Related papers: The Driven-Oscillator Evolution in the Tomografic-…
We investigate the evolution of a single qubit subject to a continuous unitary dynamics and an additional interrupting influence which occurs periodically. One may imagine a dynamically evolving closed quantum system which becomes open at…
Quantum polarization is investigated by means of a trajectory picture based on the Bohmian formulation of quantum mechanics. Relevant examples of classical-like two-mode field states are thus examined, namely Glauber and SU(2) coherent…
A stochastic representation of the dynamics of open quantum systems, suitable for non-perturbative system-reservoir interaction, non-Markovian effects and arbitrarily driven systems is presented. It includes the case of driving on…
We introduce new representations to formulate quantum mechanics on noncommutative coordinate space, which explicitly display entanglement properties between degrees of freedom of different coordinate components and hence could be called…
The evolution of a mixed quantum-classical system is expressed in the mapping formalism where discrete quantum states are mapped onto oscillator states, resulting in a phase space description of the quantum degrees of freedom. By defining…
The Liouville equation for the q-deformed 1-D classical harmonic oscillator is derived for two definitions of q-deformation. This derivation is achieved by using two different representations for the q-deformed Hamiltonian of this…
The classical Hamiltonian system of time-dependent harmonic oscillator driven by the arbitrary external time-dependent force is considered. Exact analytical solution of the corresponding equations of motion is constructed in the framework…
We study the dynamics of an optomechanical system consisting of a single-mode optical field coupled to a mechanical oscillator, where the nonlinear interaction includes both linear and quadratic terms in the oscillator's position. We…
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…
Within the framework of the probability representation of quantum mechanics, we study a superposition of generic Gaussian states associated to symmetries of a regular polygon of n sides; in other words, the cyclic groups (containing the…
We formulate a discrete two-state stochastic process with elementary rules that give rise to Born statistics and reproduce the probabilities from the Schr\"odinger equation under an associated Hamiltonian matrix, which we identify. We…
We consider two-dimensional harmonic oscillator in the complex Bargmann-Fock-Segal representation with $T^*{\mathbb R}^{2}={\mathbb C}^2$ as classical phase space. We show that the eigenfunctions $\psi_n$ of the quantum Hamiltonian…
We study the evolution of the hybrid entangled states in a bipartite (ultra) strongly coupled qubit-oscillator system. Using the generalized rotating wave approximation the reduced density matrices of the qubit and the oscillator are…
Identifying the real and imaginary parts of wave functions with coordinates and momenta, quantum evolution may be mapped onto a classical Hamiltonian system. In addition to the symplectic form, quantum mechanics also has a positive-definite…
The von Neumann trace form of quantum statistical mechanics is transformed to an integral over classical phase space. Formally exact expressions for the resultant position-momentum commutation function are given. A loop expansion for wave…
We analyse the properties of a strongly-damped quantum harmonic oscillator by means of an exact diagonalisation of the full Hamiltonian, including both the oscillator and the reservoir degrees of freedom to which it is coupled. Many of the…
We study the pure and thermal states of quantized scalar and tensor perturbations in various epochs of Universe evolution. We calculate the density matrix of non-relativistic particles in an environment of these perturbations. We show that…
In this tutorial, three examples of stochastic systems are considered: A strongly-damped oscillator, a weakly-damped oscillator and an undamped oscillator (integrator) driven by noise. The evolution of these systems is characterized by the…
We study the temporal evolution of a coherent state under the action of a parametric oscillator and a nonlinear Kerr-like medium. We make use of the interaction picture representation and use an exact time evolution operator for the time…
We show how the rotational quantum state of a linear or symmetric top rotor can be reconstructed from finite time observations of the polar angular distribution under certain conditions. The presented tomographic method can reconstruct the…