Die vorliegende Arbeit befasst sich mit dem Thema der Nichtgleichgewichts-Dispersionskräfte. Der Fokus liegt auf der kontroversen Casimir- bzw. Quantenreibung. Sie tritt auf, wenn sich zwei elektrisch neutrale Körper relativ zueinander bewegen. Vermittelt wird diese kontaktlose Reibungskraft über fluktuierende elektromagnetische (Quanten-) Felder und ist somit der Kategorie der fluktuationsinduzierten Phänome zuzuordnen, deren bekannte Beispiele die Van-der-Waals-Kraft und der Casimir-Effekt sind. Im Speziellen wurde die Situation eines mikroskopischen Objektes, welches sich mit einer festgelegten Geschwindigkeit und Höhe über eine makroskopische und flache Oberfläche beweget, untersucht. Um einen Zugang in das Themenfeld zu erlangen, wird eine kurze Einleitung in die Theorie der linearen Antwort und der Dynamik offener Systeme gegeben. Des Weiteren, werden unterschiedliche Modelle zur Beschreibung des mikroskopischen Objektes eingeführt und verschiedene Konfigurationen und Modelle bezüglich der makroskopischen Oberfläche berücksichtigt. Neben einem exakten, wenn auch komplexen, Integralausdruck werden diverse asymptotische Ausdrücke für verschiedene relevante Grenzfälle der kontaktlosen Reibung hergeleitet. Darüber hinaus, um die Asymptoten mit der exakten Lösung vergleichen zu können, wurde eine numerisch Auswertungsroutine des exakten Ausdrucks entwickelt und implementiert. Durch die Nutzung einer vollen Nichtgleichgewichtbeschreibung und das Einbeziehen sowohl der Rückwirkung des elektromagnetischen Feldes auf die Dynamik des mikroskopischen Objektes, als auch dessen Rotationsfreiheitsgrade, werden bestehende theoretische Beschreibungen erweitert. Abschließend wird ein Ausblick auf experimentelle Messungen der kontaktlosen Reibung gegeben. / The present thesis addresses the topic of nonequilibrium dispersion forces. The focus lies on the controversial Casimir or quantum friction, which occurs when two electrically neutral bodies move at a relative velocity with respect to each other. The noncontact friction force is mediated by the fluctuations of the (quantum) electromagnetic field and therefore belongs to the category of fluctuation-induced phenomena, whose prominent examples are the van der Waals force and the Casimir effect. Especially, the setup of a microscopic object moving at a fixed velocity and height above a flat macroscopic surface is investigated. To access this topic, a brief introduction into linear response and open system dynamics is given. Moreover, different models for the description of the microscopic object are introduced and various setups and models of the flat macroscopic surface are considered. Besides an exact but rather involved integral expression, several asymptotic expressions of the noncontact friction for different relevant limits are derived. Furthermore, in order to compare the asymptotic with the exact expression, a numerical approach for its evaluation was developed and implemented. Using a full nonequilibrium approach, which includes the backaction of the electromagnetic field onto the microscopic object’s dynamics, as well as its rotational degrees, existing theoretical descriptions are extended. Eventually, an outlook towards experimental measurements of the noncontact friction is given.

The vacuum, as described by Quantum Field Theory, is not as empty as classical physics once led us to believe. In fact, it is characterised by an infinite energy stored in the ground state of its constituent fields. This infinite energy has real, tangible effects on the macroscopic clusters of matter that make up our universe. Moreover, the configuration of these clusters of matter within the vacuum in turn influences the form of the vacuum itself and so forth. In this work, we shall consider the changes to the quantum vacuum brought about by the presence of time-dependent dielectrics. Such changes are thought to be responsible for phenomena such as the simple and dynamical Casimir effects and Quantum Friction. After introducing the physical and mathematical descriptions of the electromagnetic quantum vacuum, we will begin by discussing some of the basic quasi-static effects that stem directly from the existence of an electromagnetic ground state energy, known as the \textit{zero-point energy}. These effects include the famous Hawking radiation and Unruh effect amongst others. We will then use a scenario similar to that which exhibits Cherenkov radiation in order to de-mystify the 'negative frequency' modes of light that often occur due to a Doppler shift in the presence of media moving at a constant velocity by showing that they are an artefact of the approximation of the degrees of freedom of matter to a macroscopic permittivity function. Here, absorption and dissipation of electromagnetic energy will be ignored for simplicity. The dynamics of an oscillator placed within this moving medium will then be considered and we will show that when the motion exceeds the speed of light in the dielectric, the oscillator will begin to absorb energy from the medium. It will be shown that this is due to the reversal of the 'radiation damping' present for lower velocity of stationary cases. We will then consider how the infinite vacuum energy changes in the vicinity, but outside, of this medium moving with a constant velocity and show that the presence of matter removes certain symmetries present in empty space leading to transfers of energy between moving bodies mediated by the electromagnetic field. Following on from this, we will then extend our considerations by including the dissipation and dispersion of electromagnetic energy within magneto-dielectrics by using a canonically quantised model referred to as 'Macroscopic QED'. We will analyse the change to the vacuum state of the electromagnetic field brought about by the presence of media with an arbitrary time dependence. It will be shown that this leads to the creation of particles tantamount to exciting the degrees of freedom of both the medium and the electromagnetic field. We will also consider the effect these time-dependencies have on the two point functions of the field amplitudes using the example of the electric field. Finally, we will begin the application of the macroscopic QED model to the path integral methods of quantum field theory with the purpose of making use of the full range of perturbative techniques that this entails, leaving the remainder of this adaptation for future work.