Liouville-von Neumann approach and time-dependent Gaussian approximation

We show that Liouville-von Neumann approach to quantum mechanical systems, which demands the existence of invariant operators, reproduces the time-dependent variational Gaussian approximation. We find the effective action of the time-dependent systems and show that many aspects of the dynamics are independent of the details of time evolution, e.g., the squeezing of the wave-function is determined by the effective potential of the final stage of time-evolution.Comment: 10 pages, 2 figure

Casimir energy of a spherical shell in κ−\kappa-Minkowski spacetime

We study the Casimir energy of a spherical shell of radius $a$ in $\kappa$-Minkowski spacetime for a complex field with an asymmetric ordering and obtain the energy up to $O(1/\kappa^2)$. We show that the vacuum breaks particle and anti-particle symmetry if one requires the spectra to be consistent with the blackbody radiation at the commutative limit.Comment: 23 pages, 3 figures, add more analysi

Post Gaussian effective potential in the Ginzburg Landau theory of superconductivity

The post Gaussian effective potential in D=3 dimensions and the Gaussian effective potential in D=2+epsilon are evaluated for the Ginzburg-Landau theory of superconductivity. It is shown that, the next order correction to the Gaussian approximation of the Ginzburg-Landau parameter (kappa) is significant, whereas contribution from the two dimensionality is rather small. This strongly indicates that strong correlation plays a more dominant role than the two dimensionality does in high T_c superconductivity.Comment: 15 pages, RevTeX, 4 figures, minor changes has been mad

The electron temperature of the inner halo of the Planetary Nebula NGC 6543

We investigate the electron temperature of the inner halo and nebular core regions of NGC 6543, using archival Hubble Space Telescope (HST) Wide Field Planetary Camera 2 (WFPC2) images taken through narrow band [O III] filters. Balick et al. (2001) showed that the inner halo consists of a number of spherical shells. We find the temperature of this inner halo to be much higher (~15000 K) than that of the bright core nebula (~8500 K). Photo-ionization models indicate that hardening of the UV radiation from the central star cannot be the main source of the higher temperature in the halo region. Using a radiation hydrodynamic simulation, we show that mass loss and velocity variations in the AGB wind can explain the observed shells, as well as the higher electron temperature.Comment: 9 pages, 6 figures, to be published in A&