In this paper we derive an exact master equation for two coupled quantum harmonic oscillators interacting via bilinear coupling with a common environment at arbitrary temperature made up of many harmonic oscillators with a general spectral density function. We first show a simple derivation based on the observation that the two harmonic oscillator model can be effectively mapped into that of a ...

We consider a network of deterministic non-linear oscillators with nonidentical parameters. Interactions between the different oscillators are linear, but the coupling coefficients for each interaction may differ. We consider the case where coupling coefficients are sufficiently large, so that the different oscillators will have their state variables strongly tied together and variables of the ...

A nonlinear stochastic Schrödinger equation for pure states describing non-Markovian diffusion of quantum trajectories and compatible with non-Markovian master equations is presented. This provides an unravelling of the evolution of any quantum system coupled to a finite or infinite number of harmonic oscillators without any approximation. Its power is illustrated by several examples, including...

A method for calculating phase noise based on a particle diffusion model in the phase plane is introduced. This approach allows for the derivation of closed-form solutions, which can be used to see the explicit dependencies of phase noise on circuit component values. The theory is applied to the Van der Pol and Colpitts oscillators, and comparisons to simulations show close matching. Introducti...

We consider a class of one dimensional vector Non-linear Schr$\ddot{o}$dinger Equation(NLSE) in an external complex potential with Balanced Loss-Gain(BLG) and Linear Coupling(LC) among the components field. The solvability generic system is investigated for various combinations time modulated LC BLG terms, space-time dependent strength nonlinear interaction potential. use non-unitary transforma...

Ground state energies and wave functions of quartic and pure quartic oscillators are calculated by first casting the Schrödinger equation into a nonlinear Riccati form and then solving that nonlinear equation analytically in the first iteration of the quasilinearization method (QLM). In the QLM the nonlinear differential equation is solved by approximating the nonlinear terms by a sequence of l...