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The concept of extended Hamiltonian systems allows the geometrical interpretation of several integrable and superintegrable systems with polynomial first integrals of degree depending on a rational parameter. Until now, the procedure of…
Quantum oscillation phenomena, in conventional 2-dimensional electron systems and in the fractional quantum Hall effect, are usually treated in the Lifshitz-Kosevich formalism. This is justified in three dimensions by Luttinger's expansion,…
The quantum master equation is a widespread approach to describing open quantum system dynamics. In this approach, the effect of the environment on the system evolution is entirely captured by the dynamical generator, providing a compact…
On the example of a quantum oscillator the connection of the dynamical coherent state with the phase symmetry breaking and the existence of the nondissipative motion is considered. In multiparticle systems of interacting particles similar…
We study self-adjoint operators defined by factorizing second order differential operators in first order ones. We discuss examples where such factorizations introduce singular interactions into simple quantum mechanical models like the…
In this work, we perform a careful study of an special arrangement of coupled systems that consists of two external harmonic oscillators weakly coupled to an arbitrary network (data bus) of strongly interacting oscillators. Our aim is to…
We present a control-theoretic analysis of the system consisting of a two-level atom coupled with a quantum harmonic oscillator. We show that by applying external fields with just two resonant frequencies, any desired unitary operator can…
A pair of coupled quantum harmonic oscillators, one subject to a gain one to a loss, is a paradigmatic setup to implement PT-symmetric, non-Hermitian Hamiltonians in that one such Hamiltonian governs the mean-field dynamics for equal gain…
We discuss two different types of issues concerning the quantization of Einstein-Rosen waves. First of all we study in detail the possibility of using the coherent states corresponding to the dynamics of the auxiliary, free Hamiltonian…
Classical and quantum anharmonic noncommutative oscillators with quartic self-interacting potential are considered and the effect of self-interaction term on the free energy and partition function of both models is calculated to first order…
For analyzing anisotropic low relative-velocity correlation-functions and the associated emission sources, we propose an expansion in terms of cartesian spherical harmonics. The expansion coefficients represent angular moments of the…
In this paper, we study the dynamical properties of two coupled quantum harmonic oscillators coupled with bosonic non-Markovian environment both in position and momentum. We deduce the exact analytical master equation using Quantum State…
Parallel to the quantization of the complex plane, using the canonical coherent states of a right quaternionic Hilbert space, quaternion field of quaternionic quantum mechanics is quantized. Associated upper symbols, lower symbols and…
In this chapter we treat the quantum damped harmonic oscillator, and study mathematical structure of the model, and construct general solution with any initial condition, and give a quantum counterpart in the case of taking coherent state…
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…
The dynamics of time-dependent coupled oscillator model for the charged particle motion subjected to a time-dependent external magnetic field is investigated. We used canonical transformation approach for the classical treatment of the…
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…
In the presence of interactions the frequency of a simple harmonic oscillator deviates from the noninteracting one. Various methods can be used to compute the changes to the frequency perturbatively. Some of them resemble the methods used…
In this paper it is studied the influence of a minimal thermal environment on the dynamics of a quantum harmonic oscillator (labelled A), prepared in a coherent state. The environment itself consists of a second oscillator (labelled B),…
Although quantum circuits have been ubiquitous for decades in quantum computing, the first complete equational theory for quantum circuits has only recently been introduced. Completeness guarantees that any true equation on quantum circuits…