Reports on Mathematical Physics最新文献

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.

We classify the Lorentzian manifolds of dimension n ≥ 3 admitting some diagonalizable operators which satisfy the Codazzi equation. This classification is applied to characterize three-dimensional weakly-Einstein Lorentzian manifolds which fall in the conformal class of the flat metrics.

In this paper, we investigate a multidimensionally consistent coupled quadrilateral system of the discrete Boussinesq type, proposed by Fordy and Xenitidis recently. It is distinguished from the known discrete Boussinesq type equations by a special dispersion relation. A Bäcklund transformation is constructed and a one-soliton solution is derived using the Bäcklund transformation. We also give bilinear forms of the coupled equations and present formulae for multisoliton solutions. Both plane wave factor and phase factor in two-soliton solutions indicate the coupled systems belong to the discrete Boussinesq family, but there is no continuous correspondence in terms of the Miwa coordinates.

We discuss canonical rigged Hilbert space constructions. We focus on cyclic self-adjoint operators and use the one-dimensional free Hamiltonian on the half-line as a model. We propose a nonstandard construction that can be generalized to many quantum systems. Our construction is motivated by the Stone–von Neumann uniqueness theorem.

We consider four subsets of the complexified spacetime algebra, namely the real even part, the real odd part, the imaginary even part and the imaginary odd part. This naturally leads to the four connected components of the Lorentz group, supplemented each time by an additional symmetry. We then examine how these four parts impact the Dirac equation and show that four types of matter arise with positive and negative masses as well as positive and negative charges.

Generalized Ricci recurrent spacetimes (GR)_n are investigated in Gray's seven subspaces. It is proved that a (GR)_n spacetime in all subspaces but one is an Einstein spacetime. The subspace $ℐ$ cannot contain a (GR)_n spacetime. Further, the subspaces $ℐ\oplus A$ and $ℐ\oplus B$ reduce to $A$ and $B$, respectively. Next, we prove that a (GR)_n spacetime is Ricci semi-symmetric if and only if either the spacetime is Einstein or the vector field A^l is closed. Further, it is shown that the Ricci tensor of (GR)_n is Riemann compatible if A^l is closed. Finally, sufficient conditions are given on a (GR)_n warped product manifold to guarantee that the factor manifolds are Einstein. Moreover, it is shown that a generalized Ricci recurrent GRW spacetime is an Einstein spacetime.

In this note, we extend some results on positive and completely positive trace-preserving maps (called quantum channels in the CPTP case) from finite-dimensional to infinite-dimensional Hilbert space. Specifically, we mainly consider whether the fixed state of a quantum channel Φ on $T\left(\mathscr{H}\right)$ exists, where $T\left(\mathscr{H}\right)$ is the Banach algebra of all trace-class operators on the Hilbert space $\mathscr{H}$. We show that there exist the approximation states ρ_n for every quantum channel Φ. In particular, there is a quantum channel on $T\left(\mathscr{H}\right)$, which has not a fixed state. Also, we get the relationship between the fixed points of $\Phi \left(\left|A\right|\right)=\left|A\right|$ and Φ(A) = ωA, where ω is the complex number with |ω| = 1 and $A\in T\left(\mathscr{H}\right)$.