Extending PT symmetry from Heisenberg algebra to E2 algebra

The E2 algebra has three elements, J, u, and v, which satisfy the commutation relations [u,J]=iv, [v,J]=-iu, [u,v]=0. We can construct the Hamiltonian H=J^2+gu, where g is a real parameter, from these elements. This Hamiltonian is Hermitian and consequently it has real eigenvalues. However, we can also construct the PT-symmetric and non-Hermitian Hamiltonian H=J^2+igu, where again g is real. As in the case of PT-symmetric Hamiltonians constructed from the elements x and p of the Heisenberg algebra, there are two regions in parameter space for this PT-symmetric Hamiltonian, a region of unbroken PT symmetry in which all the eigenvalues are real and a region of broken PT symmetry in which some of the eigenvalues are complex. The two regions are separated by a critical value of g.Comment: 8 pages, 7 figure

Model of supersymmetric quantum field theory with broken parity symmetry

Recently, it was observed that self-interacting scalar quantum field theories having a non-Hermitian interaction term of the form $g(i\phi)^{2+\delta}$, where $\delta$ is a real positive parameter, are physically acceptable in the sense that the energy spectrum is real and bounded below. Such theories possess PT invariance, but they are not symmetric under parity reflection or time reversal separately. This broken parity symmetry is manifested in a nonzero value for $$, even if $\delta$ is an even integer. This paper extends this idea to a two-dimensional supersymmetric quantum field theory whose superpotential is ${\cal S}(\phi)=-ig(i\phi)^{1+\delta}$. The resulting quantum field theory exhibits a broken parity symmetry for all $\delta>0$. However, supersymmetry remains unbroken, which is verified by showing that the ground-state energy density vanishes and that the fermion-boson mass ratio is unity.Comment: 20 pages, REVTeX, 11 postscript figure

Simulation of granular soil behaviour using the bullet physics library

A physics engine is computer software which provides a simulation of certain physical systems, such as rigid body dynamics, soft body dynamics and fluid dynamics. Physics engines were firstly developed for using in animation and gaming industry ; nevertheless, due to fast calculation speed they are attracting more and more attetion from researchers of the engineering fields. Since physics engines are capable of performing fast calculations on multibody rigid dynamic systems, soil particles can be modeled as distinct rigid bodies. However, up to date, it is not clear to what extent they perform accurately in modeling soil behaviour from a geotechnical viewpoint. To investigate this, examples of pluviation and vibration-induced desification were simulated using the physics engine called Bullet physics library. In order to create soil samples, first, randomly shaped polyhedrons, representing gravels, were generated using the Voronoi tessellation approach. Then, particles were pluviated through a funnel into a cylinder. Once the soil particles settled in a static state, the cylinder was subjected to horizontal sinusoidal vibration for a period of 20 seconds. The same procedure for sample perparation was performed in the laboratory. The results of pluviation and vibration tests weere recorded and compared to those of simulations. A good agreement has been found between the results of simulations and laboratory tests. The findings in this study reinforce the idea that physics engines can be employed as a geotechnical engineering simulation tool

Pairing correlations beyond the mean field

We discuss dynamical pairing correlations in the context of configuration mixing of projected self-consistent mean-field states, and the origin of a divergence that might appear when such calculations are done using an energy functional in the spirit of a naive generalized density functional theory.Comment: Proceedings of the XIII Nuclear Physics Workshop ``Maria and Pierre Curie'' on ``Pairing and beyond - 50 years of the BCS model'', held at Kazimierz Dolny, Poland, September 27 - October 1, 2006. Int. J. Mod. Phys. E, in prin

Comment on ``Structure of exotic nuclei and superheavy elements in a relativistic shell model''

