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

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

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

Scalar Quantum Field Theory with Cubic Interaction

In this paper it is shown that an i phi^3 field theory is a physically acceptable field theory model (the spectrum is positive and the theory is unitary). The demonstration rests on the perturbative construction of a linear operator C, which is needed to define the Hilbert space inner product. The C operator is a new, time-independent observable in PT-symmetric quantum field theory.Comment: Corrected expressions in equations (20) and (21

Chaotic systems in complex phase space

This paper examines numerically the complex classical trajectories of the kicked rotor and the double pendulum. Both of these systems exhibit a transition to chaos, and this feature is studied in complex phase space. Additionally, it is shown that the short-time and long-time behaviors of these two PT-symmetric dynamical models in complex phase space exhibit strong qualitative similarities.Comment: 22 page, 16 figure

PT-symmetry breaking in complex nonlinear wave equations and their deformations

We investigate complex versions of the Korteweg-deVries equations and an Ito type nonlinear system with two coupled nonlinear fields. We systematically construct rational, trigonometric/hyperbolic, elliptic and soliton solutions for these models and focus in particular on physically feasible systems, that is those with real energies. The reality of the energy is usually attributed to different realisations of an antilinear symmetry, as for instance PT-symmetry. It is shown that the symmetry can be spontaneously broken in two alternative ways either by specific choices of the domain or by manipulating the parameters in the solutions of the model, thus leading to complex energies. Surprisingly the reality of the energies can be regained in some cases by a further breaking of the symmetry on the level of the Hamiltonian. In many examples some of the fixed points in the complex solution for the field undergo a Hopf bifurcation in the PT-symmetry breaking process. By employing several different variants of the symmetries we propose many classes of new invariant extensions of these models and study their properties. The reduction of some of these models yields complex quantum mechanical models previously studied.Comment: 50 pages, 39 figures (compressed in order to comply with arXiv policy; higher resolutions maybe obtained from the authors upon request

Does the complex deformation of the Riemann equation exhibit shocks?

The Riemann equation $u_t+uu_x=0$, which describes a one-dimensional accelerationless perfect fluid, possesses solutions that typically develop shocks in a finite time. This equation is \cP\cT symmetric. A one-parameter \cP\cT-invariant complex deformation of this equation, $u_t-iu(iu_x)^\epsilon= 0$ ($\epsilon$ real), is solved exactly using the method of characteristic strips, and it is shown that for real initial conditions, shocks cannot develop unless $\epsilon$ is an odd integer.Comment: latex, 8 page

Line-strength indices and velocity dispersions for 148 early-type galaxies in different environments

We have derived high quality line-strength indices and velocity dispersions for a sample of 148 early-type galaxies in different environments. The wavelength region covered by the observations ($\lambda \simeq 4600$ to 6600 Å) includes the Lick/IDS indices H${\beta}$, Mg1, Mg2, Mgb, Fe5015, Fe5270, Fe5335, Fe5406, Fe5709, Fe5782, NaD, TiO1 and TiO2. The data are intended to address possible differences of the stellar populations of early-type galaxies in low- and high-density environments. This paper describes the sample properties, explains the data reduction and presents the complete list of all the measurements. Most galaxies of the sample (85%) had no previous measurements of any Lick/IDS indices and for 30% of the galaxies we present first-time determinations of their velocity dispersions. Special care is taken to identify galaxies with emission lines. We found that 62 per cent of the galaxies in the sample have emission lines, as measured by the equivalent width of the [OIII] 5007Å line, EW[OIII] > 0.3 Å

Complex Trajectories in a Classical Periodic Potential

This paper examines the complex trajectories of a classical particle in the potential V(x)=-cos(x). Almost all the trajectories describe a particle that hops from one well to another in an erratic fashion. However, it is shown analytically that there are two special classes of trajectories x(t) determined only by the energy of the particle and not by the initial position of the particle. The first class consists of periodic trajectories; that is, trajectories that return to their initial position x(0) after some real time T. The second class consists of trajectories for which there exists a real time T such that $x(t+T)=x(t) \pm2 \pi$. These two classes of classical trajectories are analogous to valence and conduction bands in quantum mechanics, where the quantum particle either remains localized or else tunnels resonantly (conducts) through a crystal lattice. These two special types of trajectories are associated with sets of energies of measure 0. For other energies, it is shown that for long times the average velocity of the particle becomes a fractal-like function of energy.Comment: 14 pages, 13 figure