Related papers: Quantum forced oscillator via Wigner transform
As a natural extension of Fan's paper (arXiv: 0903.1769vl [quant-ph]) by employing the formula of operators' Weyl ordering expansion and the bipartite entangled state representation we find new two-fold complex integration transformation…
We introduce the Wigner functional representing a quantum field in terms of the field amplitudes and their conjugate momenta. The equation of motion for the functional of a scalar field point out the relevance of solutions of the classical…
We investigate a quantum mechanical harmonic oscillator based on the extended Snyder model. This realization of the Snyder model is constructed as a quantum phase space generated by $D$ spatial coordinates and $D(D-1)/2$ tensorial degrees…
Quantum tunneling is the phenomenon that makes superconducting circuits "quantum". Recently, there has been a renewed interest in using quantum tunneling in phase space of a Kerr parametric oscillator as a resource for quantum information…
In this paper, we investigate the interference and Bell states of a q-Deformed Harmonic Oscillator. The Wigner functions of the interference states and the four Bell states are calculated and discussed. It is shown that in the case where…
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 examine the weak quantum noise limit of Wigner equation for phase space distribution functions. It has been shown that the leading order quantum noise described in terms of an auxiliary Hamiltonian manifests itself as an additional…
The integral Wigner - Liouwille equation describing time evolution of the semi-relativistic quantum 1D harmonic oscillator have been exactly solved by combination of the Monte-Carlo procedure and molecular dynamics methods. The strong…
The quantum dynamics of a damped and forced harmonic oscillator described by a Lindblad master equation is analyzed. The master equation is converted into a matrix-vector representation and the resulting non-Hermitian Schr\"odinger equation…
The mathematical description of the quantum harmonic oscillator is essentially based on the Gaussian function. In the case of a quantum oscillator with finite-dimensional Hilbert space, the position space consists in a finite number of…
In this paper we give a general solution to the problem of the damped harmonic oscillator under the influence of an arbitrary time-dependent external force. We employ simple methods accessible for beginners and useful for undergraduate…
In this paper the general solution of the quantum damped harmonic oscillator is given.
We present a quantum theory of the shuttle instability in electronic transport through a nanostructure with a mechanical degree of freedom. A phase space formulation in terms of the Wigner function allows us to identify a cross-over from…
We use the Fourier operator to transform a time dependent mass quantum harmonic oscillator into a frequency dependent one. Then we use Lewis-Ermakov invariants to solve the Schr\"odinger equation by using squeeze operators. Finally we give…
The synchronization properties of two self-sustained quantum oscillators are studied in the Wigner representation. Instead of considering the quantum limit of the quantum van-der-Pol master equation we derive the quantum master equation…
The quantum quartic oscillator is investigated in order to test the many-body technique of the continuous unitary transformations. The quartic oscillator is sufficiently simple to allow a detailed study and comparison of various…
We show that the effects of quantum interference can be implemented in Monte-Carlo generators by modelling the generalized Wigner functions. A specific prescription for an appropriate modification of the weights of events produced by…
Tunneling of a particle through a potential barrier remains one of the most remarkable quantum phenomena. Owing to advances in laser technology, electric fields comparable to those electrons experience in atoms are readily generated and…
In this paper we study some basic quantum confinement effects through investigation of a deformed harmonic oscillator algebra. We show that spatial confinement effects on a quantum harmonic oscillator can be represented by a deformation…
The tomographic invertable map of the Wigner function onto the positive probability distribution function is studied. Alternatives to the Schr\"odinger evolution equation and to the energy level equation written for the positive probability…