Related papers: Quantization of the damped harmonic oscillator bas…
In this work we address the problem of the quantization of a simple harmonic oscillator that is perturbed by a time dependent force. The approach consists of removing the perturbation by a canonical change of coordinates. Since the…
We develop an algebraic formulation for the discrete quantum harmonic oscillator (DQHO) with a finite, equally-spaced energy spectrum and energy eigenfunctions defined on a discrete domain, which is known as the su(2) or Kravchuk…
This work studies the relationship between parametric amplification (or particle creation), adiabaticity and irreversibility in the non-quasi-static regime of a time-dependent quantum harmonic oscillator (TDHO) that evolves unitarily. We…
The classical Hamiltonian system of time-dependent harmonic oscillator driven by the arbitrary external time-dependent force is considered. Exact analytical solution of the corresponding equations of motion is constructed in the framework…
It is shown that the well-known relativistic correction of quantum Hamiltonian that is present in textbooks appears after quantization of oversimplified relativistic kinetic energy decomposition. Using the proper expression one obtains the…
It is shown that the classical damped harmonic oscillator belongs to the family of fourth-order Pais-Uhlenbeck oscillators. It follows that the solutions to the damped harmonic oscillator equation make the Pais-Uhlenbeck action stationary.…
Recent progress in quantum simulation and algorithms has demonstrated a rapid expansion in capabilities. The search continues for new techniques and applications to exploit quantum advantage. Here we propose an innovative method to…
A well-known approach to describe the dynamics of an open quantum system is to compute the master equation evolving the reduced density matrix of the system. This approach plays an important role in describing excitation transfer through…
The one-dimensional quantum harmonic oscillator problem is examined via the Laplace transform method. The stationary states are determined by requiring definite parity and good behaviour of the eigenfunction at the origin and at infinity.
In the framework of the Lindblad theory for open quantum systems we determine the degree of quantum decoherence and classical correlations of a harmonic oscillator interacting with a thermal bath. The transition from quantum to classical…
We present a Lie algebraic approach to a Hamiltonian class covering driven, parametric quantum harmonic oscillators where the parameter set -- mass, frequency, driving strength, and parametric pumping -- is time-dependent. Our…
We establish a physically meaningful representation of a quantum energy density for use in Quantum Monte Carlo calculations. The energy density operator, defined in terms of Hamiltonian components and density operators, returns the correct…
The collective and quantum behavior of many-body systems may be harnessed to achieve fast charging of energy storage devices, which have been recently dubbed quantum batteries. In this paper, we present an extensive numerical analysis of…
The damped harmonic oscillator is a workhorse for the study of dissipation in quantum mechanics. However, despite its simplicity, this system has given rise to some approximations whose validity and relation to more refined descriptions…
Quantum effects on a pair of Bateman oscillators embedded in an ambient noncommutative space (Moyal plane) is analyzed using both path integral and canonical quantization schemes within the framework of Hilbert-Schmidt operator formulation.…
The eletromagnetic field in a linear absorptive dielectric medium, is quantized in the framework of the damped polarization model. A Hamiltonian containing a reservoir with continuous degrees of freedom, is proposed. The reservoir minimally…
In the present work, we studied the q-deformed Morse and harmonic oscillator systems with appropriate canonical commutation algebra. The analytic solutions for eigenfunctions and energy eigenvalues are worked out using time-independent…
The time dependent entropy (or Leipnik's entropy) of harmonic and damped harmonic oscillators is extensively investigated by using time dependent wave function obtained by the Feynman path integral method. Our results for simple harmonic…
It is natural to investigate if the quantization of an integrable or superintegrable classical Hamiltonian systems is still integrable or superintegrable. We study here this problem in the case of natural Hamiltonians with constants of…
We define a new quantum Hermitian operator (namely, the energy variance operator) which is simply duplicated from the statistical definition of energy variance in classical physics. Its expectation value yields the standard deviation of the…