Related papers: Note on Spin Structure of the Classical Vector Spi…
We perform a systematic exact algebraic search for integrable spin-S chains which are isotropic in spin space, i.e. are su(2)-invariant. The families of spin chains found for S < 14 support recent arguments in favour of the complete…
The possible spatial transformation properties of tetrons are discussed.
A short survey of the semiclassical periodic orbit theory, initiated by M. Gutzwiller and generalized by many other authors, is given. Via so-called semiclassical trace formmulae, gross-shell effects in bound fermion systems can be…
The XY Heisenberg spin 1/2 chain is considered in the fermion representation. The construction of the ground state-vector is based on the group-theoretical approach. The exact expression for the ground state-vector will allow to study the…
An intriguing correspondence between certain finite planar tessellations and the Descartes circle arrangements is presented. This correspondence may be viewed as a visualization of the spinor structure underlying Descartes circles.
This study proposes a theoretical model for studying the spin characteristics and angular correlations of fission fragments of heavy nuclei. The mechanisms of spin formation, including the influence of transverse vibrations, are considered…
Several topics related to quantum spin models of Calogero-Sutherland type, partially solvable spin chains and Polychronakos's "freezing trick" are rigorously studied.
We describe the different classes of $\mathrm{Spin(7)}$ structures in terms of spinorial equations. We relate them to the spinorial description of $\mathrm{G}_2$ structures in some geometrical situations. Our approach enables us to analyze…
We construct analogues of the classical Heisenberg spin chain model (or the discrete Neumann system) on pseudo-spheres and light-like cones in the pseudo-Euclidean spaces and show their complete Hamiltonian integrability. Further, we prove…
Mixed quantum-classical spin systems have been proposed in spin chain theory and, more recently, in magnon spintronics. However, current models of quantum-classical dynamics beyond mean-field approximations typically suffer from…
Several examples for the role of orbital angular momentum and spin-orbit correlations in hadron structure are discussed.
Two-dimensional hexagonal and oblique lattices were investigated theoretically with the aim of observing differences in the spin expectation values between chiral and achiral systems. The spinresolved band structures were derived from the…
The Heisenberg model, a quantum mechanical analogue of the Ising model, has a large ground state degeneracy, due to the symmetry generated by the total spin. This symmetry is also responsible for degeneracies in the rest of the spectrum. We…
A universal minimal spinor set of linear differential equations describing anyons and ordinary integer and half-integer spin fields is constructed with the help of deformed Heisenberg algebra with reflection. The construction is generalized…
We review here some general properties of antiferromagnetic Heisenberg spin chains, emphasizing and discussing the role of hidden symmetries in the classification of the various phases of the models. We present also some recent results that…
We investigate topological properties of a completely integrable system on $S^2\times S^2 \times S^2$ which was recently shown to have a Lagrangian fiber diffeomorphic to $\mathbb{R} P^3$ not displaceable by a Hamiltonian isotopy [Oakley…
In this continuation paper the Schr\"odinger equation for the half-integral spin eigenfunctions is obtained and solved. We show that all the properties already derived using the Heisemberg matrix calculation and Pauli's matrices are also…
In the present note we elucidate how physical considerations based on Planck's oscillator led to the construction of Heisenberg's mechanics.
This article deals with the structure of analytic and entire vectors for the Schr\"{o}dinger representations of the Heisenberg group. Using refined versions of Hardy's theorem and their connection with Hermite expansions we obtain very…
Highly spin selective transport of electrons through a helically shaped electrostatic potential is demonstrated in the frame of a minimal model approach. The effect is significant even in the case of weak spin-orbit coupling. Two main…