Related papers: Spin equation and its solutions
It is substantiated that spin is a notion associated with the group of internal symmetry that is tightly connected with the geometrical structure of spacetime. The wave equation for the description of the particles with spin one half is…
30-component, of the first order, equation for a spin 2 particle, equivalent to the second order Pauli-Fierz one, is generalized to presence of an external electromagnetic field as well as a curved background space-time geometry. The…
We present a general procedure for determining possible (nonuniform) magnetic fields such that the Pauli equation becomes quasi-exactly solvable (QES) with an underlying $sl(2)$ symmetry. This procedure makes full use of the close…
We revisit the concepts of spin relaxation and spin decoherence of two level (spin-1/2) systems. From two toy-models, we clarify two issues related to the spin relaxation and decoherence: 1) For an ensemble of two-level particles each…
I give a very brief non-technical introduction to the intersection of the fields of spin systems and computational complexity. The focus is on spin glasses and their relationship to NP-complete problems.
Spin relaxation in the impurity band of a 2D semiconductor with spin-split spectrum in the external magnetic field is considered. Several mechanisms of spin relaxation are shown to be relevant. The first one is attributed to phonon-assisted…
We consider the problem of critical gravitational collapse of a scalar field in 2+1 dimensions with spherical (circular) symmetry. After surveying all the analytic, continuously self-similar solutions and considering their global structure,…
Here I will review the theoretical results that have been obtained for spin glasses. I will concentrate my attention on the predictions of the mean field approach in three dimensional systems and on its numerical and experimental…
We present some open problems in the field of exactly solvable models. Two of the problems are related to the correlation functions of the XXX spin chain and the XXZ spin chain, one to the entropy of subsystems and one to the six vertex…
We apply symmetry and invariance methods to analyse systems of difference equations. Non trivial symmetries are derived and their exact solutions obtained.
Non-orientable nanostructures are becoming feasable today. This lead us to the study of spin in these geometries. Hence a physically sound definition of spin is suggested. Using our definition, we study the question of the number of…
BGG-equations are geometric overdetermined systems of PDEs on parabolic geometries. Normal solutions of BGG-equations are particularly interesting and we give a simple formula for the necessary and sufficient additional integrability…
We provide a concise introduction to the symmetry approach to integrability. Some results on integrable evolution and systems of evolution equations are reviewed. Quasi-local recursion and Hamiltonian operators are discussed. We further…
Spin is commonly thought to reflect the true quantum nature of microphysics. We show that spin is related to intrinsic and field-like properties of single particles. These properties change continuously in external magnetic fields.…
Bilevel optimization is defined as a mathematical program, where an optimization problem contains another optimization problem as a constraint. These problems have received significant attention from the mathematical programming community.…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be thought as a simple two layers star model: a self-gravitating ball built up by two layers of perfect fluid having different linear…
We derive the representation theory of $SU(2)$ from the expository theory of Lie groups and Lie algebras. Based on this, the mathematics of non-relativistic quantum mechanics of a spin $\frac{1}{2}$ particle are described from a…
We review our recent exact solution to four-dimensional higher spin gauge theory invariant under a higher spin extension of SO(3,1) and we comment on its cosmological interpretation. We find an effective Einstein-scalar field theory that…
The short pulse equation (SPE) is considered as an initial-boundary value problem. It is found that the solutions of the SPE must satisfy an integral relation otherwise the temporal derivative exhibits discontinuities. This integral…
This paper is a continuation of the paper by S.P.Novikov in Funct.Anal.Appl., v.24(1990), No 4, pp 196-206. String equation is by definition the equation $[L,A]=1$ for the coefficients of two linear ordinary differential operators $L$ and…