Reports on Mathematical Physics最新文献

We write the electromagnetic self-force of a non-Lorentz-contractible uniformly charged shell of radius a as a series in powers of a, and we calculate the first three terms of this expansion. The method of calculation presented here allows the exact consideration of all linear and nonlinear terms in velocity and its derivatives corresponding to a given power of a. Our calculation is entirely done in the laboratory frame of reference.

We consider the factor υ of the characteristic polynomial w^H (x) of the Heisenberg Hamiltonian Ĥ of the XXX model, corresponding to the generic star [k = ±1, ±3] of quasimomentum k for octagonal (N = 8) magnetic ring in the two-magnon sector. This factor is recognized as the fourth-degree polynomial with integer coefficients, indecomposable over the prime number field ℚ of rationals. We demonstrate the physical meaning of the corresponding Galois group as the group of permutations of eigenenergies between the quasimomenta entering the generic star of the Brillouin zone of octagon. In particular, we point out the role of intersection of this group with Galois group of the cyclotomic field, responsible for the translational symmetry of octagon. Bound and scattered two-magnon eigenstates are identified by their spectra. Some general remarks are made on Galois symmetries within the XXX integrable model.

This article concerns the study of perfect fluid spacetimes equipped with different types of gradient solitons. It is shown that if a perfect fluid spacetime with Killing velocity vector admits a τ-Einstein soliton of gradient type, then the spacetime represents phantom regime, or ψ remains invariant under the velocity vector field ρ. Besides, we establish that in a perfect fluid spacetime with constant scalar curvature, if the Lorentzian metric is the gradient τ-Einstein soliton, then either the τ-Einstein gradient potential function is pointwise collinear with ρ, or the spacetime represents stiff matter fluid. Furthermore, we prove that under certain conditions, a perfect fluid spacetime turns into a generalized Robertson–Walker spacetime, as well as a static spacetime and such a spacetime is of Petrov type I, D or O. We also characterize perfect fluid spacetimes whose Lorentzian metric is equipped with gradient m-quasi Einstein solitons and that the perfect fluid spacetime has vanishing expansion scalar, or it represents dark energy era under certain restriction on the potential function.

It is shown that in presence of certain external fields a well-defined self-adjoint time operator exists, satisfying the standard canonical commutation relations with the Hamiltonian. Examples include uniform electric and gravitational fields with nonrelativistic and relativistic Hamiltonians. The physical intepretation of these operators is proposed in terms of time of arrival in the momentum space.

In the present paper, translation-invariant and periodic ground states are described for a mixed spin Ising model with competing interactions on the Cayley tree of order two. The limiting behaviour of various Gibbs measures of our mixed spin Ising model is discussed as well.

In this paper, the structure of Jacobi vector fields on warped product manifolds is investigated. Many characterizations of Jacobi vector fields on warped product manifolds are obtained. Consequently, conjugate points on warped product manifolds are also considered. Finally, we apply our results to characterize conjugate points of some well-known warped product spacetimes.

Nonlocal constants are functions that are constant along motion but whose value depends on the past history of the motion itself. They have been introduced to study ODEs and, among all applications, they provide first integrals in special cases. In this respect, a new approach to get nonlocal constants within the framework of Lagrangian scalar field theory is introduced. We derive locally-conserved currents from them, and we prove the consistency of our results by recovering some standard Noetherian results. Applications include the real/complex nonlinear interacting theory and the real dissipative Klein–Gordon theory.

In this work, we study cyclic codes of length n over a finite commutative non-chain ring$ℛ=F_q\left[u,v\right]/〈u^2-\gamma u,v^2-ϵv,uv-vu〉$ where$\gamma ,ϵ\in F_q^{*}$ and we find new and better quantum error-correcting codes than previously known quantum error correcting codes. Then certain constraints are imposed on the generator polynomials of cyclic codes, so these codes become linear complementary dual codes (in short LCD codes). We then verify that the Gray image of linear complementary dual codes of length n over$ℛ$ is a linear complementary dual code of length 4n over$F_q$ by establishing a Gray map.

In a previous paper [4] we tried to build the basic theory of unbounded Tomita's observable algebras called T^†-algebras which are related to unbounded operator algebras, especially unbounded Tomita-Takesaki theory, operator algebras on Krein spaces, studies of positive linear functionals on *-algebras and so on. And we defined the notions of regularity, semisimplicity and singularity of T^†-algebras and characterized them. In this paper we shall proceed further with our studies of T^†-algebras and investigate whether a T^†-algebra is decomposable into a regular part and a singular part.

This paper is devoted to the study of generalized magnetic vector fields as magnetic maps from a Kählerian manifold to its tangent bundle endowed with a Berger type deformed Sasaki metric. Some properties of Killing magnetic vector fields are provided specially in the case of an Einstein manifold and a space form. In the last section, we consider the case of unit tangent bundle.