Related papers: Second-order integrals for systems in $E_2$ involv…
We consider periodic second-order equations having an ordered pair of lower and upper solutions and show the existence of asymptotic trajectories heading towards the maximal and minimal periodic solutions which lie between them.
Integrable spin systems are an important subclass of integrable (soliton) nonlinear equations. They play important role in physics and mathematics. At present, many integrable spin systems were found and studied. They are related with the…
We are interested in existence results for second order differential inclusions, involving finite number of unilateral constraints in an abstract framework. These constraints are described by a set-valued operator, more precisely a proximal…
We obtain bi-Hamiltonian structure for a family of integrable systems on the sphere S with an additional integral of third order in momenta. These results are applied to the Goryachev system and Goryachev-Chaplygin top for which we give an…
We discuss an elementary derivation of variational symmetries and corresponding integrals of motion for the Lagrangian systems depending on acceleration. Providing several examples, we make the manuscript accessible to a wide range of…
We develop an approximate second quantization method for describing the many-particle systems in the presence of bound states of particles at low energies (the kinetic energy of particles is small in comparison to the binding energy of…
The double-slit experiment is the most direct demonstration of interference between individual quantum objects. Since similar experiments with single particles and more slits produce interference fringes reducible to a combination of…
We propose a Hamiltonian for a nonrelativistic spin 1/2 \QTR{it}{free} particle (e.g. an electron) and find that it contains information of its internal degrees of freedom in the rest coordinate system. We comment on the dynamical symmetry…
The paper presents a detailed theoretical-group analysis of three types of two-component equations of motion which describe the particle with zero mass and spin 1/2. There are studied P-, T- and C-propertias of the equations obtained.
The tensorial form of the spin-other-orbit interaction operator in the formalism of second quantization is presented. Such an expression is needed to calculate both diagonal and off-diagonal matrix elements according to an approach, based…
The coupling of non-relativistic anyons (called exotic particles) to an electromagnetic field is considered. Anomalous coupling is introduced by adding a spin-orbit term to the Lagrangian. Alternatively, one has two Hamiltonian structures,…
The fractional quantization of singular systems with second order Lagrangian is examined. The fractional singular Lagrangian is presented. The equations of motion are written as total differential equations within fractional calculus. Also,…
In [1] was considered the superintegrable system which describes the magnetic dipole with spin 1/2 (neutron) in the field of linear current. Here we present its generalization for any spin which preserves superintegrability. The dynamical…
We formulate a new model which describes higher-spin gauge interactions for matter fields in two dimensions. This model is a higher-spin generalization of d2 gravity and turns out to be integrable. No vanishing higher-spin current…
A one-dimensional model of coupled spin-1/2 spins and pseudospin-1/2 orbitals with nearest-neighbor interaction is rigorously shown to exhibit spin-orbital separation by means of a non-local unitary transformation. On an open chain, this…
We consider Euclidean path integrals with higher derivative actions, including those that depend quadratically on acceleration, velocity and position. Such path integrals arise naturally in the study of stiff polymers, membranes with…
We present a quantum kinetic theory for spin-$1/2$ particles, including the spin-orbit interaction, retaining particle dispersive effects to all orders in $\hbar$, based on a gauge-invariant Wigner transformation. Compared to previous…
Second order supersymmetric approach is taken to the system describing motion of a quantum particle in a potential endowed with position-dependent effective mass. It is shown that the intertwining relations between second order partner…
We study the properties of spin systems realized by cold polar molecules interacting via dipole-dipole interactions in two dimensions. Using a spin wave theory, that allows for the full treatment of the characteristic long-distance tail of…
The purpose of the present note is to propose, in the framework of relativistic quantum mechanics, a new Poincare-invariant equation for two particles with masses m_1, m_2 and spin s_1=s_2=1/2. It is a first-order linear differential…