In the framework of the Lindblad theory for open quantum systems, we determine the degree of quantum decoherence of a harmonic oscillator interacting with a thermal bath. It is found that the system manifests a quantum de-coherence which is more and more significant in time. We also calculate the decoherence time and show that it has the same scale as the time after which thermal fluctuations b...

The paper analyzes the interaction of an atomic system with a quantum damped harmonic oscillator. Such an oscillator is the building block in the recently proposed models of bulk dielectrics and may also serve as a simple model of a small dielectric body. Dispersion and losses are taken into account by assuming the oscillator to be coupled to a zero-temperature reservoir consisting of an infini...

We show that a number of models in virus dynamics, epidemiology and plant biology can be presented as ``damped" versions the Lotka-Volterra predator-prey model, by analogy to damped harmonic oscillator. The deepens with use Lyapunov functions, which allow us characterize their dynamics even make some estimates.

In (quant–ph/0701141) Rajeev studied quantization of the damped simple harmonic oscillator and introduced a complex–valued Hamiltonian (which is normal). In this note we point out that the quantization is interpreted as a quantum mechanics with complex time. We also present a problem on quantization of classical control systems. In the paper [1] Rajeev studied a quantization of the damped simpl...

Time evolution of the expectation values of various dynamical operators of the harmonic oscillator with dissipation is analitically obtained within the framework of the Lindblad theory for open quantum systems. We deduce the density matrix of the damped harmonic oscillator from the solution of the Fokker-Planck equation for the coherent state representation, obtained from the master equation fo...

The de Broglie-Bohm quantum trajectories are found in analytically closed forms for the eigenstates and the coherent state of the Lewis-Riesenfeld (LR) invariant of a time-dependent harmonic oscillator. It is also shown that an eigenstate (a coherent state) of an invariant can be interpreted as squeezed states obtained by squeezing an eigenstate (a coherent state) of another invariant. This pro...

We show that quantum Bateman’s system which arises in the quantization of a damped harmonic oscillator is equivalent to a quantum problem with 2D parabolic potential barrier known also as 2D inverted isotropic oscillator. It turns out that this system displays the family of complex eigenvalues corresponding to the poles of analytical continuation of the resolvent operator to the complex energy ...

The simple harmonic vibration, damping vibration and forced vibration of an oscillator attached to the massless spring are always discussed in general mechanics courses. In this article, we focus on the heavy-spring conditions. We first investigate the general situation where both viscous resistance and applied force are considered under the perspective of the renormalization group theory. Then...