A separated spin evolution quantum hydrodynamics model is employed to study low frequency electrostatic waves in plasmas having inertia-less degenerate electrons with spin-up ne↑ and spin-down ne↓ states and inertial classical ions. A two-dimensional plasma geometry is assumed having a uniform magnetic field, directed along the z-axis, i.e., B=B0ẑ. A Zakharov-Kuznetsov (ZK) type equation is derived for the electrostatic potential via the Reductive Perturbation Technique. The parametric role of the spin density polarization ratio κ in the characteristics of solitary wave structures is investigated. We have observed that both the amplitude and width of the soliton are significantly affected by the spin polarization but the amplitude remains largely un-affected by variation in the magnetic field strength. We have also carried out pulse stability analysis and have found that the pulse soliton solution of the ZK equation is unstable to oblique perturbations. The dependence of the instability growth rate on the density polarization ratio κ along with other significant plasma parameters is traced analytically. We have shown that the first order growth rate of the instability decreases with an increase in the angle between the transverse component of the perturbation and the direction of the magnetic field, in the range (0≤θ<37.8°). We have also observed that the spin polarization affects the growth and increases as we move from the strongly spin-polarized plasma to a zero polarization case.
We investigate the evolution of a discrete-time one-dimensional quantum walk driven by a position-dependent coin. The rotation angle, which depends upon the position of a quantum particle, parameterizes the coin operator. For different values of the rotation angle, we observe that such a coin leads to a variety of probability distributions, e.g. localized, periodic, classical-like, semi-classical-like, and quantum-like. Further, we study the Shannon entropy associated with position and the coin space of a quantum particle, and compare them with the case of the position-independent coin. Our results show that the entropy is smaller for most values of the rotation angle as compared to the case of the position-independent coin. We also study the effect of entanglement on the behavior of probability distribution and Shannon entropy by considering a quantum walk with two identical position-dependent entangled coins. We observe that in general, a wave function becomes more localized as compared to the case of the position-independent coin and hence the corresponding Shannon entropy is lower. Our results show that a position-dependent coin can be used as a controlling tool of quantum walks.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.