Related papers: Mass-sign duality of cubic oscillators
We give a partially alternate proof of the reality of the spectrum of the imaginary cubic oscillator in quantum mechanics.
It is shown that in one spatial dimension the quantum oscillator is dual to the charged particle situated in the field described by the superposition of Coulomb and Calogero-Sutherland potentials.
The system of two $Q$-deformed oscillators coupled so that the total Hamiltonian has the su$_Q$(2) symmetry is proved to be equivalent, to lowest order approximation, to a system of two identical Morse oscillators coupled by the…
We consider bilinear oscillatory integrals, i.e. pseudo-product operators whose symbol involves an oscillating factor. Lebesgue space inequalities are established, which give decay as the oscillation becomes stronger ; this extends the…
q-oscillator models are considered in two and higher dimensions and their symmetries are explored. New symmetries are found for both isotropic and anisotropic cases. Applications to the spectra of triatomic molecules and superdeformed…
We discuss a classical nonlinear oscillator, which is proved to be a superintegrable system for which the bounded motions are quasiperiodic oscillations and the unbounded (scattering) motions are represented by hyperbolic functions. This…
We study the existence of cylindrically symmetric electro-magneto-static solitary waves for a system of a nonlinear Klein-Gordon equation coupled with Maxwell's equations in presence of a positive mass and of a nonnegative nonlinear…
Several stationary solutions of the low energy string equations are dualized with respect to their timelike symmetry. Many of the duals have simple physical interpretations. Those of the nonextremal three dimensional black hole and black…
For a special value of the mass, a massive graviton on de Sitter space acquires an enhanced scalar gauge symmetry, and is called partially massless. The partially massless graviton possesses a duality invariance akin to electromagnetic…
Periodically modulated nonlinear oscillators often display bistability of forced vibrations. This bistability can be used for new types of quantum measurements. They are based on switching between coexisting vibrational states. Since…
We theoretically investigate the optical and mechanical properties of a double cavity optomechanical system with one stationary and two harmonically bound mirrors. We show that it is possible for the mechanical mirrors in this system to…
We formulate and prove the Lorentzian version of the positive mass theorems with arbitrary negative cosmological constant for asymptotically AdS spacetimes. This work is the continuation of the second author's recent work on the positive…
In the present work, one analyzes two systems trying to obtain physical conditions where some properties attributed to negative mass can be mimicked by positive mass particles. The first one is the well-known 1/2-spin system described by…
The dyon-oscillator duality presented in this lecture can be treated as a prototype of the Seiberg-Witten duality in nonrelativistic quantum mechanics. The key statement declares that in some spatial dimensions the oscillator-like systems…
Double-$\gamma$ vibrations in deformed nuclei are studied in the context of the interacting boson model with special reference to their anharmonic character. It is shown that large anharmonicities can be obtained with interactions that are…
A classical double oscillator model, that includes in certain parameter limits, the standard harmonic oscillator and the inverse oscillator, is interpreted as a dynamical system. We study its essential features and make a qualitative…
We examine the analytical structure of the nonlinear Lienard oscillator and show that it is a bi-Hamiltonian system depending upon the choice of the coupling parameters. While one has been recently studied in the context of a quantized…
In four dimensions, partially massless fields of all spins and depths possess a duality invariance akin to electric-magnetic duality. We construct metric-like gauge invariant curvature tensors for partially massless fields of all integer…
Classical and quantum mechanical analysis have been carried out on harmonic like oscillator with asymmetric position dependent mass. Phase space analysis are performed both classically and quantum mechanically for a plausible understanding…
In this work an observation concerning a positivity property of the quantum anharmonic oscillator is made. This positivity property is suggested by the BMV conjecture.