Quantum Walks with Entangled Coins

We present a mathematical formalism for the description of unrestricted quantum walks with entangled coins and one walker. The numerical behaviour of such walks is examined when using a Bell state as the initial coin state, two different coin operators, two different shift operators, and one walker. We compare and contrast the performance of these quantum walks with that of a classical random walk consisting of one walker and two maximally correlated coins as well as quantum walks with coins sharing different degrees of entanglement. We illustrate that the behaviour of our walk with entangled coins can be very different in comparison to the usual quantum walk with a single coin. We also demonstrate that simply by changing the shift operator, we can generate widely different distributions. We also compare the behaviour of quantum walks with maximally entangled coins with that of quantum walks with non-entangled coins. Finally, we show that the use of different shift operators on 2 and 3 qubit coins leads to different position probability distributions in 1 and 2 dimensional graphs.Comment: Two new sections and several changes from referees' comments. 12 pages and 12 (colour) figure

Exchange Narrowing Effects in the EPR Linewidth of Gd Diluted in Ce Compounds

Anomalous thermal behavior on the EPR linewidths of Gd impurities diluted in Ce compounds has been observed. In metals, the local magnetic moment EPR linewidth, \Delta H, is expected to increase linearly with the temperature. In contrast, in Ce_{x}La_{1-x}Os_{2} the Gd EPR spectra show a nonlinear increase. In this work, the mechanisms that are responsible for the thermal behavior of the EPR lines in Ce_{x}La_{1-x}Os_{2} are examined. We show that the exchange interaction between the local magnetic moments and the conduction electrons are responsible for the narrowing of the spectra at low temperatures. At high temperatures, the contribution to the linewidth of the exchange interaction between the local magnetic moments and the $Ce$ ions has an exponential dependence on the excitation energy of the intermediate valent ions. A complete fitting of the EPR spectra for powdered samples is obtained.Comment: 11 pages, 1 figur

Thermally activated exchange narrowing of the Gd3+ ESR fine structure in a single crystal of Ce1-xGdxFe4P12 (x = 0.001) skutterudite

We report electron spin resonance (ESR) measurements in the Gd3+ doped semiconducting filled skutterudite compound Ce1-xGdxFe4P12 (x = 0.001). As the temperature T varies from T = 150 K to T = 165 K, the Gd3+ ESR fine and hyperfine structures coalesce into a broad inhomogeneous single resonance. At T = 200 K the line narrows and as T increases further, the resonance becomes homogeneous with a thermal broadening of 1.1(2) Oe/K. These results suggest that the origin of these features may be associated to a subtle interdependence of thermally activated mechanisms that combine: i) an increase with T of the density of activated conduction-carriers across the T-dependent semiconducting pseudogap; ii) the Gd3+ Korringa relaxation process due to an exchange interaction, J_{fd}S.s, between the Gd3+ localized magnetic moments and the thermally activated conduction-carriers and; iii) a relatively weak confining potential of the rare-earth ions inside the oversized (Fe2P3)4 cage, which allows the rare-earths to become rattler Einstein oscillators above T = 148 K. We argue that the rattling of the Gd3+ ions, via a motional narrowing mechanism, also contributes to the coalescence of the ESR fine and hyperfine structure.Comment: 7 pages, 9 figures, accepted for publication in Phys Rev

Nonlinear dynamics of coupled transverse-rotational waves in granular chains

The nonlinear dynamics of coupled waves in one-dimensional granular chains with and without a substrate is theoretically studied accounting for quadratic nonlinearity. The multiple time scale method is used to derive the nonlinear dispersion relations for infinite granular chains and to obtain the wave solutions for semiinfinite systems. It is shown that the sum-frequency and difference-frequency components of the coupled transverse-rotational waves are generated due to their nonlinear interactions with the longitudinal wave. Nonlinear resonances are not present in the chain with no substrate where these frequency components have low amplitudes and exhibit beating oscillations. In the chain positioned on a substrate two types of nonlinear resonances are predicted. At resonance, the fundamental frequency wave amplitudes decrease and the generated frequency component amplitudes increase along the chain, accompanied by the oscillations due to the wave numbers asynchronism. The results confirm the possibility of a highly efficient energy transfer between the waves of different frequencies, which could find applications in the design of acoustic devices for energy transfer and energy rectification

Asymptotic entanglement in a two-dimensional quantum walk

The evolution operator of a discrete-time quantum walk involves a conditional shift in position space which entangles the coin and position degrees of freedom of the walker. After several steps, the coin-position entanglement (CPE) converges to a well defined value which depends on the initial state. In this work we provide an analytical method which allows for the exact calculation of the asymptotic reduced density operator and the corresponding CPE for a discrete-time quantum walk on a two-dimensional lattice. We use the von Neumann entropy of the reduced density operator as an entanglement measure. The method is applied to the case of a Hadamard walk for which the dependence of the resulting CPE on initial conditions is obtained. Initial states leading to maximum or minimum CPE are identified and the relation between the coin or position entanglement present in the initial state of the walker and the final level of CPE is discussed. The CPE obtained from separable initial states satisfies an additivity property in terms of CPE of the corresponding one-dimensional cases. Non-local initial conditions are also considered and we find that the extreme case of an initial uniform position distribution leads to the largest CPE variation.Comment: Major revision. Improved structure. Theoretical results are now separated from specific examples. Most figures have been replaced by new versions. The paper is now significantly reduced in size: 11 pages, 7 figure

Effects of Selected Herbicides on Treated and Rotational Crops

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Matching fields of a long superconducting film

We obtain the vortex configurations, the matching fields and the magnetization of a superconducting film with a finite cross section. The applied magnetic field is normal to this cross section, and we use London theory to calculate many of its properties, such as the local magnetic field, the free energy and the induction for the mixed state. Thus previous similar theoretical works, done for an infinitely long superconducting film, are recovered here, in the special limit of a very long cross section.Comment: Contains a REVTeX file and 4 figure