A recent paper [M. Rashdan, Phys. Rev. C 63, 044303 (2001)] introduces the new parameterization NL-RA1 of the relativistic mean-field model which is claimed to give a better description of nuclear properties than earlier ones. Using this model ^{298}114 is predicted to be a doubly-magic nucleus. As will be shown in this comment these findings are to be doubted as they are obtained with an unrealistic parameterization of the pairing interaction and neglecting ground-state deformation.Comment: 2 pages REVTEX, 3 figures, submitted to comment section of Phys. Rev. C. shortened and revised versio

Spatially resolved spectroscopy of Coma cluster early-type galaxies IV. Completing the dataset

The long-slit spectra obtained along the minor axis, offset major axis and diagonal axis are presented for 12 E and S0 galaxies of the Coma cluster drawn from a magnitude-limited sample studied before. The rotation curves, velocity dispersion profiles and the H_3 and H_4 coefficients of the Hermite decomposition of the line of sight velocity distribution are derived. The radial profiles of the Hbeta, Mg, and Fe line strength indices are measured too. In addition, the surface photometry of the central regions of a subsample of 4 galaxies recently obtained with Hubble Space Telescope is presented. The data will be used to construct dynamical models of the galaxies and study their stellar populations.Comment: 40 pages, 7 figures, 6 tables. Accepted for publication in ApJ

Skyrme functional from a three-body pseudo-potential of second-order in gradients. Formalism for central terms

In one way or the other, all modern parametrizations of the nuclear energy density functional (EDF) do not respect the exchange symmetry associated with Pauli's principle. It has been recently shown that this practice jeopardizes multi-reference (MR) EDF calculations by contaminating the energy with spurious self-interactions that, for example, lead to finite steps or even divergences when plotting it as a function of collective coordinates. As of today, the only viable option to bypass these pathologies is to rely on EDF kernels that enforce Pauli's principle from the outset by strictly and exactly deriving from a genuine, i.e. density-independent, Hamilton operator. We wish to develop the most general Skyrme-like EDF parametrization containing linear, bilinear and trilinear terms in the density matrices with up to two gradients, under the key constraint that it derives strictly from an effective Hamilton operator. The most general three-body Skyrme-like pseudo-potential containing up to two gradient operators is constructed to generate the trilinear part. The present study is limited to central terms. Spin-orbit and tensor will be addressed in a forthcoming paper. (See paper for full abstract)Comment: 38 pages revtex, no figur

Symmetry restoration for odd-mass nuclei with a Skyrme energy density functional

In these proceedings, we report first results for particle-number and angular-momentum projection of self-consistently blocked triaxial one-quasiparticle HFB states for the description of odd-A nuclei in the context of regularized multi-reference energy density functionals, using the entire model space of occupied single-particle states. The SIII parameterization of the Skyrme energy functional and a volume-type pairing interaction are used.Comment: 8 pages, 3 figures, workshop proceeding

PT-Symmetry Quantum Electrodynamics--PTQED

The construction of $\mathcal{PT}$-symmetric quantum electrodynamics is reviewed. In particular, the massless version of the theory in 1+1 dimensions (the Schwinger model) is solved. Difficulties with unitarity of the $S$-matrix are discussed.Comment: 11 pages, 1 figure, contributed to Proceedings of 6th International Workshop on Pseudo-Hermitian Hamiltonians in Quantum Physic

Vector Casimir effect for a D-dimensional sphere

The Casimir energy or stress due to modes in a D-dimensional volume subject to TM (mixed) boundary conditions on a bounding spherical surface is calculated. Both interior and exterior modes are included. Together with earlier results found for scalar modes (TE modes), this gives the Casimir effect for fluctuating ``electromagnetic'' (vector) fields inside and outside a spherical shell. Known results for three dimensions, first found by Boyer, are reproduced. Qualitatively, the results for TM modes are similar to those for scalar modes: Poles occur in the stress at positive even dimensions, and cusps (logarithmic singularities) occur for integer dimensions $D\le1$. Particular attention is given the interesting case of D=2.Comment: 20 pages, 1 figure, REVTe