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Quartile: search.filters.quartile.Q2Subject: search.filters.subject.Mathematical physics

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    Analytical solution of a stochastic content-based network model
    (Iop Publishing, 2005) Mungan, M; Balcan, D; Erzan, A; Department of Physics; Kabakçıoğlu, Alkan; Faculty Member; Department of Physics; College of Sciences; 49854
    We define and completely solve a content-based directed network whose nodes consist of random words and an adjacency rule involving perfect or approximate matches for an alphabet with an arbitrary number of letters. The analytic expression for the out-degree distribution shows a crossover from a leading power law behaviour to a log-periodic regime bounded by a different power law decay. The leading exponents in the two regions have a weak dependence on the mean word length, and an even weaker dependence on the alphabet size. The in-degree distribution, on the other hand, is much narrower and does not show any scaling behaviour.
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    Can Nth order Born approximation be exact?
    (IOP Publishing Ltd, 2024) Loran, Farhang; Department of Mathematics; Mostafazadeh, Ali; Department of Mathematics; College of Sciences
    For the scattering of scalar waves in two and three dimensions and electromagnetic waves in three dimensions, we identify a condition on the scattering interaction under which the Nth order Born approximation gives the exact solution of the scattering problem for some N >= 1.
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    PT-symmetric cubic anharmonic oscillator as a physical model
    (Iop Publishing Ltd, 2005) N/A; Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231
    We perform a perturbative calculation of the physical observables, in particular, pseudo-Hermitian position and momentum operators, the equivalent Hermitian Hamiltonian operator and the classical Hamiltonian for the PT-symmetric cubic anharmonic oscillator, H = -1/2m p(2) + 1/2 mu(2) x(2) + i epsilon x(3). Ignoring terms of order epsilon(4) and higher, we show that this system describes an ordinary quartic anharmonic oscillator with a position-dependent mass, and real and positive coupling constants. This observation elucidates the classical origin of the reality and positivity of the energy spectrum. We also discuss the quantum-classical correspondence for this PT-symmetric system, compute the associated conserved probability density and comment on the issue of factor ordering in the pseudo-Hermitian canonical quantization of the underlying classical system.