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In the last decade, it was shown that the Liouville field theory is an effective theory of Dirac fermions in the random gauge potential (FRGP). We show that the Dirac wave functions in FRGP can be written in terms of descendents of the Liouville vertex operator. In the quasiclassical approximation of the Liouville theory, our model predicts that the localization length ξ scales with the energy E as $$ \xi \sim E^{{{ - b^2 } \mathord{\left/ {\vphantom {{ - b^2 } {(1 + b^2 )^2 }}} \right. \kern-\nulldelimiterspace} {(1 + b^2 )^2 }}} $$, where b is the strength of the disorder. The self-duality of the theory under the transformation b → 1/ b is discussed. We also calculate the distribution functions of t0 =| ψ0( x)|2, (i.e. p( t0); ψ0( x) is the ground state wave function), which behaves as the log-normal distribution function. It is also shown that in small t0, p( t0) behaves as a chi-square distribution. [ABSTRACT FROM AUTHOR]

Using a tight-binding model and a transfer-matrix technique, we numerically investigate the effects of the coupling strength and the role of solitons on the electronic transmission through a system in which trans-polyacetylene (trans-PA) molecule is sandwiched between two semi-infinite single-walled carbon nanotubes (SWNT). We rely on Landauer formalism as the basis for studying the conductance properties of this system. Our calculations show that the solitons play an important role in the response of this system causing a large enhancement in the conductance. Also our results suggest that the conductance is sensitive to the CNT/molecule coupling strength. [ABSTRACT FROM AUTHOR]

In this letter, titanium dioxide nanoparticles (TiO2) were synthesized via a sol-gel method and combining titanium tetrachloride (TiCl4) and ethanol. The activation energy was investigated on the phase transformation from anatase to rutile in the presence and absence of ultrasound waves. The anatase nanocrystallites were only crystallized up to the calcination of 500 °C. By increasing the calcination in the region after 500 °C, rutile nanocrystallites grew in samples, and mixed-phase TiO2 nanoparticles were obtained. Our results show that applying ultrasound waves decreases both onset transition temperature and the activation energy of the phase transformation from anatase to rutile. The activation energy showed a considerable reduction at about 18.5 k J/mol by applying the ultrasound waves. [ABSTRACT FROM AUTHOR]