Nonlinear wave-wave interactions in quantum plasmas

Wave-wave interaction in plasmas is a topic of important research since the 16th century. The formation of Langmuir solitons through the coupling of high-frequency (hf) Langmuir and low-frequency (lf) ion-acoustic waves, is one of the most interesting features in the context of turbulence in modern plasma physics. Moreover, quantum plasmas, which are ubiquitous in ultrasmall electronic devices, micromechanical systems as well as in dense astrophysical environments are a topic of current research. In the light of notable interests in such quantum plasmas, we present here a theoretical investigation on the nonlinear interaction of quantum Langmuir waves (QLWs) and quantum ion-acoustic waves (QIAWs), which are governed by the one-dimensional quantum Zakharov equations (QZEs). It is shown that a transition to spatiotemporal chaos (STC) occurs when the length scale of excitation of linear modes is larger than that of the most unstable ones. Such length scale is, however, to be larger (compared to the classical one) in presence of the quantum tunneling effect. The latter induces strong QIAW emission leading to the occurrence of collision and fusion among the patterns at an earlier time than the classical case. Moreover, numerical simulation of the QZEs reveals that many solitary patterns can be excited and saturated through the modulational instability (MI) of unstable harmonic modes. In a longer time, these solitons are seen to appear in the state of STC due to strong QIAW emission as well as by the collision and fusion in stochastic motion. The energy in the system is thus strongly redistributed, which may switch on the onset of Langmuir turbulence in quantum plasmas.Comment: 6 pages, 6 figures (To appear in AIP Conf. Proceedings 2010

Electron Correlations and Two-Photon States in Polycyclic Aromatic Hydrocarbon Molecules: A Peculiar Role of Geometry

We present numerical studies of one- and two-photon excited states ordering in a number of polycyclic aromatic hydrocarbon molecules: coronene, hexa-peri-hexabenzocoronene and circumcoronene, all possessing $D_{6h}$ point group symmetry versus ovalene with $D_{2h}$ symmetry, within the Pariser-Parr-Pople model of interacting $\pi$-electrons. The calculated energies of the two-photon states as well as their relative two-photon absorption cross-sections within the interacting model are qualitatively different from single-particle descriptions. More remarkably, a peculiar role of molecular geometry is found. The consequence of electron correlations is far stronger for ovalene, where the lowest spin-singlet two-photon state is a quantum superposition of pairs of lowest spin triplet states, as in the linear polyenes. The same is not true for $D_{6h}$ group hydrocarbons. Our work indicates significant covalent character, in valence bond language, of the ground state, the lowest spin triplet state and a few of the lowest two-photon states in $D_{2h}$ ovalene but not in those with $D_{6h}$ symmetry.Comment: 11 pages, 3 figures, 3 table

Rossby rogons in atmosphere and in the solar photosphere

The generation of Rossby rogue waves (Rossby rogons), as well as the excitation of bright and dark Rossby envelpe solitons are demonstrated on the basis of the modulational instability (MI) of a coherent Rossby wave packet. The evolution of an amplitude modulated Rossby wave packet is governed by one-dimensional (1D) nonlinear Schr\"odinger equation (NLSE). The latter is used to study the amplitude modulation of Rossby wave packets for fluids in Earth's atmosphere and in the solar photosphere. It is found that an ampitude modulated Rossby wave packet becomes stable (unstable) against quasi-stationary, long wavelength (in comparision with the Rossby wave length) perturbations, when the carrier Rossby wave number satisfies $k^2 < 1/2$ or $\sqrt{2}+13$ or $1/2<k^2<\sqrt{2}+1$). It is also shown that a Rossby rogon or a bright Rossby envelope soliton may be excited in the shallow water approximation for the Rossby waves in solar photosphere. However, the excitation of small or large scale perturbations may be possible for magnetized plasmas in the ionosphereic $E-$layer.Comment: 6 pages, 5 figures; To appear in Europhysics Letter

Spinodal decomposition: An alternate mechanism of phase conversion

The scenario of homogeneous nucleation is investigated for a first order quark-hadron phase transition in a rapidly expanding background of quark gluon plasma. It is found that significant supercooling is possible before hadronization begins. This study also suggests that spinodal decomposition competes with nucleation and may provide an alternative mechanism for phase conversion.Comment: LaTeX, 4 pages with 3 Postscript figures. Talk given at International Conference on Physics and Astrophysics of Quark Gluon Plasma (ICPAQGP 2001), Nov. 26-30, 2001, Jaipur, Indi

Nonlinear dynamics of large amplitude dust acoustic shocks and solitary pulses in dusty plasmas

We present a fully nonlinear theory for dust acoustic (DA) shocks and DA solitary pulses in a strongly coupled dusty plasma, which have been recently observed experimentally by Heinrich et al. [Phys. Rev. Lett. 103, 115002 (2009)], Teng et al. [Phys. Rev. Lett. 103, 245005 (2009)], and Bandyopadhyay et al. [Phys. Rev. Lett. 101, 065006 (2008)]. For this purpose, we use a generalized hydrodynamic model for the strongly coupled dust grains, accounting for arbitrary large amplitude dust number density compressions and potential distributions associated with fully nonlinear nonstationary DA waves. Time-dependent numerical solutions of our nonlinear model compare favorably well with the recent experimental works (mentioned above) that have reported the formation of large amplitude non-stationary DA shocks and DA solitary pulses in low-temperature dusty plasma discharges.Comment: 9 pages, 4 figures. To be published in Physical Review

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