Continuous deformations of the Grover walk preserving localization

The three-state Grover walk on a line exhibits the localization effect characterized by a non-vanishing probability of the particle to stay at the origin. We present two continuous deformations of the Grover walk which preserve its localization nature. The resulting quantum walks differ in the rate at which they spread through the lattice. The velocities of the left and right-traveling probability peaks are given by the maximum of the group velocity. We find the explicit form of peak velocities in dependence on the coin parameter. Our results show that localization of the quantum walk is not a singular property of an isolated coin operator but can be found for entire families of coins

Соотношение путей углеводного синтеза при введении свободных и фосфорилированных сахаров в листья картофеля

Показано, что регуляция путей биосинтеза углеводов может осуществляться через изменение концентрации промежуточных и конечных метаболитов. При этом одним из факторов, регулирующих направленность синтеза углеводов, является активность АДФГ- и УДФГ-пирофосфорилаз. По-видимому, регуляция работы этих ферментов может осуществляться низкомолекулярными метаболитами по принципу обратной связи

Anomalous superconductivity and its competition with antiferromagnetism in doped Mott insulators

Proximity to a Mott insulating phase is likely to be an important physical ingredient of a theory that aims to describe high-temperature superconductivity in the cuprates. Quantum cluster methods are well suited to describe the Mott phase. Hence, as a step towards a quantitative theory of the competition between antiferromagnetism (AFM) and d-wave superconductivity (SC) in the cuprates, we use Cellular Dynamical Mean Field Theory to compute zero temperature properties of the two-dimensional square lattice Hubbard model. The d-wave order parameter is found to scale like the superexchange coupling J for on-site interaction U comparable to or larger than the bandwidth. The order parameter also assumes a dome shape as a function of doping while, by contrast, the gap in the single-particle density of states decreases monotonically with increasing doping. In the presence of a finite second-neighbor hopping t', the zero temperature phase diagram displays the electron-hole asymmetric competition between antiferromagnetism and superconductivity that is observed experimentally in the cuprates. Adding realistic third-neighbor hopping t'' improves the overall agreement with the experimental phase diagram. Since band parameters can vary depending on the specific cuprate considered, the sensitivity of the theoretical phase diagram to band parameters challenges the commonly held assumption that the doping vs T_{c}/T_{c}^{max} phase diagram of the cuprates is universal. The calculated ARPES spectrum displays the observed electron-hole asymmetry. Our calculations reproduce important features of d-wave superconductivity in the cuprates that would otherwise be considered anomalous from the point of view of the standard BCS approach.Comment: 13 pages, 7 figure

Induced local spin-singlet amplitude and pseudogap in high TcT_{c} cuprates

In this paper we show that local spin-singlet amplitude with d-wave symmetry, , can be induced by short-range spin correlations even in the absence of pairing interactions. Fluctuation theory is formulated to make connection between pseudogap temperature $T^{*}$, pseudogap size $\Delta_{pg}$ and . In the present scenario for the pseudogap, the normal state pseudogap is caused by the induced local spin-singlet amplitude due to short-range spin correlations, which compete in the low energy sector with superconducting correlations to make $T_{c}$ go to zero near half-filling. Calculated $T^{*}$ falls from a high value onto the $T_{c}$ line and closely follows mean-field N\'{e}el temperature $T_{N}^{MF}$. The calculated $\Delta_{pg}$ is in good agreement with experimental results. We propose an experiment in which the present scenario can be critically tested.Comment: 5 pages, 3 figure

Fractional recurrence in discrete-time quantum walk

Quantum recurrence theorem holds for quantum systems with discrete energy eigenvalues and fails to hold in general for systems with continuous energy. We show that during quantum walk process dominated by interference of amplitude corresponding to different paths fail to satisfy the complete quantum recurrence theorem. Due to the revival of the fractional wave packet, a fractional recurrence characterized using quantum P\'olya number can be seen.Comment: 10 pages, 11 figure : Accepted to appear in Central European Journal of Physic

Exploring the dark accelerator HESS J1745-303 with Fermi Large Area Telescope

We present a detailed analysis of the gamma-ray emission from HESS J1745-303 with the data obtained by the Fermi Gamma-ray Space Telescope in the first ~29 months observation.The source can be clearly detected at the level of ~18-sigma and ~6-sigma in 1-20 GeV and 10-20 GeV respectively. Different from the results obtained by the Compton Gamma-ray Observatory, we do not find any evidence of variability. Most of emission in 10-20 GeV is found to coincide with the region C of HESS J1745-303. A simple power-law is sufficient to describe the GeV spectrum with a photon index of ~2.6. The power-law spectrum inferred in the GeV regime can be connected to that of a particular spatial component of HESS J1745-303 in 1-10 TeV without any spectral break. These properties impose independent constraints for understanding the nature of this "dark particle accelerator".Comment: 8 pages, 3 figures, 1 table, accepted for publication in Ap

Localization of the Grover walks on spidernets and free Meixner laws

A spidernet is a graph obtained by adding large cycles to an almost regular tree and considered as an example having intermediate properties of lattices and trees in the study of discrete-time quantum walks on graphs. We introduce the Grover walk on a spidernet and its one-dimensional reduction. We derive an integral representation of the $n$-step transition amplitude in terms of the free Meixner law which appears as the spectral distribution. As an application we determine the class of spidernets which exhibit localization. Our method is based on quantum probabilistic spectral analysis of graphs.Comment: 32 page

On the universality of the Discrete Nonlinear Schroedinger Equation

We address the universal applicability of the discrete nonlinear Schroedinger equation. By employing an original but general top-down/bottom-up procedure based on symmetry analysis to the case of optical lattices, we derive the most widely applicable and the simplest possible model, revealing that the discrete nonlinear Schroedinger equation is ``universally'' fit to describe light propagation even in discrete tensorial nonlinear systems and in the presence of nonparaxial and vectorial effects.Comment: 6 Pages, to appear in Phys. Rev.