108 research outputs found

    Spectral density of the quantum Ising model in two fields: Gaussian and multi-Gaussian approximations

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    Spectral density of quantum Ising model in two fields for large but finite number of spins NN, is discussed in detail. When all coupling constants are of the same order, spectral densities in the bulk are well approximated by a Gaussian function which is typical behaviour for many-body models with short-range interactions. The main part of the paper is devoted to the investigation of a different characteristic case when spectral densities have peaks related with strong degeneracies of unperturbed states in certain limits of coupling constants. In the strict limit N→∞N\to\infty, peaks overlap and disappear but for values of NN accessible in numerical calculations they often strongly influence spectral densities and other quantities as well. A simple method is developed which permits to find general approximation formulae for multi-peak structure of spectral density in good agreement with numerics.Comment: 32 pages, 13 figure

    The distribution of the ratio of consecutive level spacings in random matrix ensembles

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    We derive expressions for the probability distribution of the ratio of two consecutive level spacings for the classical ensembles of random matrices. This ratio distribution was recently introduced to study spectral properties of many-body problems, as, contrary to the standard level spacing distributions, it does not depend on the local density of states. Our Wigner-like surmises are shown to be very accurate when compared to numerics and exact calculations in the large matrix size limit. Quantitative improvements are found through a polynomial expansion. Examples from a quantum many-body lattice model and from zeros of the Riemann zeta function are presented.Comment: 5 pages, 4 figure

    Exact nonequilibrium dynamics of finite-temperature Tonks-Girardeau gases

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    Describing finite-temperature nonequilibrium dynamics of interacting many-particle systems is a notoriously challenging problem in quantum many-body physics. Here we provide an exact solution to this problem for a system of strongly interacting bosons in one dimension in the Tonks-Girardeau regime of infinitely strong repulsive interactions. Using the Fredholm determinant approach and the Bose-Fermi mapping we show how the problem can be reduced to a single-particle basis, wherein the finite-temperature effects enter the solution via an effective "dressing" of the single-particle wavefunctions by the Fermi-Dirac occupation factors. We demonstrate the utility of our approach and its computational efficiency in two nontrivial out-of-equilibrium scenarios: collective breathing mode oscillations in a harmonic trap and collisional dynamics in the Newton's cradle setting involving real-time evolution in a periodic Bragg potential.Comment: Final published version in PRA style; moved Supplemental Material into main text; 6 pages, 3 figure

    Collective many-body bounce in the breathing-mode oscillations of a Tonks-Girardeau gas

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    We analyse the breathing-mode oscillations of a harmonically quenched Tonks-Giradeau (TG) gas using an exact finite-temperature dynamical theory. We predict a striking collective manifestation of impenetrability---a collective many-body bounce effect. The effect, while being invisible in the evolution of the in-situ density profile of the gas, can be revealed through a nontrivial periodic narrowing of its momentum distribution, taking place at twice the rate of the fundamental breathing-mode frequency. We identify physical regimes for observing the many-body bounce and construct the respective nonequilibrium phase diagram as a function of the quench strength and the initial temperature of the gas. We also develop a finite-temperature hydrodynamic theory of the TG gas, wherein the many-body bounce is explained by an increased thermodynamic pressure of the gas during the isentropic compression, which acts as a potential barrier at the inner turning points of the breathing cycle.Comment: 5 pages, 4 figures, and Supplemental Material. arXiv admin note: substantial text overlap with arXiv:1608.0872

    REMOVAL OF BASIC BLUE 3 AND REACTIVE ORANGE 16 BY ADSORPTION ONTO QUARTENIZED SUGAR CANE BAGASSE

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    Abstract The effectiveness of using sugar cane bagasse, an agricultural by-product, as a sorbent to remove basic and reactive dyes from aqueous solution was studied. The quartenized sugar cane bagasse (QSB) is capable in removing both Basic Blue 3 (BB3) and Reactive Orange 16 (RO16). The sorption of dye solutions was strongly affected by pH, where the optimum pH is 6-8. The kinetics of the dye sorption processes fitted a pseudo-second order kinetic model. Results indicated that the adsorption isotherms fitted well into both the Langmuir and Freundlich isotherms. The removal of BB3 was favourable at higher temperature, indicating that the sorption process was endothermic. On the other hand, sorption of RO16 on QSB was more favourable at low temperature. Keywords: Sugar cane bagasse; quartenization; sorption; reactive dyes; basic dyes Abstrak Keberkesanan menggunakan sisa tebu, produk sampingan pertanian, sebagai penjerap untuk menyingkirkan pewarna basik dan reaktif daripada larutan telah dikaji. Sisa tebu yang diquarternasi (QSB) adalah berupaya untuk menyingkirkan keduadua pewarna Basik Biru 3 (BB3) dan Reaktif Oren 16 (RO16). Penjerapan pewarna adalah dipengaruhi oleh pH, di mana pH optimum ialah 6-8. Kinetik proses erapan pewarna didapati mengikut model kinetik tertib pseudo-kedua. Keputusan eksperimen menunjukkan bahawa isoterma penjerapan mematuhi kedua-dua isoterma Langmuir dan Freundlich. Penyingkiran BB3 adalah lebih baik pada suhu tinggi, menunjukkan proses erapan adalah endotermik. Manakala erapan RO16 ke atas QSB adalah lebih digemari pada suhu rendah

    Transverse Electronic Transport through DNA Nucleotides with Functionalized Graphene Electrodes

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    Graphene nanogaps and nanopores show potential for the purpose of electrical DNA sequencing, in particular because single-base resolution appears to be readily achievable. Here, we evaluated from first principles the advantages of a nanogap setup with functionalized graphene edges. To this end, we employed density functional theory and the non-equilibrium Green's function method to investigate the transverse conductance properties of the four nucleotides occurring in DNA when located between the opposing functionalized graphene electrodes. In particular, we determined the electrical tunneling current variation as a function of the applied bias and the associated differential conductance at a voltage which appears suitable to distinguish between the four nucleotides. Intriguingly, we observe for one of the nucleotides a negative differential resistance effect.Comment: 19 pages, 7 figure
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