The quantum theory of a damped harmonic oscillator has been continuously studied since 1939. For quantization, an oscillation usually uses reservoir that includes number finite and discrete oscillators. However, set oscillators is unable to study the Ohmic damping (damping proportional velocity). In this research, continuous used investigate damping. Using continuum instead will enrich results ...

In addition to the passive observation of a non­ linear oscillator and the description of the measured data with Lyapounow exponents [1, 2], fractal dimensions [3-5], entropies [6], etc. it is possible to charcterize a non-linear oscillator by an active method, namely by determining its response to specific perturbations. The resonances of harmonic systems which are brought about by a sinusoida...

We consider position-dependent mass (PDM) Lagrangians/Hamiltonians in their standard textbook form, where the long-standing \emph{gain-loss balance} between kinetic and potential energies is kept intact to allow conservation of total energy (i.e., $L=T-V$, $H=T+V$, $dH/dt=dE/dt=0$). Under such settings, we discuss report on $n$-dimensional PDM damped harmonic oscillators (DHO). use some point c...

We present an analytical expression for the observed signal in time- and phase-resolved pump-probe studies, with particular emphasis on terahertz time-domain spectroscopy. Maxwell's equations are solved for the response of damped, harmonic oscillators to a driving probe field in the perturbative regime. Our analytical expressions agree with the one previously reported in the literature [Nemec e...

In this paper, we introduce a quantum decomposition algorithm (QDA) that decomposes the problem [Formula: see text] into summation of eigenvalues times phase–space variables. One interesting feature QDA stems from its ability to simulate damped spin systems by means pure harmonic oscillators adjusted with original eigenvalue problem. We test proposed in case undriven qubit spontaneous emission ...

The aim of this paper is to introduce and investigate chaotic and hyperchaotic complex jerk equations. The jerk equations describe various phenomena in engineering and physics, for example, electrical circuits, laser physics, mechanical oscillators, damped harmonic oscillators, and biological systems. Properties of these systems are studied and their Lyapunov exponents are calculated. The dynam...