Quantum spin system with quenched randomness are both important and theoretically challenging. They are widely used as models for metallic alloys in condensed matter physics, see [2] for a review. They are also important in combinatorial optimization problems especially in relation to quantum annealing procedures [3] and quantum error correcting codes [4]. One approach to studying such macrosco...

Abstract The aim of this paper is to study the oscillation solutions nonlinear degenerate elliptic equation in Heisenberg group $H^{n}$ H n . We first derive a critical inequality Based on it, we establish Picone-type differential and Sturm-type comparison principle. Th...

The inclusion of a Dzyaloshinskii-Moriya short-range antisymmetric interaction in the Heisenberg Hamiltonian induces spontaneous magnetization, at nonzero temperatures, in one and two dimensions. It is shown that quantum fluctuations are reduced by the DzyaloshinskiiMoriya interaction, but short-range correlations are increased, thereby allowing the existence of long-range magnetic order in the...

The special affine Fourier transform (SAFT) is an extended version of the classical and incorporates various signal processing tools which include transforms, fractional transform, linear canonical other related transforms. This paper aims to introduce a novel octonion (O−SAFT) establish several classes uncertainty inequalities for proposed transform. We begin by studying norm split energy cons...