Journal of Mathematical Physics (J MATH PHYS )

Publisher: American Institute of Physics, American Institute of Physics


Journal of Mathematical Physics is published monthly by the American Institute of Physics. Its purpose is the publication of papers in mathematical physics ñ that is, the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories. The mathematics should be written in a manner that is understandable to theoretical physicists. Occasionally, reviews of mathematical subjects relevant to physics and special issues combining papers on a topic of current interest may be published.

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    Journal of Mathematical Physics website
  • Other titles
    Journal of mathematical physics
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  • Material type
    Periodical, Internet resource
  • Document type
    Journal / Magazine / Newspaper, Internet Resource

Publisher details

American Institute of Physics

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    • Publishers version/PDF may be used on author's personal website or institutional website
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    • NIH-funded articles are automatically deposited with PubMed Central with open access after 12 months
    • For Medical Physics see AAPM policy
    • This policy does not apply to Physics Today
    • Publisher last contacted on 27/09/2013
  • Classification
    ​ green

Publications in this journal

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    ABSTRACT: In this paper, we present a method to compute solutions of coupled integral equations for quantum scattering problems in the presence of a complex potential. We show how the elastic and absorption cross sections can be obtained from the numerical solution of these equations in the asymptotic region at large radial distances.
    Journal of Mathematical Physics 01/2015; 56(1):012104.
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    ABSTRACT: We investigate the connection between singular Weyl-Titchmarsh-Kodaira theory and the double commutation method for one-dimensional Dirac operators. In particular, we compute the singular Weyl function of the commuted operator in terms of the data from the original operator. These results are then applied to radial Dirac operators in order to show that the singular Weyl function of such an operator belongs to a generalized Nevanlinna class $N_{\kappa_0}$ with $\kappa_0=\lfloor|\kappa| + \frac{1}{2}\rfloor$, where $\kappa\in \mathbb{R}$ is the corresponding angular momentum.
    Journal of Mathematical Physics 01/2015; 56(1):012102.
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    ABSTRACT: The affine Weyl groups with their corresponding four types of orbit functions are considered. Two independent admissible shifts, which preserve the symmetries of the weight and the dual weight lattices, are classified. Finite subsets of the shifted weight and the shifted dual weight lattices, which serve as a sampling grid and a set of labels of the orbit functions, respectively, are introduced. The complete sets of discretely orthogonal orbit functions over the sampling grids are found and the corresponding discrete Fourier transforms are formulated. The eight standard one-dimensional discrete cosine and sine transforms form special cases of the presented transforms.
    Journal of Mathematical Physics 11/2014; 55(11).
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    ABSTRACT: In this paper we study the evolution of superoscillating initial data for the quantum driven harmonic oscillator. Our main result shows that superoscillations are amplified by the harmonic potential and that the analytic solution develops a singularity in finite time. We also show that for a large class of solutions of the Schr\"odinger equation, superoscillating behavior at any given time implies superoscillating behavior at any other time.
    Journal of Mathematical Physics 11/2014; 55(11).
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    ABSTRACT: A set of cylindrical solutions to Einstein's field equations for power law densities is described. The solutions have a Bessel function contribution to the metric. For matter cylinders regular on axis, the first two solutions are the constant density Gott-Hiscock string and a cylinder with a metric Airy function. All members of this family have the Vilenkin limit to their mass per length. Some examples of Bessel shells and Bessel motion are given.
    Journal of Mathematical Physics 11/2014; 55(10).
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    ABSTRACT: Knots are commonly found in molecular chains such as DNA and proteins, and they have been considered to be useful models for structural analysis of these molecules. One interested quantity is the minimum number of monomers necessary to realize a molecular knot. The minimum lattice length $\mbox{Len}(K)$ of a knot $K$ indicates the minimum length necessary to construct $K$ in the cubic lattice. Another important quantity in physical knot theory is the ropelength which is one of knot energies measuring the complexity of knot conformation. The minimum ropelength $\mbox{Rop}(K)$ is the minimum length of an ideally flexible rope necessary to tie a given knot $K$. Much effort has been invested in the research project for finding upper bounds on both quantities in terms of the minimum crossing number $c(K)$ of the knot. It is known that $\mbox{Len}(K)$ and $\mbox{Rop}(K)$ lie between $\mbox{O}(c(K)^{\frac{3}{4}})$ and $\mbox{O}(c(K) [\ln (c(K))]^5)$, but unknown yet whether any family of knots has superlinear growth. In this paper, we focus on 2-bridge knots and links. Linear growth upper bounds on the minimum lattice length and minimum ropelength for nontrivial 2-bridge knots or links are presented: $\mbox{Len}(K) \leq 8 c(K) + 2$. $\mbox{Rop}(K) \leq 11.39 c(K) + 12.37$.
    Journal of Mathematical Physics 11/2014; 55(11).