Energetics of the Undamped Stochastic Harmonic Oscillator

Stochastic Quantization of the Time-Dependent Harmonic Oscillator

We extend the stochastic quantization method recently developed by Haba and Kleinert to non-autonomous mechanical systems, in the case of the time-dependent harmonic oscillator. In comparison with the autonomous case, the quantization procedure involves the solution of a nonlinear, auxiliary equation. PACS numbers: 03.65.-w; 02.50.Ey; 03.65.Ca

Undamped Harmonic Oscillator Driven by Additive Gaussian White Noise: a Statistical Analysis

While consistency of the maximum likelihood estimator of the drift matrix in a multi-dimensional continuous time Ornstein-Uhlenbeck process holds under rather general conditions, little is known about the rate of convergence and the limiting distribution of the estimator when the underlying process is not ergodic. The objective of the paper is to investigate these questions for an important exa...

Harmonic Oscillator

Periodic Solutions of the Duffing Harmonic Oscillator by He's Energy Balance Method

Duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. This paper presents He´s Energy Balance Method (EBM) for solving nonlinear differential equations. Two strong nonlinear cases have been studied analytically. Analytical results of the EBM are compared with the solutions obtained by using He´s Frequency Amplitude Formulation (FAF) and numerical solu...

Quantizing the damped harmonic oscillator

We consider the Fermi quantization of the classical damped harmonic oscillator (dho). In past work on the subject, authors double the phase space of the dho in order to close the system at each moment in time. For an infinite-dimensional phase space, this method requires one to construct a representation of the CAR algebra for each time. We show that unitary dilation of the contraction semigrou...