Related papers: The damped harmonic oscillator in deformation quan…
Extended phase space (EPS) formulation of quantum statistical mechanics treats the ordinary phase space coordinates on the same footing and thereby permits the definite the canonical momenta conjugate to these coordinates . The extended…
Dimer decimation scheme is introduced in order to study the kicked quantum systems exhibiting localization transition. The tight-binding representation of the model is mapped to a vectorized dimer where an asymptotic dissociation of the…
It is shown that general solutions of the free-particle Schroedinger equation can be mapped onto solutions of the Schroedinger equation for the harmonic oscillator. This is done in such a way that the time evolution of a free particle…
The quantum description of a particle moving in a deformed potential is investigated. A pseudostate (PS) basis is used to represent the states of the composite system. This PS basis is obtained by diagonalizing the system Hamiltonian in a…
Non hermitian Hamiltonians play an important role in the study of dissipative quantum systems. We show that using states with time dependent normalization can simplify the description of such systems especially in the context of the…
There are discussed the exact solution of the time--dependent Schr\"{o}dinger equation for a damped quantum oscillator subject to a periodical frequency delta--kicks describing squeezed states which are expressed in terms of Chebyshev…
We generalize the wave functions of the displaced and squeezed number states, found by Nieto, to a time-dependent harmonic oscillator with variable mass and frequency. These time-dependent displaced and squeezed number states are obtained…
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…
In this talk I discuss a recently developed "Unfolded Quantization Framework". It allows to introduce a Hamiltonian Second Quantization based on a Hopf algebra endowed with a coproduct satisfying, for the Hamiltonian, the physical…
A system of two coupled quantum harmonic oscillators with the Hamiltonian ${\hat H}=\frac{1}{2}\left(\frac{1}{m_1}{\hat p}^{2}_1 + \frac{1}{m_2}{\hat p}^{2}_2+A x^2_1+B x^2_2+ C x_1 x_2\right)$ can be found in many applications of quantum…
We demonstrate the possibility of controlling the border between the quantum and the classical world by performing nonselective measurements on quantum systems. We consider a quantum harmonic oscillator initially prepared in a Schroedinger…
In this study, we introduce a two dimensional complex harmonic oscillator potential with space and time reflection symmetries. The corresponding time independent Schr\"odinger equation yields real eigenvalues with complex eigenfunctions. We…
We experimentally perform the simulation of open quantum dynamics in single-qudit systems. Using a spatial light modulator as a dissipative optical device, we implement dissipative-dynamical maps onto qudits encoded in the transverse…
In the harmonic oscillator representation, the Schrodinger equation has a form of a set of infinite number of algebraical equations which are labeled by the radial quantum number "n". It is shown that at n>>1 these equations are…
The resonances associated with a fractional damped oscillator which is driven by an oscillatory external force are studied. It is shown that such resonances can be manipulated by tuning up either the coefficient of the fractional damping or…
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 of a harmonic oscillator interacting with a thermal bath. It is found that the system manifests a quantum decoherence which is…
Photoinduced charge dynamics in dimerized systems is studied on the basis of the exact diagonalization method and the time-dependent Schr\"odinger equation for a one-dimensional spinless-fermion model at half filling and a two-dimensional…
Coherently displaced harmonic oscillator number states of a harmonically bound ion can be coupled to two internal states of the ion by a laser-induced motional sideband interaction. The internal states can subsequently be read out in a…
In this paper, we examine the thermodynamic behavior of a quantum harmonic oscillator with a position-dependent mass (PDM), where spatial inhomogeneity is modeled through a deformation parameter {\alpha}. Based on the exact energy spectrum,…