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Dynamical systems with nonlinear damping show interesting behavior in the periodic and chaotic phases. The Froude pendulum with cubical and linear damping is a paradigm for such a system. In this work the driven Froude pendulum is studied by the harmonic balancing method; the resulting nonlinear response curves are studied further for resonance and stability of symmetric oscillations with relatively...
We examine the behavior of transmission coefficient T across the rectangular barrier when attractive potential well is present on one or both sides and also the same is studied for a smoother barrier with smooth adjacent wells having Woods-Saxon shape. We find that presence of well with suitable width and depth can substantially alter T at energies below the barrier height leading to resonant-like...
We propose a novel mathematical approach for the calculation of resonances in weakly bound systems. For any potential, families of strictly isospectral potentials (with very different shape) having desirable and adjustable features can be generated. For systems having no bound ground state, an isospectral potential with a bound state in the continuum is possible. The quasi-bound state in the original...
We present an evaluation of some recent attempts to understand the role of pseudo-Hermitian and $$ \mathcal{P}\mathcal{T} $$ -symmetric Hamiltonians in modelling unitary quantum systems and elaborate on a particular physical phenomenon whose discovery originated in the study of complex scattering potentials.
We provide probabilistic interpretation of resonant states. We do this by showing that the integral of the modulus square of resonance wave functions (i.e., the conventional norm) over a properly expanding spatial domain is independent of time, and therefore leads to probability conservation. This is in contrast with the conventional employment of a bi-orthogonal basis that precludes probabilistic...
This systematic study reports various electron impact cross-sections, rate constants and transport properties of $$\hbox {NH}_2$$ NH 2 radical in the low-energy limit. The collision study is based on R-matrix formalism and involves the use of various scattering models employing different active spaces. Both electron excited inelastic cross-sections and resonances are found influenced by...
We consider the s-channel resonance to fit the 2 TeV ATLAS diboson excess. We address the production mechanism of the resonance, its decay and coupling measurement. In order to explain only the hadronic channel excess, we consider the scenario where resonance decays to two new beyond Standard Model (BSM) particles (in the mass range of W / Z boson) and also explore the possibility of three-particle...
We examine the vibrational resonance (VR) of particles moving in a strongly nonlinear damped medium with a harmonically perturbed potential consisting of a background smooth triple-well potential superimposed by a fast oscillating periodic function and subjected to weak and high-frequency (HF) driving forces. The combined effects of the nonlinear damping inhomogeneity and roughness induced by the...
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