The antiferromagnetic $J_1-J_2$ model is a spin-1/2 chain with isotropic exchange $J_1 > 0$ between first neighbors and $J_2 = \alpha J_1$ second neighbors. supports both gapless quantum phases nondegenerate ground states gapped $\Delta(\alpha) doubly degenerate states. Exact thermodynamics limited to $\alpha 0$, the linear Heisenberg antiferromagnet (HAF). diagonalization of small systems at f...

In this article, the open problem of finding exact value norm Hilbert matrix operator on weighted Bergman spaces \(A^p_\alpha\) is adressed. The was conjectured to be \(\frac{\pi}{\sin \frac{(2+\alpha)\pi}{p}}\) by Karapetrovic. We obtain a complete solution conjecture for \(\alpha > 0\) and \(2+\alpha+\sqrt{\alpha^2+\frac{7}{2}\alpha+3} \le p < 2(2+\alpha)\) partial \(2+2\alpha 2+\alpha+\sqrt{...

Abstract Fixed-energy quantum inversion method is applied to determine model independent $$\alpha $$ α -particle scattering potentials within the energy range between 0 and 50 MeV. Only experimentally allowed even phase shifts are used in calculation. Detailed results exhibited at low higher energies show up ...

In this paper, we introduce a new quantum divergence$$\Phi (X,Y) = \Tr \left[\left(\dfrac{1-\alpha}{\alpha}+ \dfrac{\alpha}{1-\alpha}\right)X+2Y - \dfrac{X^{1 -\alpha}Y^{\alpha}}{\alpha}- \dfrac{X^{\alpha}Y^{1-\alpha}}{1-\alpha} \right],$$where $0&amp;lt; \alpha &amp;lt;1$.We study the least square problem with respect to divergence. We also show that divergence satisfies Data Processing Inequa...