92 research outputs found
Understanding the optical theorem of scattering: Scattering surface area against scattering cross-section, an example with ellipsoidal scattering
No full textIn this paper, we propose using the scattering surface area rather than the scattering cross-section to characterize the scattering behavior of ellipsoidal rigid bodies. We examined the scattering behavior of ellipsoidal rigid bodies, focusing on the relationship between their surface area and total scattering cross-section. Building on the foundational work of Carson Flammer, we utilize the spheroidal coordinate system to derive solutions for both prolate and oblate spheroids. Our analysis reveals that under the long-wavelength approximation, the total scattering cross-section is equivalent to the surface area of the ellipsoid, a relationship that holds true for both small and moderate eccentricities. This finding extends the established optical theorem, previously validated for spherical bodies, to more complex geometries
Random SU(2) invariant tensors
No full textSU(2) invariant tensors are states in the (local) SU(2) tensor product representation but invariant under the global group action. They are of importance in the study of loop quantum gravity. A random tensor is an ensemble of tensor states. An average over the ensemble is carried out when computing any physical quantities. The random tensor exhibits a phenomenon known as 'concentration of measure', which states that for any bipartition the average value of entanglement entropy of its reduced density matrix is asymptotically the maximal possible as the local dimensions go to infinity. We show that this phenomenon is also true when the average is over the SU(2) invariant subspace instead of the entire space for rank-n tensors in general. It is shown in our earlier work Li et al (2017 New J. Phys. 19 063029) that the subleading correction of the entanglement entropy has a mild logarithmic divergence when n = 4. In this paper, we show that for n > 4 the subleading correction is not divergent but a finite number. In some special situation, the number could be even smaller than 1/2, which is the subleading correction of random state over the entire Hilbert space of tensors.</p
Perturbational Decomposition Analysis for Quantum Ising Model with Weak Transverse Fields
No full textThis work presents a perturbational decomposition method for simulating quantum evolution under the one-dimensional Ising model with both longitudinal and transverse fields. By treating the transverse field terms as perturbations in the expansion, our approach is particularly effective in systems with moderate longitudinal fields and weak to moderate transverse fields relative to the coupling strength. Through systematic numerical exploration, we characterize parameter regimes and evolution time windows where the decomposition achieves measurable improvements over conventional Trotter decomposition methods. The developed perturbational approach and its characterized parameter space may provide practical guidance for choosing appropriate simulation strategies in different parameter regimes of the one-dimensional Ising model
Preparation of novel polyamine-type chelating resin with hyperbranched structures and its adsorption performance
No full textThis paper explored the method of combining atom transfer radical polymerization (ATRP) technology and hyperbranched polymer principle to prepare the high capacity chelating resin. First, surface-initiated atom transfer radical polymerization (SI-ATRP) method was used to graft glycidyl methacrylate (GMA) on chloromethylated cross-linked styrene-divinylbenzene resin, and then the novel polyamine chelating resin with a kind of hyperbranched structure was prepared through the amination reaction between amino group of (2-aminoethyl) triamine and epoxy group in GMA. This resin had a selective effect on As(V) and Cr(VI) at a relatively low pH and can be used for the disposal of waste water containing As(V) and Cr(VI). It had a relatively strong adsorption effect on Cu(II), Pb(II), Cd(II) and Cr(III) and can be used for the disposal of heavy metal ion waste water. The finding was that, the adsorption capacity of resin on the studied heavy metal ions was higher than that of the chelating resin synthesized by traditional technology and also higher than that of the resin modified by ATRP technology and bifunctional chelator, indicating that the combination of ATRP and hyperbranched polymer concept is an effective method to prepare chelating resin with high capacity.</jats:p
Into the Seed: Auxin Controls Seed Development and Grain Yield
No full textSeed development, which involves mainly the embryo, endosperm and integuments, is regulated by different signaling pathways, leading to various changes in seed size or seed weight. Therefore, uncovering the genetic and molecular mechanisms of seed development has great potential for improving crop yields. The phytohormone auxin is a key regulator required for modulating different cellular processes involved in seed development. Here, we provide a comprehensive review of the role of auxin biosynthesis, transport, signaling, conjugation, and catabolism during seed development. More importantly, we not only summarize the research progress on the genetic and molecular regulation of seed development mediated by auxin but also discuss the potential of manipulating auxin metabolism and its signaling pathway for improving crop seed weight
Symmetric versus bosonic extension for bipartite states
No full textA bipartite state ρAB has a k-symmetric extension if there exists a (k+1)-partite state ρAB1B2⋯Bk with marginals ρABi=ρAB, i. The k-symmetric extension is called bosonic if ρAB1B2⋯Bk is supported on the symmetric subspace of B1B2⋯Bk. Understanding the structure of symmetric and bosonic extension has various applications in the theory of quantum entanglement, quantum key distribution, and the quantum marginal problem. In particular, bosonic extension gives a tighter bound for the quantum marginal problem based on separability. In general, it is known that a ρAB admitting symmetric extension may not have bosonic extension. In this work, we show that, when the dimension of the subsystem B is 2 (i.e., a qubit), ρAB admits a k-symmetric extension if and only if it has a k-bosonic extension. Our result has an immediate application to the quantum marginal problem and indicates a special structure for qubit systems based on group representation theory.</p
Preparation of Sandwich-like NiCo2O4/rGO/NiO Heterostructure on Nickel Foam for High-Performance Supercapacitor Electrodes
No full textInvariant perfect tensors
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Invariant tensors are states in the SU(2) tensor product representation that are invariant under SU(2) action. They play an important role in the study of loop quantum gravity. On the other hand, perfect tensors are highly entangled many-body quantum states with local density matrices maximally mixed. Recently, the notion of perfect tensors has attracted a lot of attention in the fields of quantum information theory, condensed matter theory, and quantum gravity. In this work, we introduce the concept of an invariant perfect tensor (IPT), which is an n-valent tensor that is both invariant and perfect. We discuss the existence and construction of IPTs. For bivalent tensors, the IPT is the unique singlet state for each local dimension. The trivalent IPT also exists and is uniquely given by Wigner’s
3
j
symbol. However, we show that, surprisingly, 4-valent IPTs do not exist for any identical local dimension d. On the contrary, when the dimension is large, almost all invariant tensors are asymptotically perfect, which is a consequence of the phenomenon of the concentration of measure for multipartite quantum states
Highly porous graphitic biomass carbon as advanced electrode materials for supercapacitors
No full text3D porous graphitic biomass carbon as advanced supercapacitor electrode materials synthesized by a low-cost and effective one-step method.</p
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