Dispersive estimates for harmonic oscillator systems

Quantum Harmonic Oscillator Systems with Disorder

We study many-body properties of quantum harmonic oscillator lattices with disorder. A sufficient condition for dynamical localization, expressed as a zero-velocity LiebRobinson bound, is formulated in terms of the decay of the eigenfunction correlators for an effective one-particle Hamiltonian. We show how state-of-the-art techniques for proving Anderson localization can be used to prove that ...

Harmonic Oscillator

Driven harmonic oscillator as a quantum simulator for open systems

We show theoretically how a driven harmonic oscillator can be used as a quantum simulator for the non-Markovian damped harmonic oscillator. In the general framework, our results demonstrate the possibility to use a closed system as a simulator for open quantum systems. The quantum simulator is based on sets of controlled drives of the closed harmonic oscillator with appropriately tailored elect...

Dispersive Estimates, Strichartz Estimates and Smoothing Effects

In this short expository note, we will discuss three subjects: dispersive estimates, Strichartz estimates and smoothing effects which are of great importance in the study of dispersive equations. We will focus on the Euclidean setting and try to derive the interplay among above three objects. We will mainly focus on linear problems in various contexts. Some nonlinear application will also be me...

Quantum Harmonic Oscillator Sonification

This work deals with the sonification of a quantum mechanical system and the processes that occur as a result of its quantum mechanical nature and interactions with other systems. The quantum harmonic oscillator is not only regarded as a system with sonifiable characteristics but also as a storage medium for quantum information. By representing sound information quantum mechanically and storing...