Related papers: Caldirola-Kanai Oscillator in Classical Formulatio…
In this introductory course we sketch the framework of quantum probability in order to discuss open quantum systems, in particular the damped harmonic oscillator.
We obtain the tomogram of squeezed correlated states of a quantum parametric damped oscillator in an explicit form. We study the damping within the framework of the Caldirola--Kanai model and chose the parametric excitation in the form of a…
We return to the description of the damped harmonic oscillator by means of a closed quantum theory with a general assessment of previous works, in particular the Bateman-Caldirola-Kanai model and a new model recently proposed by one of the…
An optical realization of the damped quantum oscillator, based on transverse light dynamics in an optical resonator with slowly-moving mirrors, is theoretically suggested. The optical resonator setting provides a simple implementation of…
There are discussed the exact solution of the time--dependent Schr\"{o}dinger equation for a damped quantum oscillator subject to a periodical frequency delta--kicks describing squeezed states which are expressed in terms of Chebyshev…
The systems with multimode nonstationary Hamiltonians quadratic in position and momentum operators are reviewed. The tomographic probability distributions (tomograms) for the Fock states and Gaussian states of the quadratic systems are…
Quantization of the damped harmonic oscillator is taken as leitmotiv to gently introduce elements of quantum probability theory for physicists. To this end, we take (graduate) students in physics as entry level and explain the physical…
For the non-conservative Caldirola-Kanai system, describing a quantum damped harmonic oscillator, a couple of constant-of-motion operators generating the Heisenberg-Weyl algebra can be found. The inclusion of the standard time evolution…
The quantum theory of the damped harmonic oscillator has been a subject of continual investigation since the 1930s. The obstacle to quantization created by the dissipation of energy is usually dealt with by including a discrete set of…
In classical mechanics, driven systems with dissipation often exhibit complex, fractal dynamics known as strange attractors. This paper addresses the fundamental question of how such structures manifest in the quantum realm. We investigate…
In this work, we present a quantization scheme for the damped harmonic oscillator (QDHO) using a framework known as momentous quantum mechanics. Our method relies on a semiclassical dynamical system derived from an extended classical…
In this chapter we treat the quantum damped harmonic oscillator, and study mathematical structure of the model, and construct general solution with any initial condition, and give a quantum counterpart in the case of taking coherent state…
The dynamical equation of quantum mechanics are rewritten in form of dynamical equations for the measurable, positive marginal distribution of the shifted, rotated and squeezed quadrature introduced in the so called "symplectic tomography".…
A closed expression for the density operator of the damped harmonic oscillator is extracted from the master equation based on the Lindblad theory for open quantum systems. The entropy and effective temperature of the system are subsequently…
We consider several models of the damped oscillators in nonrelativistic quantum mechanics in a framework of a general approach to the dynamics of the time-dependent Schroedinger equation with variable quadratic Hamiltonians. The Green…
The tomographic probability distribution is used to decribe the kinetic equations for open quantum systems. Damped oscillator is studied. Purity parameter evolution for different damping regime is considered.
The investigation of quantum-classical correspondence may lead to gain a deeper understanding of the classical limit of quantum theory. We develop a quantum formalism on the basis of a linear-invariant theorem, which gives an exact…
Glauber coherent states of quantum systems are reviewed. We construct the tomographic probability distributions of the oscillator states. The possibility to describe quantum states by tomographic probability distributions (tomograms) is…
We provide a new canonical approach for studying the quantum mechanical damped harmonic oscillator based on the doubling of degrees of freedom approach. Explicit expressions for Lagrangians of the elementary modes of the problem,…
A new formulation of quantum mechanics based on differential commutator brackets is developed. We have found a wave equation representing the fermionic particle. In this formalism, the continuity equation mixes the Klein-Gordon and…