Model solution for volume reflection of relativistic particles in a bent crystal

For volume reflection process in a bent crystal, exact analytic expressions for positively- and negatively-charged particle trajectories are obtained within a model of parabolic continuous potential in each interplanar interval, with the neglect of incoherent multiple scattering. In the limit of the crystal bending radius greatly exceeding the critical value, asymptotic formulas are obtained for the particle mean deflection angle in units of Lindhard's critical angle, and for the final beam profile. Volume reflection of negatively charged particles is shown to contain effects of rainbow scattering and orbiting, whereas with positively charged particles none of these effects arise within the given model. The model predictions are compared with experimental results and numerical simulations. Estimates of the volume reflection mean angle and the final beam profile robustness under multiple scattering are performed.Comment: 21 pages, 11 figure

Boundary conditions at spatial infinity for fields in Casimir calculations

The importance of imposing proper boundary conditions for fields at spatial infinity in the Casimir calculations is elucidated.Comment: 8 pages, 1 figure, submitted to the Proceedings of The Seventh Workshop QFEXT'05 (Barcelona, September 5-9, 2005

Few-body resonances of unequal-mass systems with infinite interspecies two-body s-wave scattering length

Two-component Fermi and Bose gases with infinitely large interspecies s-wave scattering length $a_s$ exhibit a variety of intriguing properties. Among these are the scale invariance of two-component Fermi gases with equal masses, and the favorable scaling of Efimov features for two-component Bose gases and Bose-Fermi mixtures with unequal masses. This paper builds on our earlier work [D. Blume and K. M. Daily, arXiv:1006.5002] and presents a detailed discussion of our studies of small unequal-mass two-component systems with infinite $a_s$ in the regime where three-body Efimov physics is absent. We report on non-universal few-body resonances. Just like with two-body systems on resonance, few-body systems have a zero-energy bound state in free space and a diverging generalized scattering length. Our calculations are performed within a non-perturbative microscopic framework and investigate the energetics and structural properties of small unequal-mass two-component systems as functions of the mass ratio $\kappa$, and the numbers $N_{1}$ and $N_2$ of heavy and light atoms. For purely attractive Gaussian two-body interactions, we find that the $(N_1,N_2)=(2,1)$ and $(3,1)$ systems exhibit three-body and four-body resonances at mass ratios $\kappa = 12.314(2)$ and 10.4(2), respectively. The three- and four-particle systems on resonance are found to be large. This suggests that the corresponding wave function has relatively small overlap with deeply-bound dimers, trimers or larger clusters and that the three- and four-body systems on resonance have a comparatively long lifetime. Thus, it seems feasible that the features discussed in this paper can be probed experimentally with present-day technology.Comment: 17 pages, 17 figure

Energies of Quantum QED Flux Tubes

In this talk I present recent studies on vacuum polarization energies and energy densities induced by QED flux tubes. I focus on comparing three and four dimensional scenarios and the discussion of various approximation schemes in view of the exact treatment.Comment: 9 pages latex, Talk presented at the QFEXT 05 workshop in Barcelona, Sept. 2005. To appear in the proceeding

The Response to a Perturbation in the Reflection Amplitude

We apply inverse scattering theory to calculate the functional derivative of the potential $V(x)$ and wave function $\psi(x,k)$ of a one-dimensional Schr\"odinger operator with respect to the reflection amplitude $r(k)$.Comment: 16 pages, no figure

KKbar molecules with momentum-dependent interactions

It is shown that the momentum-dependent kaon-antikaon interactions generated via vector meson exchange from the standard SU_V(3) x SU_A(3) interaction Lagrangian lead to a non-local potential in coordinate space that can be incorporated without approximation into a non-relativistic version of the Bethe-Salpeter wave equation containing a radial-dependent effective kaon mass appearing in a fully symmetrized kinetic energy operator, in addition to a local potential. Estimates of the mass and decay widths of f_0(980) and a_0(980), considered as KKbar molecules of isospin 0 and 1, as well as for K^+K^- atomic bound states (kaonium) are presented, and compared with previous studies of a similar nature. It is argued that without a better knowledge of hadronic form factors it is not possible to distinguish between the molecular versus elementary particle models for the structure of the light scalar mesons.Comment: 14 pages, 2 tables, 5 figures. Added subsection on s-channel exchange, additional remarks on the possible effect of gluon exchange, and 1 additional figur

Bound and resonant impurity states in a narrow gaped armchair graphene nanoribbon

An analytical study of discrete and resonant impurity quasi-Coulomb states in a narrow gaped armchair graphene nanoribbon (GNR) is performed. We employ the adiabatic approximation assuming that the motions parallel ("slow") and perpendicular ("fast") to the boundaries of the ribbon are separated adiabatically. The energy spectrum comprises a sequence of series of quasi-Rydberg levels relevant to the "slow" motion adjacent from the low energies to the size-quantized levels associated with the "fast" motion. Only the series attributed to the ground size-quantized sub-band is really discrete, while others corresponding to the excited sub-bands consist of quasi-discrete (Fano resonant) levels of non-zero energetic widths, caused by the coupling with the states of the continuous spectrum branching from the low lying sub-bands. In the two- and three-subband approximation the spectrum of the complex energies of the impurity electron is derived in an explicit form. Narrowing the GNR leads to an increase of the binding energy and the resonant width both induced by the finite width of the ribbon. Displacing the impurity centre from the mid-point of the GNR causes the binding energy to decrease while the resonant width of the first excited Rydberg series increases. As for the second excited series their widths become narrower with the shift of the impurity. A successful comparison of our analytical results with those obtained by other theoretical and experimental methods is presented. Estimates of the binding energies and the resonant widths taken for the parameters of typical GNRs show that not only the strictly discrete but also the some resonant states are quite stable and could be studied experimentally in doped GNRs

Starspot Jitter in Photometry, Astrometry and Radial Velocity Measurements

Analytical relations are derived for the amplitude of astrometric, photometric and radial velocity perturbations caused by a single rotating spot. The relative power of the star spot jitter is estimated and compared with the available data for $\kappa^1$ Ceti and HD 166435, as well as with numerical simulations for $\kappa^1$ Ceti and the Sun. A Sun-like star inclined at i=90\degr at 10 pc is predicted to have a RMS jitter of 0.087 \uas in its astrometric position along the equator, and 0.38 m s$^{-1}$ in radial velocities. If the presence of spots due to stellar activity is the ultimate limiting factor for planet detection, the sensitivity of SIM Lite to Earth-like planets in habitable zones is about an order of magnitude higher that the sensitivity of prospective ultra-precise radial velocity observations of nearby stars.Comment: accepted in ApJ Letters, Nov. 200

Two and three-dimensional oscillons in nonlinear Faraday resonance

We study 2D and 3D localised oscillating patterns in a simple model system exhibiting nonlinear Faraday resonance. The corresponding amplitude equation is shown to have exact soliton solutions which are found to be always unstable in 3D. On the contrary, the 2D solitons are shown to be stable in a certain parameter range; hence the damping and parametric driving are capable of suppressing the nonlinear blowup and dispersive decay of solitons in two dimensions. The negative feedback loop occurs via the enslaving of the soliton's phase, coupled to the driver, to its amplitude and width.Comment: 4 pages; 1 figur