Related papers: Quantum Markovian Kinetic Equation for Harmonic Os…
We present a general construction of matrix product states for stationary density matrices of one-dimensional quantum spin systems kept out of equilibrium through boundary Lindblad dynamics. As an application we review the isotropic…
The equilibrium properties of an open harmonic oscillator are considered in three steps: First the creation and destruction operators are generalized for open dynamics and the creation operator is used to construct coherent states. The…
The Lindblad equation describes the time evolution of a density matrix of a quantum mechanical system. Stationary solutions are obtained by time-averaging the solution, which will in general depend on the initial state. We provide an…
The eigenvalues of the Liouvillians of Markovian master equation for a harmonic oscillator have a generic form. The Liouvillians considered are quadratic in the position coordinates or creation and annihilation operators, as well as having…
In this article we obtained the harmonic oscillator solution for quaternionic quantum mechanics ($\mathbbm{H}$QM) in the real Hilbert space, both in the analytic method and in the algebraic method. The quaternionic solutions have many…
A family of quantum anharmonic oscillators is studied in any finite spatial dimension in the scheme of first quantization and the investigation of their eigenenergies is presented. The statistical properties of the calculated eigenenergies…
The concept of weak invariants is examined in the thermodynamic context. Discussions are made about the temporally-local equilibrium states, corrections to them, and isoenergetic processes based on the quantum master equations of the…
A closed expression for the density operator of the damped harmonic oscillator is extracted from the master equation based on the Lindblad theory for open quantum systems. The entropy and effective temperature of the system are subsequently…
We generalized the squeeze and displacement operators of the one-dimensional harmonic oscillator to the three-dimensional case and based on these operators we construct the corresponding coherent and squeezed states. We have also calculated…
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…
We study a 1-dimensional XX chain under nonequilibrium driving and local dephasing described by the Lindblad master equation. The analytical solution for the nonequilibrium steady state found for particular parameters in [J.Stat.Mech.,…
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…
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…
One-dimensional problem for quantum harmonic oscillator with "regular+random" frequency subjected to the external "regular+random" force is considered. Averaged transition probabilities are found.
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…
We describe quantum behaviors of a simple harmonic oscillator, starting from the classical mechanics. By imposing two conditions on the phase points generated from a symplectic algorithm, we obtain discrete energy levels, satisfying $E_n…
We construct a generalised expression for the normal ordering of (a+a^{\dagger})^{m} for integral values of m and use the result to study the quantum anharmonic oscillator problem in the Heisenberg approach. In particular, we derive…
Finding the transient and steady state properties of open quantum systems is a central problem in various fields of quantum technologies. Here, we present a quantum-assisted algorithm to determine the steady states of open system dynamics.…
The system of nonlinear Langevin equations was obtained by using Hamiltonian's operator of two coupling quantum oscillators which are interacting with heat bath. By using the analytical solution of these equations, the analytical…
A generic non-integrable (unitary) out-of-equilibrium quantum process, when interrogated across many times, is shown to yield the same statistics as an (non-unitary) equilibrated process. In particular, using the tools of quantum stochastic…