Asymptotic properties of multistate random walks. I. Theory

A calculation is presented of the long-time behavior of various random walk properties (moments, probability of return to the origin, expected number of distinct sites visited) formultistate random walks on periodic lattices. In particular, we consider inhomogeneous periodic lattices, consisting of a periodically repeated unit cell which contains a finite number of internal states (sites). The results are identical to those for perfect lattices except for a renormalization of coefficients. For walks without drift, it is found that all the asymptotic random walk properties are determined by the diffusion coefficients for the multistate random walk. The diffusion coefficients can be obtained by a simple matrix algorithm presented here. Both discrete and continuous time random walks are considered. The results are not restricted to nearest-neighbor random walks but apply as long as the single-step probability distributions associated with each of the internal states have finite means and variances.     

Spectroscopic Study on the Photophysical Properties of Lanthanide Complexes with Long Chain Mono-Docosyl Phthalate

Ortho phthalic anhydride was modified with long chain alcohol (1-docosanol) to its corresponding monodocosyl phthalate (22-Phth). Subsequently, three novel lanthanide (Eu³⁺, Tb³⁺, and Dy³⁺) complexes with the long chain monodocosyl phthalate were synthesized and characterized by elemental analysis and Infrared spectra. The photophysical properties of these complexes were studied in detail with ultraviolet-visible absorption spectra, low temperature phosphorescence spectra and fluorescent spectra. The triplet state energy of 22-Phth was determined to be around 25,000 cm⁻¹ from the maximum phosphorescent peak at 400 nm, suggesting 22-Phth is suitable for the sensitization of the luminescence of Eu³⁺, Tb³⁺, and Dy³⁺. The fluorescence excitation and emission spectra for these lanthanide complexes of the three ligands take agreement with the above predict from energy match principle.     

Study of Exotic Nuclei

A high-sensitive fluorescence cell has been developed with an aim to perform laser spectroscopy of exotic nuclei. This fluorescence cell has been tested off-line for stable isotope ¹³³Cs. Also, an investigation of the nuclear root mean square (r.m.s.) charge and neutron radii, and of the binding energies of the cesium long isotopic chain has been carried out in the relativistic mean field (RMF) and relativistic Hartree–Bogoliubov (RHB) formalisms. The RMF/RHB calculations are compared with the experimental data and are found to be in good agreement.     

Quenching of the Haldane gap in LiVSi<Subscript>2</Subscript>O<Subscript>6</Subscript> and related compounds

We report results of susceptibility χ and ⁷Li NMR measurements on LiVSi₂O₆. The temperature dependence of the magnetic susceptibility χ(T) exhibits a broad maximum, typical for low-dimensional magnetic systems. Quantitatively it is in agreement with the expectation for an S=1 spin chain, represented by the structural arrangement of V ions. The NMR results indicate antiferromagnetic ordering below T_N=24 K. The intra- and interchain coupling J and J_p for LiVSi₂O₆, and also for its sister compounds LiVGe₂O₆, NaVSi₂O₆ and NaVGe₂O₆, are obtained via a modified random phase approximation which takes into account results of quantum Monte Carlo calculations. While J_p is almost constant across the series, J varies by a factor of 5, decreasing with increasing lattice constant along the chain direction. The comparison between experimental and theoretical susceptibility data suggests the presence of an easy-axis magnetic anisotropy, which explains the formation of an energy gap in the magnetic excitation spectrum below T_N, indicated by the variation of the NMR spin-lattice relaxation rate at T≪T_N.     

Quantum Dynamics in the Fermi–Pasta–Ulam Problem

We study a quantum chain of oscillators with nonlinear quartic interactions, under the “narrow packet” approximation. We analyse the dynamics of quantum corrections and the conditions at which the quantum solution for average complex amplitude converges to the corresponding classical unstable solution which describes the four-wave decay processes of phonons. We develop an asymptotic theory by using a small quasiclassical parameter, and determine the characteristic time scale for which the evolution of decay processes is essentially specified by quantum effects. AMS Subject classification: Primary: 35F10 Secondary: 35Q40, 35B40     

Out of Equilibrium Correlations in the XY Chain

We study the transversal spin–spin correlations in the non-equilibrium steady state of the XY chain constructed by coupling a finite cutout of the chain to the two infinite parts to its left and right acting as thermal reservoirs at different temperatures. We prove that the spatial decay of these correlations is at least exponentially fast.     

Multiple mobility edges in a 1D Aubry chain with Hubbard interaction in presence of electric field: Controlled electron transport

Electronic behavior of a 1D Aubry chain with Hubbard interaction is critically analyzed in presence of electric field. Multiple energy bands are generated as a result of Hubbard correlation and Aubry potential, and, within these bands localized states are developed under the application of electric field. Within a tight-binding framework we compute electronic transmission probability and average density of states using Green's function approach where the interaction parameter is treated under Hartree–Fock mean field scheme. From our analysis we find that selective transmission can be obtained by tuning injecting electron energy, and thus, the present model can be utilized as a controlled switching device.     

Vortices in a Rotating Spin-Orbit-Coupled Bose-Einstein Condensate under Extreme Elongation in a Harmonic Plus Quartic Trap

We consider the ground-state properties of a rotating spin-orbit-coupled Bose-Einstein condensate under extreme elongation in a harmonic plus quartic potential. The effects of spin-orbit coupling and rotation on the ground-state vortex structures are investigated. In the absence of spin-orbit coupling, new nucleated vortices gradually form vortex lines and annular vortex structures with the increase of the rotation frequency. In the presence of spin-orbit coupling, part of the vortices arrange in a line and form a stable vortex chain, and the remanent vortices coexist in pairs aside such vortex chain. More specially, the remanent vortices of each component repel each other and form vortex pair for isotropic spin-orbit coupling, while attract each other and locate in the same positions for anisotropic spin-orbit coupling.     

Terahertz planar antennas for future wireless communication: A technical review

With the monotonic increasing demand of the higher bandwidth for the next generation wireless communication system, the extension of the operating frequency of the communication system to the millimeter/Terahertz wave regime of the electromagnetic spectrum where several low-attenuation windows exist is inevitable. However, before the commercial implementation of the wireless communication in these low-attenuation windows, there are various obstacles which need to be addressed by the scientists and researchers. The atmospheric path loss is the main obstacle to the full-fledged implementation of the terahertz wireless communication. The remedy to this problem is the use of high-power sources, efficient detectors and high gain antenna systems. This paper reviews these technical issues with the special attention to the planar antennas which might contribute to the compact, inexpensive, and low profile future terahertz wireless communication system design.     

Quantum Teleportation via Completely Anisotropic Heisenberg Chain in Inhomogeneous Magnetic Field

The quantum teleportation with the entangled thermal state is investigated based on the completely anisotropic Heisenberg chain in the presence of the externally inhomogeneous magnetic field. The effects of the anisotropy and magnetic field for the quantum fidelity are studied in detail. The zero temperature limit and the features of the nonzero temperature for this nonclassical fidelity are obt8ained. We find that the quantum teleportation demands more stringent conditions than the thermal entanglement of the resource by investigating the threshold temperature of the thermal concurrence and the critical temperature of the maximal teleportation fidelity. The useful quantum teleportation should avoid the point of the phase transition of the system and the anisotropy of the chain and the external magnetic field can control the applicability of the resource in the quantum teleportation.