Theory of nonlinear optical properties of phenyl-substituted polyacetylenes

In this paper we present a theoretical study of the third-order nonlinear optical properties of poly(diphenyl)polyacetylene (PDPA) pertaining to the third-harmonic-generation (THG) process. We study the aforesaid process in PDPA's using both the independent electron Hueckel model, as well as correlated-electron Pariser-Parr-Pople (P-P-P) model. The P-P-P model based calculations were performed using various configuration interaction (CI) methods such as the the multi-reference-singles-doubles CI (MRSDCI), and the quadruples-CI (QCI) methods, and the both longitudinal and the transverse components of third-order susceptibilities were computed. The Hueckel model calculations were performed on oligo-PDPA's containing up to fifty repeat units, while correlated calculations were performed for oligomers containing up to ten unit cells. At all levels of theory, the material exhibits highly anisotropic nonlinear optical response, in keeping with its structural anisotropy. We argue that the aforesaid anisotropy can be divided over two natural energy scales: (a) the low-energy response is predominantly longitudinal and is qualitatively similar to that of polyenes, while (b) the high-energy response is mainly transverse, and is qualitatively similar to that of trans-stilbene.Comment: 13 pages, 7 figures (included), to appear in Physical Review B (April 15, 2004

Ion collection by oblique surfaces of an object in a transversely-flowing strongly-magnetized plasma

The equations governing a collisionless obliquely-flowing plasma around an ion-absorbing object in a strong magnetic field are shown to have an exact analytic solution even for arbitrary (two-dimensional) object-shape, when temperature is uniform, and diffusive transport can be ignored. The solution has an extremely simple geometric embodiment. It shows that the ion collection flux density to a convex body's surface depends only upon the orientation of the surface, and provides the theoretical justification and calibration of oblique `Mach-probes'. The exponential form of this exact solution helps explain the approximate fit of this function to previous numerical solutions.Comment: Four pages, 2 figures. Submitted to Phys. Rev. Letter

Exact Solution of Return Hysteresis Loops in One Dimensional Random Field Ising Model at Zero Temperature

Minor hysteresis loops within the main loop are obtained analytically and exactly in the one-dimensional ferromagnetic random field Ising-model at zero temperature. Numerical simulations of the model show excellent agreement with the analytical results

Harmonic generation of gravitational wave induced Alfven waves

Here we consider the nonlinear evolution of Alfven waves that have been excited by gravitational waves from merging binary pulsars. We derive a wave equation for strongly nonlinear and dispersive Alfven waves. Due to the weak dispersion of the Alfven waves, significant wave steepening can occur, which in turn implies strong harmonic generation. We find that the harmonic generation is saturated due to dispersive effects, and use this to estimate the resulting spectrum. Finally we discuss the possibility of observing the above process.Comment: 7 page

Nonlinear Interactions Between Gravitational Radiation and Modified Alfven Modes in Astrophysical Dusty Plasmas

We present an investigation of nonlinear interactions between Gravitational Radiation and modified Alfv\'{e}n modes in astrophysical dusty plasmas. Assuming that stationary charged dust grains form neutralizing background in an electron-ion-dust plasma, we obtain the three wave coupling coefficients, and calculate the growth rates for parametrically coupled gravitational radiation and modified Alfv\'{e}n-Rao modes. The threshold value of the gravitational wave amplitude associated with convective stabilization is particularly small if the gravitational frequency is close to twice the modified Alfv\'en wave-frequency. The implication of our results to astrophysical dusty plasmas is discussed.Comment: A few typos corrected. Published in Phys. Rev.

Stabilisation of BGK modes by relativistic effects

Context. We examine plasma thermalisation processes in the foreshock region of astrophysical shocks within a fully kinetic and self-consistent treatment. We concentrate on proton beam driven electrostatic processes, which are thought to play a key role in the beam relaxation and the particle acceleration. Our results have implications for the effectiveness of electron surfing acceleration and the creation of the required energetic seed population for first order Fermi acceleration at the shock front. Aims. We investigate the acceleration of electrons via their interaction with electrostatic waves, driven by the relativistic Buneman instability, in a system dominated by counter-propagating proton beams. Methods. We adopt a kinetic Vlasov-Poisson description of the plasma on a fixed Eulerian grid and observe the growth and saturation of electrostatic waves for a range of proton beam velocities, from 0.15c to 0.9c. Results. We can report a reduced stability of the electrostatic wave (ESW) with increasing non-relativistic beam velocities and an improved wave stability for increasing relativistic beam velocities, both in accordance with previous findings. At the highest beam speeds, we find the system to be stable again for a period of ≈160 plasma periods. Furthermore, the high phase space resolution of the Eulerian Vlasov approach reveals processes that could not be seen previously with PIC simulations. We observe a, to our knowledge, previously unreported secondary electron acceleration mechanism at low beam speeds. We believe that it is the result of parametric couplings to produce high phase velocity ESW’s which then trap electrons, accelerating them to higher energies. This allows electrons in our simulation study to achieve the injection energy required for Fermi acceleration, for beam speeds as low as 0.15c in unmagnetised plasma

Bound states near a moving charge in a quantum plasma

It is investigated how the shielding of a moving point charge in a one-component fully degenerate fermion plasma affects the bound states near the charge at velocities smaller than the Fermi one. The shielding is accounted for by using the Lindhard dielectric function, and the resulting potential is substituted into the Schr\"odinger equation in order to obtain the energy levels. Their number and values are shown to be primarily determined by the value of the charge and the quantum plasma coupling parameter, while the main effect of the motion is to split certain energy levels. This provides a link between quantum plasma theory and possible measurements of spectra of ions passing through solids.Comment: Published in EPL, see http://epljournal.edpsciences.org/articles/epl/abs/2011/09/epl13478/epl13478.htm

Hysteresis in the Random Field Ising Model and Bootstrap Percolation

We study hysteresis in the random-field Ising model with an asymmetric distribution of quenched fields, in the limit of low disorder in two and three dimensions. We relate the spin flip process to bootstrap percolation, and show that the characteristic length for self-averaging $L^*$ increases as $exp(exp (J/\Delta))$ in 2d, and as $exp(exp(exp(J/\Delta)))$ in 3d, for disorder strength $\Delta$ much less than the exchange coupling J. For system size $1 << L < L^*$, the coercive field $h_{coer}$ varies as $2J - \Delta \ln \ln L$ for the square lattice, and as $2J - \Delta \ln \ln \ln L$ on the cubic lattice. Its limiting value is 0 for L tending to infinity, both for square and cubic lattices. For lattices with coordination number 3, the limiting magnetization shows no jump, and $h_{coer}$ tends to J.Comment: 4 pages, 4 figure