Information theory and one-dimensional disordered conductors

A novel method is proposed to treat the problem of the random resistance of a strictly one-dimensional conductor with static disorder. It is suggested, for the probability distribution of the transfer matrix of the conductor, the distribution of maximum information-entropy, constrained by the following physical requirements: 1) flux conservation, 2) time-reversal invariance and 3) scaling, with the length of the conductor, of the two lowest cumulants of ζ, where = sh2ζ. The preliminary results discussed in the text are in qualitative agreement with those obtained by sophisticated microscopic theories.

Vacancy ordered phases and one-dimensional quasiperiodicity

The metastable vacancy ordered phases observed in aluminium transition metal alloys on rapid solidification or vapour deposition can be considered as a periodic arrangement of a truncated quasiperiodic string based on the Fibonacci sequence along the left angle bracket111right-pointing angle bracket stacking direction of the original CsCl cell. Using the projection formalism developed in the context of quasicrystals, the diffraction patterns of the vacancy ordered phases are calculated for both commensurate and incommensurate projection from a periodic cubic cell in four dimensions. These are compared with experimentally observed patterns. It is shown that at increasingly longer periodicity the patterns from commensurate crystals become indistinguishable from the truly quasiperiodic one. It is suggested that there is a strong link between vacancy ordered phases and quasicrystals.

Electric-field-dependent average resistance and the resistance fluctuation in one-dimensional disordered systems

Following an invariant-imbedding approach, we obtain analytical expressions for the ensemble-averaged resistance (ρ) and its Sinai’s fluctuations for a one-dimensional disordered conductor in the presence of a finite electric field F. The mean resistance shows a crossover from the exponential to the power-law length dependence with increasing field strength in agreement with known numerical results. More importantly, unlike the zero-field case the resistance distribution saturates to a Poissonian-limiting form proportional to A‖F‖exp(-A‖F‖ρ) for large sample lengths, where A is constant.

Nonlinear conduction and electrical switching in one-dimensional conductors

Many one-dimensional conductors show pronounced nonlinear electrical conduction. Some of them show very interesting electrical switching from a low conducting state to a high conducting state. Such electrical switching is often associated with memory. These are discussed with particular emphasis on charge transfer complexestmbine-tcnq, tmpd-tcnq, Cs2(tcnq)3,tea-(tcnq) 2 ando-tolidine-iodine.

Information theory and resistance fluctuations in one-dimensional disordered conductors

A novel method is proposed to treat the problem of the random resistance of a strictly one-dimensional conductor with static disorder. For the probability distribution of the transfer matrix R of the conductor we propose a distribution of maximum information entropy, constrained by the following physical requirements: (1) flux conservation, (2) time-reversal invariance, and (3) scaling with the length of the conductor of the two lowest cumulants of ω, where R=exp(iω→⋅Jbhat). The preliminary results discussed in the text are in qualitative agreement with those obtained by sophisticated microscopic theories.

A rational approach to the synthesis of one-dimensional acoustic filters

The velocity ratio algorithm developed from a heuristic study of transfer matrix multiplication has been employed to bring out the relative effects of the elements constituting a linear, one-dimensional acoustic filter, the overall dimensions of which are fixed, and synthesize a suitable straight-through configuration for a low-pass, wide-band, non-dissipative acoustic filter. The potential of the foregoing approach in applications to the rational design of practical acoustic filters such as automotive mufflers is indicated.

Synthesis of a one-dimensional coordination polymer containing pendant hydrosulfide groups

In view of the recent interest in compounds containing M-SH units, an organotin hydrosulfide compound, Me2Sn(SH)(O2CMe) (1) was prepared by controlled hydrolysis of the diorganotin thioacetate. Under similar mild hydrolytic conditions the corresponding benzoate could not be isolated. Instead, the thiobenzoate complex, Me2Sn(SOCPh)(2) (3) was obtained in excellent yields indicating that there was no hydrolysis. Both 1 and 3 were characterized by X-ray crystallography. Some properties of the polymeric compound 1, such as spectral, electrical conductivity and NLO response were also studied. The reactivity and properties were explained using density functional calculations.

Supersolid and solitonic phases in the one-dimensional extended Bose-Hubbard model

We report our findings on the quantum phase transitions in cold bosonic atoms in a one-dimensional optical lattice using the finite-size density-matrix renormalization-group method in the framework of the extended Bose-Hubbard model. We consider wide ranges of values for the filling factors and the nearest-neighbor interactions. At commensurate fillings, we obtain two different types of charge-density wave phases and a Mott insulator phase. However, departure from commensurate fillings yields the exotic supersolid phase where both the crystalline and the superfluid orders coexist. In addition, we obtain the signatures for the solitary waves and the superfluid phase.

