Relationship Between Quantum Walk and Relativistic Quantum Mechanics

Quantum walk models have been used as an algorithmic tool for quantum computation and to describe various physical processes. This paper revisits the relationship between relativistic quantum mechanics and the quantum walks. We show the similarities of the mathematical structure of the decoupled and coupled form of the discrete-time quantum walk to that of the Klein-Gordon and Dirac equations, respectively. In the latter case, the coin emerges as an analog of the spinor degree of freedom. Discrete-time quantum walk as a coupled form of the continuous-time quantum walk is also shown by transforming the decoupled form of the discrete-time quantum walk to the Schrodinger form. By showing the coin to be a means to make the walk reversible, and that the Dirac-like structure is a consequence of the coin use, our work suggests that the relativistic causal structure is a consequence of conservation of information. However, decoherence (modelled by projective measurements on position space) generates entropy that increases with time, making the walk irreversible and thereby producing an arrow of time. Lieb-Robinson bound is used to highlight the causal structure of the quantum walk to put in perspective the relativistic structure of quantum walk, maximum speed of the walk propagation and the earlier findings related to the finite spread of the walk probability distribution. We also present a two-dimensional quantum walk model on a two state system to which the study can be extended.Comment: 12 pages and 1 figure, Published versio

Tuning of tetrahedrality in a silicon potential yields a series of monatomic (metal-like) glassformers of very high fragility

We obtain monatomic glass formers in simulations by modifying the tetrahedral character in a silicon potential to explore a triple point zone between potentials favoring diamond (dc) and bcc crystals. dc crystallization is always preceded by a polyamorphic transformation of the liquid, and is frustrated when the Kauzmann temperature of the high temperature liquid intersects the liquid-liquid coexistence line. The glass forming liquids are extraordinarily fragile. Our results suggest that Si and Ge liquids may be vitrified at a pressure close to the diamond-beta-tin-liquid triple point.Comment: 12 pages, including 3 figures. This revised version covers the same as the original submission plus a discussion of the effect of the polyamorphic transformation on the glass formation ability of the tetrahedral liquids studie

Crossover to Potential Energy Landscape Dominated Dynamics in a Model Glass-forming Liquid

An equilibrated model glass-forming liquid is studied by mapping successive configurations produced by molecular dynamics simulation onto a time series of inherent structures (local minima in the potential energy). Using this ``inherent dynamics'' approach we find direct numerical evidence for the long held view that below a crossover temperature, $T_x$, the liquid's dynamics can be separated into (i) vibrations around inherent structures and (ii) transitions between inherent structures (M. Goldstein, J. Chem. Phys. {\bf 51}, 3728 (1969)), i.e., the dynamics become ``dominated'' by the potential energy landscape. In agreement with previous proposals, we find that $T_x$ is within the vicinity of the mode-coupling critical temperature $T_c$. We further find that at the lowest temperature simulated (close to $T_x$), transitions between inherent structures involve cooperative, string like rearrangements of groups of particles moving distances substantially smaller than the average interparticle distance.Comment: Expanded from 4 to 7 page

Bilarge neutrino mixing in R-parity violating supersymmetry: the role of right-chiral neutrino superfields

We consider the possibility of neutrino mass generation in a supersymmetric model where lepton number can be violated by odd units. The different patterns of mixing in the quark and lepton sectors are attributed to the persence of right-chiral neutrino superfields which (a) enter into Yukawa couplings via non-renormalizable interaction with hidden sector fields, and (b) can violate lepton number by odd units. Both of these features are shown to be the result of some global quantum number which is violated when SUSY is broken in the hidden sector. It is shown how such a scenario, together with all known R-parity violating effects, can lead to neutrino masses and bilarge mixing via seesaw as well as radiative mechanisms. Some sample values of the various parameters involved, consistent with electroweak symmetry breaking constraints, are presented as illustrations.Comment: 19 pages. Minor modificaitons are made in the text. This version is to appear in Physical Review

A quantum information theoretic analysis of three flavor neutrino oscillations

Correlations exhibited by neutrino oscillations are studied via quantum information theoretic quantities. We show that the strongest type of entanglement, genuine multipartite entanglement, is persistent in the flavour changing states. We prove the existence of Bell-type nonlocal features, in both its absolute and genuine avatars. Finally, we show that a measure of nonclassicality, dissension, which is a generalization of quantum discord to the tripartite case, is nonzero for almost the entire range of time in the evolution of an initial electron-neutrino. Via these quantum information theoretic quantities capturing different aspects of quantum correlations, we elucidate the differences between the flavour types, shedding light on the quantum-information theoretic aspects of the weak force.Comment: 9 pages, 6 figure

Dynamic Radio-Frequency Transverse Susceptibility in Magnetic Nanoparticle Systems

A novel resonant method based on a tunnel-diode oscillator (TDO) is used to study the dynamic transverse susceptibility in a Fe nanoparticle system. The magnetic system consists of an aggregate of nanometer-size core (Au)-shell (Fe) structure, synthesized by reverse micelle methods. Static and dynamic magnetization measurements carried out in order to characterize the system reveal a superparamagnetic behavior at high temperature. The field-dependent transverse susceptibility at radio-frequencies (RF), for different temperatures reveals distinct peak structure at characteristics fields (H_k, H_c) which changes with temperature. It is proposed that relaxation processes could explain the influence of the temperature on the field dependence of the transverse susceptibility on the MI.Comment: 3 pages, 2-column, 3 figures, To be published in J. Appl. Phys. 2000 (44th Annual MMM proceedings

Studies on mechanical behavior of glass epoxy composites with induced defects and correlations with NDT characterization parameters

Degradation in mechanical properties (compression, flexural and ILS) of glass epoxy composite laminates with induced defects (simulating delaminations) was studied. The defects were characterized by using the A-scan ultrasonic pulse-echo technique. The two A-scan parameters, viz. the back wall echo amplitude and time of flight, were followed respectively, as functions of the defect size (diameter) and its location in the laminate thickness. The mechanical properties of laminates were evaluated destructively for different defect sizes and locations. An attempt has been made to express the mechanical properties in terms of the two NDT scan parameters characterizing the defects and empirical equations presente

An algorithm for clock synchronization with the gradient property in sensor networks

We introduce a distributed algorithm for clock synchronization in sensor networks. Our algorithm assumes that nodes in the network only know their immediate neighborhoods and an upper bound on the network's diameter. Clock-synchronization messages are only sent as part of the communication, assumed reasonably frequent, that already takes place among nodes. The algorithm has the gradient property of [2], achieving an O(1) worst-case skew between the logical clocks of neighbors. As in the case of [3,8], the algorithm's actions are such that no constant lower bound exists on the rate at which logical clocks progress in time, and for this reason the lower bound of [2,5] that forbids constant skew between neighbors does not apply