This paper describes the physical relationships that exist between the Fourier transform and the response spectrum of a strong-motion accelerogram. By developing the new concept of the "Damped Fourier Spectrum" (D.F.S.), we show that the velocity and displacement of the damped oscillator can be represented by a linear combination of the real and imaginary parts of the D.F.S. and by the initial ...

Inclusion of the instantaneous Kerr nonlinearity in the FDTD framework leads to implicit equations that have to be solved iteratively. In principle, explicit integration can be achieved with the use of anharmonic oscillator equations, but it tends to be unstable and inappropriate for studying strong-field phenomena like laser filamentation. In this paper, we show that nonlinear susceptibility c...

the potential function of lippincott and schroeder for linear hydrogen bond has been re-examined and extended to nonlinear hydrogen bond. the parameters originally introduced to the potential function by lippincott and schroeder have been determined from the structural parameters such as 0.. .odistance 0-h bond distance, h.. .o distance and hoo angle. thevalidity of harmonic oscillator approxim...

We show that two-dimensional anti-de Sitter spacetime (AdS2) can be put in correspondence, holographically, both with the harmonic oscillator and the free particle. When AdS2 has an horizon the corresponding mechanical system is a thermal harmonic oscillator at temperature given by the Hawking temperature of the horizon. The spectrum of the quantum harmonic oscillator is obtained from classical...

The vibrational partition function of ethane is calculated in the temperature range of 200-600 K using well-converged energy levels that were calculated by vibrational configuration interaction, and the results are compared to the harmonic oscillator partition function. This provides the first test of the harmonic oscillator approximation for a molecule with more than five atoms. The absolute f...

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 solve explicitly the two-dimensional harmonic oscillator and the harmonic oscillator in a background magnetic field in noncommutative phase-space without making use of any type of representation. A key observation that we make is that for a specific choice of the noncommutative parameters, the time reversal symmetry of the systems get restored since the energy spectrum becomes degenerate. Th...

We study the preparation of entangled pure Gaussian states via reservoir engineering. In particular, we consider a chain consisting of (2א+ 1) quantum harmonic oscillators where the central oscillator of the chain is coupled to a single reservoir. We then completely parametrize the class of (2א+1)-mode pure Gaussian states that can be prepared by this type of quantum harmonic oscillator chain. ...