-symmetric cubic anharmonic oscillator as a physical model

-Symmetric Cubic Anharmonic Oscillator as a Physical Model

We perform a perturbative calculation of the physical observables, in particular pseudoHermitian position and momentum operators, the equivalent Hermitian Hamiltonian operator, and the classical Hamiltonian for the PT -symmetric cubic anharmonic oscillator, H = 1 2mp 2+ 1 2μ 2x2+iǫx3. Ignoring terms of order ǫ4 and higher, we show that this system describes an ordinary quartic anharmonic oscill...

A perturbative treatment of a generalized PT -Symmetric Quartic Anharmonic Oscillator

We examine a generalized PT -symmetric quartic anharmonic oscillator model to determine the various physical variables perturbatively in powers of a small quantity ε.We make use of the Bender-Dunne operator basis elements and exploit the properties of the toatally symmetric operator Tm,n.

Wigner function for a driven anharmonic oscillator

We consider the quantum model of a driven anharmonic oscillator, in the presence of dissipation, and present an exact analytic solution for the corresponding Wigner function in the steady-state regime. This provides explicit phase-space images of the resulting state of the cavity mode, and allows us to understand how the quantum interference is built up into it. The photon number probability di...

Gaussian Basis Sets for Model Anharmonic Oscillator Systems

Global Solvability of the Anharmonic Oscillator Model from Nonlinear Optics

The eld equations describing the propagation of electromagnetic waves in a nonlinear dielectric medium whose polarization responds locally to the electric eld as an anharmonic oscillator with potential V (P) have smooth solutions global in space and time for arbitrary smooth initial data as soon as V has bounded derivatives of order less than or equal to three. This is true in spite of the fact...