The quantum damped oscillator revisited

Kazuyuki Fujii, Tatsuo Suzuki

Mario Cesar Baldiotti, R. Fresneda, Dmitri M Gitman

Pintu Bhattachary, Ravi Ranjan

We display some important definitions of q-calculus along with some essential formulae of q-Laplace transform. Then, we apply them to realize the locomotion of a damped harmonic oscillator for over-damped, under damped, and critically damped situation. Thus, the mathematical statement of motion of a damped harmonic oscillator (DHO) is revisited and reviewed in view of quantum calculus. The dimensionality of all the parameters associated to the problem are discussed to find exact solutions. It is also found that, as q tends to 1, the solution takes the form as it is in classical Leibnitz calculus.

Chung‐In Um, Kyu-Hwang Yeon, Thomas F. George

Oleg Yu. Dinariev

Andrey R. Kolovsky

We revisit quantum dynamics of the damped and driven nonlinear oscillator. In the classical case this system has two stationary solutions (the limit cycles) in the certain parameter region, which is the origin of the celebrated bistability phenomenon. The quantum-classical correspondence for the oscillator dynamics is discussed in details.