Universality in Random Walk Models with Birth and Death

Models of random walks are considered in which walkers are born at one location and die at all other locations with uniform death rate. Steady-state distributions of random walkers exhibit dimensionally dependent critical behavior as a function of the birth rate. Exact analytical results for a hyperspherical lattice yield a second-order phase transition with a nontrivial critical exponent for all positive dimensions $D\neq 2,~4$. Numerical studies of hypercubic and fractal lattices indicate that these exact results are universal. Implications for the adsorption transition of polymers at curved interfaces are discussed.Comment: 11 pages, revtex, 2 postscript figure

Non-perturbative calculations for the effective potential of the PTPT symmetric and non-Hermitian (−gϕ4)(-g\phi^{4}) field theoretic model

We investigate the effective potential of the $PT$ symmetric $(-g\phi^{4})$ field theory, perturbatively as well as non-perturbatively. For the perturbative calculations, we first use normal ordering to obtain the first order effective potential from which the predicted vacuum condensate vanishes exponentially as $G\to G^+$ in agreement with previous calculations. For the higher orders, we employed the invariance of the bare parameters under the change of the mass scale $t$ to fix the transformed form totally equivalent to the original theory. The form so obtained up to $G^3$ is new and shows that all the 1PI amplitudes are perurbative for both $G\ll 1$ and $G\gg 1$ regions. For the intermediate region, we modified the fractal self-similar resummation method to have a unique resummation formula for all $G$ values. This unique formula is necessary because the effective potential is the generating functional for all the 1PI amplitudes which can be obtained via $\partial^n E/\partial b^n$ and thus we can obtain an analytic calculation for the 1PI amplitudes. Again, the resummed from of the effective potential is new and interpolates the effective potential between the perturbative regions. Moreover, the resummed effective potential agrees in spirit of previous calculation concerning bound states.Comment: 20 page

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

Microlensing events from the 11-year observations of the Wendelstein Calar Alto Pixellensing Project

We present the results of the decade-long M31 observation from the Wendelstein Calar Alto Pixellensing Project (WeCAPP). WeCAPP has monitored M31 from 1997 till 2008 in both R- and I-filters, thus provides the longest baseline of all M31 microlensing surveys. The data are analyzed with the difference imaging analysis, which is most suitable to study variability in crowded stellar fields. We extracted light curves based on each pixel, and devised selection criteria that are optimized to identify microlensing events. This leads to 10 new events, and sums up to a total of 12 microlensing events from WeCAPP, for which we derive their timescales, flux excesses, and colors from their light curves. The color of the lensed stars fall between (R-I) = 0.56 to 1.36, with a median of 1.0 mag, in agreement with our expectation that the sources are most likely bright, red stars at post main-sequence stage. The event FWHM timescales range from 0.5 to 14 days, with a median of 3 days, in good agreement with predictions based on the model of Riffeser et al. (2006).Comment: 44 pages, 16 figures, 5 tables. ApJ accepte

Use of Equivalent Hermitian Hamiltonian for PTPT-Symmetric Sinusoidal Optical Lattices

We show how the band structure and beam dynamics of non-Hermitian $PT$-symmetric sinusoidal optical lattices can be approached from the point of view of the equivalent Hermitian problem, obtained by an analytic continuation in the transverse spatial variable $x$. In this latter problem the eigenvalue equation reduces to the Mathieu equation, whose eigenfunctions and properties have been well studied. That being the case, the beam propagation, which parallels the time-development of the wave-function in quantum mechanics, can be calculated using the equivalent of the method of stationary states. We also discuss a model potential that interpolates between a sinusoidal and periodic square well potential, showing that some of the striking properties of the sinusoidal potential, in particular birefringence, become much less prominent as one goes away from the sinusoidal case.Comment: 11 pages, 8 figure

Spontaneous Symmetry Breaking of phi4(1+1) in Light Front Field Theory

We study spontaneous symmetry breaking in phi^4_(1+1) using the light-front formulation of the field theory. Since the physical vacuum is always the same as the perturbative vacuum in light-front field theory the fields must develop a vacuum expectation value through the zero-mode components of the field. We solve the nonlinear operator equation for the zero-mode in the one-mode approximation. We find that spontaneous symmetry breaking occurs at lambda_critical = 4 pi(3+sqrt 3), which is consistent with the value lambda_critical = 54.27 obtained in the equal time theory. We calculate the value of the vacuum expectation value as a function of the coupling constant in the broken phase both numerically and analytically using the delta expansion. We find two equivalent broken phases. Finally we show that the energy levels of the system have the expected behavior within the broken phase.Comment: 17 pages, OHSTPY-HEP-TH-92-02

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

Observation of Asymmetric Transport in Structures with Active Nonlinearities

A mechanism for asymmetric transport based on the interplay between the fundamental symmetries of parity (P) and time (T) with nonlinearity is presented. We experimentally demonstrate and theoretically analyze the phenomenon using a pair of coupled van der Pol oscillators, as a reference system, one with anharmonic gain and the other with complementary anharmonic loss; connected to two transmission lines. An increase of the gain/loss strength or the number of PT-symmetric nonlinear dimers in a chain, can increase both the asymmetry and transmittance intensities.Comment: 5 pages, 5 figure

Direct Measurement of intermediate-range Casimir-Polder potentials

We present the first direct measurements of Casimir-Polder forces between solid surfaces and atomic gases in the transition regime between the electrostatic short-distance and the retarded long-distance limit. The experimental method is based on ultracold ground-state Rb atoms that are reflected from evanescent wave barriers at the surface of a dielectric glass prism. Our novel approach does not require assumptions about the potential shape. The experimental data confirm the theoretical prediction in the transition regime.Comment: 4 pages, 3 figure