相关论文: On Cyclic Harmonic Oscillators
A harmonic oscillator with time-dependent mass $m(t)$ and a time-dependent (squared) frequency $\omega^2(t)$ occurs in the modelling of several physical systems. It is generally believed that systems, with $m(t)>0$ and $\omega^2(t)>0$…
We consider multiscale Hamiltonian systems in which harmonic oscillators with several high frequencies are coupled to a slow system. It is shown that the oscillatory energy is nearly preserved over long times eps^{-N} for arbitrary N>1,…
We have obtained explicit analytical formulas for the mean energy and its variance (characterizing the energy fluctuations) of a quantum harmonic oscillator with time-dependent frequency in the adiabatic regimes after the frequency passes…
We consider a quantum space with rotationally invariant noncommutative algebra of coordinates and momenta. The algebra contains tensors of noncommutativity constructed involving additional coordinates and momenta. In the rotationally…
We present analytical expressions and numerical results for the rates of energy exchange between oscillators and with the environment in a heterogeneous ensemble of globally coupled mechanical phase oscillators. The system is in stationary…
The paper introduces a simple quantum model to calculate in a general way allowed frequencies and energy levels of the anharmonic oscillator. The theoretical basis of the approach has been introduced in two early papers aimed to infer the…
Evolution of coherent states is considered for a particle confined to a cylinder moving in a harmonic oscillator potential. Because of the discontinuous changes as time goes by of the phase representing the position of a particle on a…
For a harmonic oscillator with time-dependent (positive) mass and frequency, an unitary operator is shown to transform the quantum states of the system to those of a harmonic oscillator system of unit mass and time-dependent frequency, as…
We consider countable system of harmonic oscillators on the real line with quadratic interaction potential with finite support and local external force (stationary stochastic process) acting only on one fixed particle. In the case of…
An explicit solution of the equation for the classical harmonic oscillator with smooth switching of the frequency has been found . A detailed analysis of a quantum harmonic oscillator with such frequency has been done on the base of the…
We consider a system in which some high frequency harmonic oscillators are coupled with a slow system. We prove that up to very long times the energy of the high frequency system changes only by a small amount. The result we obtain is…
Two methods to change a quantum harmonic oscillator frequency without transitions in a finite time are described and compared. The first method, a transitionless-tracking algorithm, makes use of a generalized harmonic oscillator and a…
We solve explicitly the two-dimensional harmonic oscillator and the harmonic oscillator in a background magnetic field in noncommutative phase-space without making use of any type of representation. A key observation that we make is that…
Exchange of quantum states between two interacting harmonic oscillator along their evolution time is discussed. It is analyzed the conditions for such exchange starting from a generic initial state and demonstrating that the effect occurs…
The total energy of the ground state of the quantum harmonic oscillator is obtained with minimal assumptions. The vacuum energy density of the universe is derived and a cutoff frequency is obtained for the upper bound of the quantum…
The unitary operator which transforms a harmonic oscillator system of time-dependent frequency into that of a simple harmonic oscillator of different time-scale is found, with and without an inverse-square potential. It is shown that for…
The ongoing discussion whether thermodynamic properties can be extracted from a (possibly approximate) quantum mechanical time evolution using time averages is fed with an instructive example. It is shown for the harmonic oscillator how the…
Singularities in macroscopic systems at discontinuous phase transitions are replaced in finite systems by sharp but continuous changes. Both the energy differences between metastable and stable phases and the energy barriers separating…
We consider a radiation from a uniformly accelerating harmonic oscillator whose minimal coupling to the scalar field changes suddenly. The exact time evolutions of the quantum operators are given in terms of a classical solution of a forced…
We study the evolution of the energy of a harmonic oscillator when its frequency slowly varies with time and passes through zero value. We consider both the classical and quantum descriptions of the system. We show that after a single…