Adiabatic quantum computation with a one-dimensional projector Hamiltonian

Adiabatic quantum computation is based on the adiabatic evolution of quantum systems. We analyze a particular class of quantum adiabatic evolutions where either the initial or final Hamiltonian is a one-dimensional projector Hamiltonian on the corresponding ground state. The minimum-energy gap, which governs the time required for a successful evolution, is shown to be proportional to the overlap of the ground states of the initial and final Hamiltonians. We show that such evolutions exhibit a rapid crossover as the ground state changes abruptly near the transition point where the energy gap is minimum. Furthermore, a faster evolution can be obtained by performing a partial adiabatic evolution within a narrow interval around the transition point. These results generalize and quantify earlier works.

Selective detection of single-enantiomer spectrum of chiral molecules aligned in the polypeptide liquid crystalline solvent: Transition selective one-dimensional H-1-H-1 COSY

One-dimensional (1D) proton NMR spectra of enantiomers are generally undecipherable in chiral orienting poly-gamma-benzyl-L-glutamate (PBLG)/CDCl3 solvent. This arises due to large number of couplings, in addition to superposition of spectra from both the enantiomers, severely hindering the H-1 detection. On the other hand in the present study the benefit is derived front the presence of several couplings among the entire network of interacting protons. Transition selective 1D H-1-H-1 correlation experiment (1D-COSY) which utilizes the Coupling assisted transfer of magnetization not only for unraveling the overlap but also for the selective detection of enantiopure spectrum is reported. The experiment is simple, easy to implement and provides accurate eanantiomeric excess in addition to the determination of the proton-proton couplings of an enantiomer within a short experimental time (few minutes). (C) 2009 Elsevier Inc. All rights reserved.

Topological properties of the one dimensional exponential random geometric graph

In this article we study the one-dimensional random geometric (random interval) graph when the location of the nodes are independent and exponentially distributed. We derive exact results and limit theorems for the connectivity and other properties associated with this random graph. We show that the asymptotic properties of a graph with a truncated exponential distribution can be obtained using the exponential random geometric graph. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2008.

One-dimensional zig-zag type coordination polymers of Ni(II) and Cu(II) containing 1,3-benzenedicarboxylate and 1,3-diaminopropane: Structural, spectral and thermal studies

Two coordination polymers [Ni(ipt)(dap)(2)](n) (1) and [Cu(ipt)(dap)H2O](n) center dot nH(2)O (2) with an overall one-dimensional arrangement and having isophthalate (ipt) as bridging moieties and chelating 1,3-diaminopropane (dap) as structure modulating units have been prepared and characterized by crystallographic, spectroscopic and thermo-analytical studies. Both have an overall one-dimensional zig-zag nature but with a distorted octahedral NiN4O2 chromophore for 1 and a distorted square pyramidal CuN2O3 chromophore for 2. Even though the ipt units are acting as bridging units through mono-dentatively coordinating carboxylate functions in both polymers, compound 1 has the carboxylate oxygen linkages at the trans positions, while in 2 the oxygen linkages occur at the cis positions leading to a different type of zig-zag arrangement. Relevant spectral and bonding parameters also could be evaluated for the compounds using UV-Vis and EPR spectra. Thermal stability and possible structural modifications on thermal treatment of the compounds were also investigated and the relevant thermodynamic and kinetic parameters evaluated from the thermal data. (C) 2007 Elsevier B.V. All rights reserved.

A class of one-dimensional steady-state flows in radiation-gas-dynamics

The study of steady-state flows in radiation-gas-dynamics, when radiation pressure is negligible in comparison with gas pressure, can be reduced to the study of a single first-order ordinary differential equation in particle velocity and radiation pressure. The class of steady flows, determined by the fact that the velocities in two uniform states are real, i.e. the Rankine-Hugoniot points are real, has been discussed in detail in a previous paper by one of us, when the Mach number M of the flow in one of the uniform states (at x=+∞) is greater than one and the flow direction is in the negative direction of the x-axis. In this paper we have discussed the case when M is less than or equal to one and the flow direction is still in the negative direction of the x-axis. We have drawn the various phase planes and the integral curves in each phase plane give various steady flows. We have also discussed the appearance of discontinuities in these flows.