Related papers: Randomly Walking 1D Quantum Harmonic Oscillator. A…
The problem of quantum harmonic oscillator with "regular+random" square frequency, subjected to "regular+random external force, is considered in framework of representation of the wave function by complex-valued random process. Average…
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…
The system of oscillator interacting with vacuum is considered as a problem of random motion of quantum reactive harmonic oscillator (QRHO). It is formulated in terms of a wave functional regarded as complex probability process in the…
Using the Wigner-Weyl mapping of quantum mechanics to phase space we consider exactly the quantum mechanics of an harmonic oscillator driven by an external white noise force or whose frequency is time dependent, either adiabatically or…
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…
We calculate transition amplitudes and probabilities between the coherent and Fock states of a quantum harmonic oscillator with a moving center for an arbitrary law of motion. These quantities are determined by the Fourier transform of the…
We discuss the positional fluctuations of a quantum harmonic oscillator in a heat bath. Analytic expressions are given for the probability distribution functions of the oscillator position in general and limiting (classical and ground…
We address the problem of determining whether or not a harmonic oscillator has been perturbed by an external force. Quantum detection and estimation theory has been used in devising optimum measurement schemes. Detection probability has…
Complete description of the classical and quantum dynamics of a particle in an anisotropic, rotating, harmonic trap is given. The problem is studied in three dimensions and no restrictions on the geometry are imposed. In the generic case,…
In the presence of interactions the frequency of a simple harmonic oscillator deviates from the noninteracting one. Various methods can be used to compute the changes to the frequency perturbatively. Some of them resemble the methods used…
It is shown, by considering the case of the harmonic oscillator, that quantum fluctuations may be the most significant contribution to the random walk of a single molecule. From this point, the controversy on the existence of a standard…
We study the behavior of a quantum particle trapped in a confining potential in one dimension under multiple sudden changes of velocity and/or acceleration. We develop the appropriate formalism to deal with such situation and we use it to…
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…
In this work we present the simplest generic form of the propagator for the time-dependent quadratic Hamiltonian. We manifest the simplicity of our method by giving explicitly the propagators for a free particle in time-dependent electric…
We discuss in detail a well known method for obtaining the frequencies of the normal modes of coupled harmonic oscillators that is based on the simultaneous diagonalization of two symmetric matrices. We apply it to some simple illustrative…
We study the time evolution for the quantum harmonic oscillator subjected to a sudden change of frequency. It is based on an approximate analytic solution to the time dependent Ermakov equation for a step function. This approach allows for…
In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a…
The quantization of a constant of motion for the harmonic oscillator with a time-explicitly depending external force is carried out. This quantization approach is compared with the normal Hamiltonian quantization approach. Numerical results…
We investigate quantum walks in multiple dimensions with different quantum coins. We augment the model by assuming that at each step the amplitudes of the coin state are multiplied by random phases. This model enables us to study in detail…
We consider the Dirac equation with a generalized uncertainty principle in the presence of the Harmonic interaction and an external magnetic field. By doing the study in the momentum space, the problem solved in an exact analytical manner…