On the ideal centre of the space of vector valued integrable functions

Let E be a Banach lattice and L¹(μ, E) be the space of E-valued Bochner integrable functions. Some order properties of L¹(μ, E) are given. It is shown that L_s^∞(μ, Z(E)) is the ideal centre of L¹(μ, E) and it is obtained a Radon-Nikodym type theorem for B -integrable functions.      

Iridium(III) hydrido amino acid compounds: Chiral complexes and a helical extended lattice

[Ir(COD)(PMe₃)₃]Cl, 1, reacts with amino acids in water to yield cationic hydride amino acid complexes, [Ir(aa)(H)(PMe₃)₃]Cl, 2. In general, complexes 2 display octahedral geometry with a meridional arrangement of the PMe₃ ligands, with the amino acid chelating through O and N and with hydride trans to N. Disubstituted amino acids on the other hand favor the formation of octahedral complexes with a facial arrangement of PMe₃ ligands. The crystal structure of the valine complex, 2c, was obtained and, in addition to confirming the structure of the complex, showed a helical extended lattice structure due to intermolecular N-H-O bonding.     

Control of tripod-scheme cold-atom wavepackets by manipulating a non-Abelian vector potential

Tripod-scheme cold atoms interacting with laser beams have attracted considerable interest for their role in synthesizing effective non-Abelian vector potentials. Such effective vector potentials can be exploited to realize an all-optical imprinting of geometric phases onto matter waves. By working on carefully designed extensions of our previous work, we show that coherent lattice structure of cold-atom sub-wavepackets can be formed and that the non-Abelian Aharonov-Bohm effect can be easily manifested via the translational motion of cold atoms. We also show that by changing the frame of reference, effects due to a non-Abelian vector potential may be connected with a simple dynamical phase effect, and that under certain conditions it can be understood as an Abelian geometric phase in a different frame of reference. Results should help design better schemes for the control of cold-atom matter waves.     

Multi-Soliton Solutions and Integrable Discretization for a Coupled Modified Volterra Lattice Equation

In this paper, we study a coupled modified Volterra lattice equation which is an integrable semidiscrete version of the coupled KdV and the coupled mKdV equation. By using the Darboux transformation, we obtain its new explicit solutions including multi-soliton and multi-positon. Furthermore, an integrable discretization of the coupled modified Volterra lattice equation is constructed.     

Possible extinction of Berezinskii–Kosterlitz–Thouless transition by diagonal interactions in the checkerboard lattice

We study the thermodynamics of the classical anisotropic antiferromagnetic Heisenberg model in a checkerboard lattice. The checkerboard lattice is distinguished from the antiferromagnetic square lattice (with coupling constant J) by the presence of a diagonal crossing (coupling constant $J^{\prime }$) in half of the sites. This lattice model is the direct analog of the three-dimensional pyrochlore lattice on a two-dimensional surface. Besides, we considered a single-ion anisotropy D that breaks the $O(3)$ symmetry and contributes to planar spin fields. Since the model is two-dimensional endowed with an $O(2)$ symmetry, a Berezinskii–Kosterlitz–Thouless (BKT) transition is expected to take place. We also investigated the BKT temperature as a function of the coupling constants $J^{\prime }$ and D. The problem is developed through a continuous representation given by the $O(3)$ Nonlinear Sigma Model (NLSM). Computer simulations were also carried out, and the results were in accordance with the analytical model.     

Spin-1/2 Ising model on a AFM/FM two-layer Bethe lattice in a staggered magnetic field

A bilayer spin-1/2 Ising model consisting of two superposed Bethe lattices with antiferromagnetic/ferromagnetic interactions is studied by the use of exact recursion relations in a pairwise approach in the presence of an external staggered magnetic field. Besides the ground state phase diagrams calculated in different possible planes of the model parameters space, the thermal variations of the order-parameters and the free energy are investigated to obtain the temperature-dependent phase diagrams of the model for different values of the coordination numbers q. Our calculations reveal that depending on the strength of the model parameters, the model exhibits a variety of interesting phase transitions and therefore phase diagrams.     

The Distributional Henstock-Kurzweil Integral and Applications: A Survey

This study presents a summary of the current state of research on the distributional Henstock-Kurzweil integral. Basic properties such as integration by parts, Hake theorem, inner product, Hölder inequality, second mean value theorem, orderings, Banach lattice, convergence theorems, fixed point theorems, are shown. This study also summarizes its applications in integral and differential equations.     

SU(2) symmetry in a Hubbard model with spin-orbit coupling

We study the underlying symmetry in a spin-orbit coupled tight-binding model with Hubbard interaction. It is shown that, in the absence of the on-site interaction, the system possesses the SU(2) symmetry arising from the time reversal symmetry. The influence of the on-site interaction on the symmetry depends on the topology of the networks: The SU(2) symmetry is shown to be the spin rotation symmetry of a simply-connected lattice even in the presence of the Hubbard interaction. On the contrary, the on-site interaction breaks the SU(2) symmetry of a multi-connected lattice. This fact indicates that a discrete spin-orbit coupled system has exclusive features from its counterpart in a continuous system. The obtained rigorous result is illustrated by a simple ring system.