Reports on Mathematical Physics最新文献

In the standard approach to Finsler geometry the metric is defined as a vertical Hessian and the Chern or Cartan connections appear as just two among many possible natural linear connections on the pullback tangent bundle. Here it is shown that the Hessian nature of the metric, the nonlinear connection and the Chern or Cartan connections can be derived from a few compatibility axioms between metric and Finsler connection. This result provides a metrical formulation of Finsler geometry which is well adapted to field theory, and which has proved useful in Einstein–Cartan-like approaches to Finsler gravity.

We consider a problem occurring in a magnetostatic levitation. The problem leads to a linear PDE in a strip. In engineering literature a particular solution is obtained. Such a solution enables one to compute lift and drag forces of the levitating object. It is in agreement with the experiment. We show that such a solution is unique in a class of bounded regular functions. Moreover, as a byproduct, we obtain nonstandard uniqueness results in two linear PDEs in unbounded domains. One of them is an eigenvalue problem for the Laplacian in the strip in the nonstandard class of functions.

According to the ‘folk knowledge', the Hartree–Fock (H-F) approximation applied to the Hubbard model becomes exact in the limit of small coupling U (the smaller |U|, the better is the H-F approximation). In [1] Bach and Poelchau have substantiated a certain version of this assertion by providing a rigorous estimate of the difference between the true ground-state energy of the simplest version of the Hubbard model and the H-F approximation to this quantity. In this paper we extend their result in two directions: (i) we show how to apply it to the system the hopping matrix of which has period greater than 1 (the case without strict translational invariance) — this allows us to consider systems the dispersion function of which is not (as assumed in [1]) a Morse function; (ii) we point out that the same technique allows to establish analogous estimates for a class of multiband Hubbard models.

Dynamical symmetry algebra for a semiconfined harmonic oscillator model with a position-dependent effective mass is constructed. Selecting the starting point as a well-known factorization method of the Hamiltonian under consideration, we have found three basis elements of this algebra. The algebra defined through those basis elements is an su (1,1) Heisenberg–Lie algebra. Different special cases and the limit relations from the basis elements to the Heisenberg–Weyl algebra of the nonrelativistic quantum harmonic oscillator are discussed, too.

According to the basic idea of category theory, any Einstein algebra, essentially an algebraic formulation of general relativity, can be considered from the point of view of any object of the category of C^∞-algebras; such an object is then called a stage. If we contemplate a given Einstein algebra from the point of view of the stage, which we choose to be an “algebra with infinitesimals” (Weil algebra), then we can suppose it penetrates a submicroscopic level, on which quantum gravity might function. We apply Vinogradov's notion of geometricity (adapted to this situation), and show that the corresponding algebra is geometric, but then the infinitesimal level is unobservable from the macro-level. However, the situation can change if a given algebra is noncommutative. An analogous situation occurs when as stages, instead of Weil algebras, we take many other C^∞-algebras, for example those that describe spaces in which with ordinary points coexist “parametrised points”, for example closed curves (loops). We also discuss some other consequences of putting Einstein algebras into the conceptual environment of category theory.

The purpose of this article is to study the almost Ricci-Bourguignon soliton on warped product space. Some results for solenoidal and concurrent vector fields are obtained on warped product space with almost Ricci-Bourguignon soliton. We provide the relation between the warped manifold and its base manifold (fiber manifold) for an almost Ricci-Bourguignon soliton. We also generalize the Bochner formula in warped product space. Next, we study the Riemannian map whose total manifold admits an almost Ricci-Bourguignon soliton. We find the condition for a kernel of Riemannian map to become an almost Ricci-Bourguignon soliton. Moreover, we give an example for almost Ricci-Bourguignon soliton on warped product space.

It has been shown that a positive semi-definite Hamiltonian H, that has a tridiagonal matrix representation in a given basis$\left\{|{\varphi }_n〉\right\}$, can be represented in the form H = A^†A, where A is a forward shift operator satisfying$A|{\varphi }_n〉=c_n|{\varphi }_n〉+d_n|{\varphi }_n-1〉$ playing the role of an annihilation operator. Here, the coherent states |z) are defined as eigenstates of A. We also exhibit a complete set of coherent states {|c_n)}, labeled by the discrete points c_n, which we may also use as a basis. We find a solution of the coherent state |z), indexed by the continuous parameter z as a series expansion in terms of the {|c_n)}. We further show how to compute the time development of the coherent state |z) and we illustrate this with examples. As a major result, we find the explicit closed form solution |z) for the Morse oscillator.

Various types of functions, their generalizations and extentions have been widely explored, especially for their applications in various fields of research. In this article, we show that the use of methods of an operational nature, such as umbral calculus, allows us to acquire the hybrid form of the Bessel and Tricomi functions in terms of Mittag-Leffler functions. Certain novel identities such as generating functions, series representations, differential equations, derivative formulae, summation formula and Jacobi-Anger expansion for Mittag-Leffler-Bessel functions are obtained. Some integral formulae for the Oth-order Mittag-Leffler-Bessel functions are established. In addition, the Mittag-Leffler-Tricomi functions are constructed and some captivating properties of these polynomials are explored. The natural transforms of the Mittag-Leffler-Bessel functions and Mittag-Leffler-Tricomi functions are investigated and Laplace and Sumudu transforms are obtained as special cases. The graphical representations of these hybrid functions are given for special values of the parameters.

Two simultaneous nonlocal group constraints of the Ablowitz-Kaup-Newell-Segur matrix eigenvalue problems are discussed, of which one constraint changes the eigenvalue parameter into its negative of the complex conjugate and the other constraint does not change the eigenvalue parameter. Under those two constraints, mixed-type nonlocal integrable nonlinear Schrödinger hierarchies are generated. Further, based on specific distributions of eigenvalues and adjoint eigenvalues, a formulation of soliton solutions is established via the corresponding reflection-less generalized Riemann-Hilbert problems, where eigenvalues and adjoint eigenvalues could be equal.

The exact solutions of fractional order (2+1)-dimensional Burgers system are determined by using symmetry approach and power series technique. Also, the graphical behaviour of the obtained solutions is provided for better interpretation. The conservation laws for the system are reported by using the new conservation theorem.