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A theoretical study has been carried out to analyze the available results from the inelastic neutron scattering experiment performed on a quasi-two dimensional spin-1 2 ferromagnetic material K 2 CuF 4 . Our formalism is based on a conventional semi-classical like treatment involving a model of an ideal gas of vortices/anti-vortices corresponding to an anisotropic XY Heisenberg ferromagnet on a square lattice. The results for dynamical structure functions for our model corresponding to spin-1 2 , show occurrence of negative values in a large range of energy transfer even encompassing the experimental range, when convoluted with a realistic spectral window function. This result indicates failure of the conventional theoretical framework to be applicable to the experimental situation corresponding to low spin systems. A full quantum formalism seems essential for treating such systems. PACS: 78.70.Nx-inelastic neutron scattering in condensed matter, 75.10.Jm-Heisenberg model, 75.30.Kz-Kosterlitz-Thouless transition in magnetic systems *

Discrete time-crystals are periodically driven quantum many-body systems with broken discrete time translational symmetry, a non-equilibrium steady state representing self-organization of motion of quantum particles. Observations of discrete time-crystalline order are currently limited to magneto-optical experiments and it was never observed in a transport experiment performed on systems connected to external electrodes. Here we demonstrate that both discrete time-crystal and quasi-crystal survive a very general class of environments corresponding to single-particle gain and loss through system-electrode coupling over experimentally relevant timescales. Using dynamical symmetries, we analytically identify the conditions for observing time-crystalline behavior in a periodically driven open Fermi-Hubbard chain attached to electrodes. We show that the spin-polarized transport current directly manifests the existence of a time-crystalline behavior. Our findings are verifiable in present-day experiments with quantum-dot arrays and Fermionic ultra-cold atoms in optical lattices.

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This article is concerned with construction of planar parametric surfaces enclosed by four arbitrary boundary curves. The available conventional methods for this purpose are algebraic interpolation method (like the Coons method) and partial differential equation method. These methods usually yield some problems. This article proposes a new method namely boundary interpolation method where the geometric properties of the boundary curves have been taken into account. A technique of simultaneous displacement of the interpolated curves from the opposite boundaries has been adopted. The geometric properties considered for displacement include weighted combination of geometric and linear displacement vectors of the two opposite generating curves. The algorithm has two adjustable parameters that control the characteristics of interpolation of one set of curves from their parents. Case studies show that this algorithm gives reasonably smooth boundary-fitted planar parametric surface compared with the other two conventional methods.