The problem of duality symmetry in free field models is examined in details by performing a mode expansion of these fields which provides a mapping with the purely quantum mechanical example of a harmonic oscillator. By analysing the duality symmetry in the harmonic oscillator, we show that the massless scalar theory in two dimensions display, along with the expected discrete Z 2 symmetry, the ...

— We prove stability of the bound states for the quantum harmonic oscillator under non-resonant, time quasi-periodic perturbations by proving that the associated Floquet Hamiltonian has pure point spectrum. Résumé (Stabilité de l’oscillateur harmonique quantique sous les perturbations quasipériodiques) Nous démontrons la stabilité des états bornés de l’oscillateur harmonique sous les perturbati...

In this article we obtained the harmonic oscillator solution for quaternionic quantum mechanics ($\mathbbm{H}$QM) in real Hilbert space, both analytic method and algebraic method. The solutions have many additional possibilities if compared to complex ($\mathbbm{C}$QM), thus there are possible applications these results future research.

Irreversibility is introduced to quantum graphs by coupling the graphs to a bath of harmonic oscillators. The interaction which is linear in the harmonic oscillator amplitudes is localized at the vertices. It is shown that for sufficiently strong coupling, the spectrum of the system admits a new continuum mode which exists even if the graph is compact, and a single harmonic oscillator is couple...

Overview Central topic of this thesis is the investigation of the quantum nature of light. This investigation is carried out in two separate experiments which are described in part I and part II respectively. In part I, classical and non-classical laser radiation is characterized at the quantum mechanical level with respect to its amplitude and phase uctuations, its photon number distribution a...

The quantum theory of the damped harmonic oscillator has been a subject of continual investigation since the 1930s. The obstacle to quantization created by the dissipation of energy is usually dealt with by including a discrete set of additional harmonic oscillators as a reservoir. But a discrete reservoir cannot directly yield dynamics such as Ohmic damping (proportional to velocity) of the os...

We use the so-called Liouville-von Neumann (LvN) approach to study the nonequilibrium quantum dynamics of time-dependent second order phase transitions. The LvN approach is a canonical method that unifies the functional Schrödinger equation for the quantum evolution of pure states and the LvN equation for the quantum description of mixed states of either equilibrium or nonequilibrium. As nonequ...

We obtain a class of oscillation modes with damping and absorption that are connected to the classical harmonic oscillator modes through the supersymmetric one-dimensional matrix procedure similar to relationships of the same type between Dirac and Schrödinger equations in particle physics. A single coupling parameter characterizes both the damping and absorption features of these modes, which ...

We study kicked quantum systems by using the squeezed state approach. Taking the kicked quantum harmonic oscillator as an example, we demonstrate that chaos in an underlying classical system can be enhanced as well as suppressed by quantum fluctuations. Three different energy diffusions are observed in the kicked quantum harmonic oscillator, namely, localization, linear diffusion, and quadratic...