Related papers: Quantum Markovian Kinetic Equation for Harmonic Os…
We consider countable system of harmonic oscillators on the real line with quadratic interaction potential with finite support and local external force (stationary stochastic process) acting only on one fixed particle. In the case of…
In this article, we formulate the study of the unitary time evolution of systems consisting of an infinite number of uncoupled time-dependent harmonic oscillators in mathematically rigorous terms. We base this analysis on the theory of a…
For the 1-D harmonic oscillator with position depending variable mass, a Hamiltonian and constant of motion are given through a consistent approach. Then, the quantization of this system is carried out using the operator $\hat p$, for the…
We consider the forced harmonic oscillator quantized according to infinite statistics ( a special case of the `quon' algebra proposed by Greenberg ). We show that in order for the statistics to be consistently evolved the forcing term must…
In the existing literature various numerical techniques have been developed to quantize the confined harmonic oscillator in higher dimensions. In obtaining the energy eigenvalues, such methods often involve indirect approaches such as…
We investigate symmetric oscillators, and in particular their quantization, by employing semiclassical and quantum phase functions introduced in the context of Liouville-Green transformations of the Schr\"{o}dinger equation. For anharmonic…
Solving problems related to open quantum systems has attracted many interests. Here, we propose a variational quantum algorithm to find the steady state of open quantum systems. In this algorithm, we employ parameterized quantum circuits to…
Multiple scale techniques are well-known in classical mechanics to give perturbation series free from resonant terms. When applied to the quantum anharmonic oscillator, these techniques lead to interesting features concerning the solution…
This work is concerned with determination of the steady-state structure of time-independent Lindblad master equations, especially those possessing more than one steady state. The approach here is to treat Lindblad systems as generalizations…
The quantum harmonic oscillator with parity-time ($\mathcal{PT}$) symmetry, obtained from the ordinary (Hermitian) quantum harmonic oscillator by an imaginary displacement of the spatial coordinate, provides an important and…
A phenomenological construction of quantum Langevin equations, based on the physical criteria of (i) the canonical equal-time commutators, (ii) the Kubo formula, (iii) the virial theorem and (iv) the quantum fluctuation-dissipation theorem…
We discuss the extension of the Lewis and Riesenfeld method of solving the time-dependent Schr\"odinger equation to cases where the invariant has continuous eigenvalues and apply it to the case of a generalized time-dependent inverted…
Event generating algorithm corresponding to a linear master equation of Lindblad's type is described and illustrated on two examples: that of a particle detector and of a fuzzy clock. Relation to other approaches to foundations of quantum…
Master equations of Lindblad type have attained prominent status in the fields of quantum optics and quantum information since they are guaranteed to satisfy fundamental notions of quantum dynamics such as complete positivity. When Lindblad…
We derive an exact non-Markovian master equation that generalizes the previous work [Hu, Paz and Zhang, Phys. Rev. D {\bf 45}, 2843 (1992)] to damped harmonic oscillators with time-varying parameters. This is achieved by exploiting the…
Using Schwinger Variational Principle we solve the problem of quantum harmonic oscillator with time dependent frequency. Here, we do not take the usual approach which implicitly assumes an adiabatic behavior for the frequency. Instead, we…
We consider a six-parameter family of the square integrable wave functions for the simple harmonic oscillator, which cannot be obtained by the standard separation of variables. They are given by the action of the corresponding maximal…
We formulate exact generalized nonequilibrium fluctuation relations for the quantum mechanical harmonic oscillator coupled to multiple harmonic baths. Each of the different baths is prepared in its own individual (in general nonthermal)…
A systematic approach to the non-Markovian quantum dynamics of open systems is given by the projection operator techniques of nonequilibrium statistical mechanics. Combining these methods with concepts from quantum information theory and…
The Hamiltonian of the harmonic oscillator is usually defined as a differential operator, but an integral representation can be obtained by using the coherent state quantization. The finite frame quantization is a finite counterpart of the…