figures. To appear in the Proceedings of the Symposium "Symmetries in Nature, in memoriam Marcos Moshinsky

Dimensional enhancement of kinetic energies

Simple thermodynamics considers kinetic energy to be an extensive variable which is proportional to the number, N, of particles. We present a quantum state of N non-interacting particles for which the kinetic energy increases quadratically with N. This enhancement effect is tied to the quantum centrifugal potential whose strength is quadratic in the number of dimensions of configuration space.Comment: 9 pages, accepted by Phys. Rev.