Related papers: Quantization of the Damped Harmonic Oscillator Rev…
We numerically study the quantum dynamics of a $\mathcal{PT}$-symmetric kicked harmonic oscillator. We observe that directed current of momentum and ballistic diffusion of energy coexist under the non-resonant conditions, whereas both the…
The scattering and bound states of the many-body systems, related to the short-range Dyson model, are studied. First, we show that the scattering states can be realized as coherent states and the scattering Hamiltonian can be connected to a…
A model of an electrical point contact coupled to a mechanical system (oscillator) is studied to simulate the dephasing effect of measurement on a quantum system. The problem is solved at zero temperature under conditions of strong…
A calorimetric measurement has recently been proposed as a promising technique to measure thermodynamic quantities in a dissipative superconducting qubit. These measurements rely on the fact that the system is projected into energy…
A Bose-Hubbard Hamiltonian, modeling cold bosons in an optical lattice, is used to simulate the dynamics of interacting open quantum systems as subsystems a larger closed system, avoiding complications like the introduction of baths,…
We develop a general theoretical framework of semiclassical phase reduction for analyzing synchronization of quantum limit-cycle oscillators. The dynamics of quantum dissipative systems exhibiting limit-cycle oscillations are reduced to a…
We obtain analytic solutions to various models of dissipation of the quantum harmonic oscillator, employing a simple method in the Wigner function Fourier transform description of the system; and study as an exemplification, the driven open…
We reveal a new face of the old clich\'ed system: a dissipative quantum harmonic oscillator. We formulate and study a quantum counterpart of the energy equipartition theorem satisfied for classical systems.Both mean kinetic energy $E_k$ and…
We propose a parametric hazard model obtained by enforcing positivity in the damped harmonic oscillator. The resulting model has closed-form hazard and cumulative hazard functions, facilitating likelihood and Bayesian inference on the…
Quantum systems which interact with their environment are often modeled by maximal dissipative operators or so-called Pseudo-Hamiltonians. In this paper the scattering theory for such open systems is considered. First it is assumed that a…
A certain notion of canonical equivalence in quantum mechanics is proposed. It is used to relate quantal systems with discrete ones. Discrete systems canonically equivalent to the celebrated harmonic oscillator as well as the quartic and…
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…
We recycle Cruz et al.'s (Phys. Lett. A 369 (2007) 400) work on the classical and quantum position-dependent mass (PDM) oscillators. To elaborate on the ordering ambiguity, we properly amend some of the results reported in their work and…
Motivated by recent discussions of entanglement in the context of high energy scattering, we consider the relation between the entanglement entropy of a highly excited state of a quantum system and the classical entanglement entropy of the…
In this paper, the $d$-dimensional quantum harmonic oscillator with a pseudo-differential time quasi-periodic perturbation \begin{equation}\label{0} \text{i}\dot{\psi}=(-\Delta+V(x)+\epsilon W(\omega t,x,-\text{i}\nabla))\psi,\ \ \ \ \…
We introduce a new approach to deriving approximate analytical solutions of a harmonic oscillator damped by purely nonlinear, or combinations of linear and nonlinear damping forces. Our approach is based on choosing a suitable trial…
We develop a quantum model based on the correspondence between energy distribution between harmonic oscillators and the partition of an integer number. A proper choice of the interaction Hamiltonian acting within this manifold of states…
The dissipative harmonic oscillator has two representations. In the first representation the central oscillator couples with its position to an oscillator bath. In the second one it couples with its momentum to the bath. Both…
We study the known coherent states of a quantum harmonic oscillator from the standpoint of the original developed noncommutative integration method for linear partial differential equations. The application of the method is based on the…
The use of fractional momentum operators and fractionary kinetic energy used to model linear damping in dissipative systems such as resistive circuits and a spring-mass ensambles was extended to a quantum mechanical formalism. Three…