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Journal of Physics A: Mathematical and Theoretical - latest papers

Latest articles for Journal of Physics A: Mathematical and Theoretical

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  • Stability analysis of the ( 1 + 1 ) ...
    The aim of this paper is to perform a nonlinear stability analysis of the -dimensional Nambu–Goto action gas models. The energy-Casimir method is employed to discuss in detail the Lyapunov stability of the Chaplygin and Born–Infeld models. Particular solutions are considered, and their stability is studied in order to illustrate the application of our results.

  • Row and column detection complexities of character tables
    Character tables of finite groups and closely related commutative algebras have been investigated recently using new perspectives arising from the AdS/CFT correspondence and low-dimensional topological quantum field theories. Two important elements in these new perspectives are physically motivated definitions of quantum complexity for the algebras and a notion of row-column duality. These elements are encoded in properties of the character table of a group G and the associated algebras, notably the centre of the group algebra and the fusion algebra of irreducible representations of the group. Motivated by these developments, we define a notion of generator complexity for commutative Frobenius algebras with combinatorial bases. In the context of finite groups, this gives rise to row and column versions of generator complexity for character tables. We investigate the relation between these complexities under the exchange of rows and columns. We observe regularities that arise in the statistical averages over small character tables and propose corresponding conjectures for arbitrarily large character tables.

  • Analytical results for the distribution of first return times of non-backtracking random walks on configuration model networks
    We present analytical results for the distribution of first return (FR) times of non-backtracking random walks (NBWs) on undirected configuration model networks consisting of N nodes with degree distribution P(k). We focus on the case in which the network consists of a single connected component. Starting from a random initial node i at time t = 0, an NBW hops into a random neighbor of i at time t = 1 and at each subsequent step it continues to hop into a random neighbor of its current node, excluding the previous node. We calculate the tail distribution of FR times from a random initial node to itself. It is found that is given by a discrete Laplace transform of the degree distribution P(k). This result exemplifies the relation between structural properties of a network, captured by the degree distribution, and properties of dynamical processes taking place on the network. Using the tail-sum formula, we calculate the mean FR time . Surprisingly, coincides with the result obtained from Kac’s lemma that applies to simple random walks (RWs). We also calculate the variance , which accounts for the variability of FR times between different NBW trajectories. We apply this formalism to Erdős–Rényi networks, random regular graphs and configuration model networks with exponential and power-law degree distributions and obtain closed-form expressions for as well as its mean and variance. These results provide useful insight on the advantages of NBWs over simple RWs in network exploration, sampling and search processes.

  • Renormalization of Schrödinger equation for potentials with inverse-square singularities: generalized trigonometric Pöschl–Teller model
    We introduce a renormalization procedure necessary for the complete description of the energy spectra of a one-dimensional stationary Schrödinger equation with a potential that exhibits inverse-square singularities. We apply and extend the methods introduced in our recent paper on the hyperbolic Pöschl–Teller potential (with a single singularity) to its trigonometric version. This potential, defined between two singularities, is analyzed across the entire bidimensional coupling space. The fact that the trigonometric Pöschl–Teller (TPT) potential is supersymmetric and shape-invariant simplifies the analysis and eliminates the need for self-adjoint extensions in certain coupling regions. However, if at least one coupling is strongly attractive, the renormalization is essential to construct a discrete energy spectrum family of one or two parameters. We also investigate the features of a singular symmetric double well obtained by extending the range of the TPT potential. It has a non-degenerate energy spectrum and eigenstates with well-defined parity.

  • Bound states of quasiparticles with quartic dispersion in an external potential: WKB approach
    The Wentzel–Kramers–Brillouin semiclassical method is formulated for quasiparticles with quartic-in-momentum dispersion which presents the simplest case of a soft energy-momentum dispersion. It is shown that matching wave functions in the classically forbidden and allowed regions requires the consideration of higher-order Airy-type functions. The asymptotics of these functions are found by using the method of steepest descents and contain additional exponentially suppressed contributions known as hyperasymptotics. These hyperasymptotics are crucially important for the correct matching of wave functions in vicinity of turning points for higher-order differential equations. A quantization condition for bound state energies is obtained, which generalizes the standard Bohr–Sommerfeld quantization condition for particles with quadratic energy-momentum dispersion and contains non-perturbative in correction. This non-perturbative correction, usually associated with tunneling effects or the presence of complex turning points, occurs even for the harmonic potential with quartic dispersion where complex turning points and tunneling are absent. The quantization condition is used to find bound state energies in the case of quadratic and quartic potentials.