Effect of many modes on self-polarization and photochemical suppression in cavities

The standard description of cavity-modified molecular reactions typically involves a single (resonant) mode, while in reality, the quantum cavity supports a range of photon modes. Here, we demonstrate that as more photon modes are accounted for, physicochemical phenomena can dramatically change, as illustrated by the cavity-induced suppression of the important and ubiquitous process of proton-coupled electron-transfer. Using a multi-trajectory Ehrenfest treatment for the photon-modes, we find that self-polarization effects become essential, and we introduce the concept of self-polarization-modified Born–Oppenheimer surfaces as a new construct to analyze dynamics. As the number of cavity photon modes increases, the increasing deviation of these surfaces from the cavity-free Born–Oppenheimer surfaces, together with the interplay between photon emission and absorption inside the widening bands of these surfaces, leads to enhanced suppression. The present findings are general and will have implications for the description and control of cavity-driven physical processes of molecules, nanostructures, and solids embedded in cavities

The Boden-Hu conjecture holds precisely up to rank eight

Consider moduli schemes of vector bundles over a smooth projective curve endowed with parabolic structures over a marked point. Boden and Hu observed that a slight variation of the weights leads to a desingularisation of the moduli scheme, and they conjectured that one can always obtain a small resolution this way. The present text proves this conjecture in some cases (including all bundles of rank up to eight) and gives counterexamples in all other cases (in particular in every rank beyond eight). The main tool is a generalisation of Ext-groups involving more than two quasiparabolic bundles.Comment: 17 page

Stochastic analysis of ocean wave states with and without rogue waves

This work presents an analysis of ocean wave data including rogue waves. A stochastic approach based on the theory of Markov processes is applied. With this analysis we achieve a characterization of the scale dependent complexity of ocean waves by means of a Fokker-Planck equation, providing stochastic information of multi-scale processes. In particular we show evidence of Markov properties for increment processes, which means that a three point closure for the complexity of the wave structures seems to be valid. Furthermore we estimate the parameters of the Fokker-Planck equation by parameter-free data analysis. The resulting Fokker-Planck equations are verified by numerical reconstruction. This work presents a new approach where the coherent structure of rogue waves seems to be integrated into the fundamental statistics of complex wave states.Comment: 18 pages, 13 figure

Dark solitons, modulation instability and breathers in a chain of weakly non-linear oscillators with cyclic symmetry

In the aerospace industry the trend for light-weight structures and the resulting complex dynamic behaviours currently challenge vibration engineers. In many cases, these light-weight structures deviate from linear behaviour, and complex nonlinear phenomena can be expected. We consider a cyclically symmetric system of coupled weakly nonlinear undamped oscillators that could be considered a minimal model for different cyclic and symmetric aerospace structures experiencing large deformations. The focus is on localised vibrations that arise from wave envelope modulation of travelling waves. For the defocussing parameter range of the approximative nonlinear evolution equation, we show the possible existence of dark solitons and discuss their characteristics. For the focussing parameter range, we characterise modulation instability and illustrate corresponding nonlinear breather dynamics. Furthermore, we show that for stronger nonlinearity or randomness in initial conditions, transient breather-type dynamics and decay into bright solitons appear. The findings suggest that significant vibration localisation may arise due to mechanisms of nonlinear modulation dynamics

Mixed Quantum-Classical Dynamics in Cavity Quantum Electrodynamics

Considering the ultimate limit of molecules interacting with a few photons, the classical description of the electromagnetic field does not suffice anymore and the quantum nature of light needs to be taken into account. Moreover, to describe chemical processes mediated by quantum light, an accurate, flexible and computationally efficient treatment of light-matter interactions is required. Therefore the present work focuses on the theoretical approaches of light-matter interaction in cavity quantum electrodynamics. In particular, we investigate the extension of mixed-quantum classical trajectory methods as well as the concept of time-dependent potential energy surfaces, both traditionally introduced for electron-nuclear problems, to the photonic degrees of freedom. The goal is to pave the way for a full ab initio and computationally feasible description of quantum effects in strongly correlated light-matter systems. We find, that classical Wigner dynamics for photons can be used to describe quantum effects such as spontaneous emission, correlation functions, bound photon states and cavity-induced suppression of proton-coupled electron transfer by properly accounting for the quantum statistics of the vacuum field while using classical/semi-classical trajectories to describe the time-evolution. Additionally, this classical Wigner treatment for the photons allows us to go beyond the usual single-mode picture, and to include the many photon modes supported in most realistic cavities, in a numerically efficient way. Here, we find that as more photon modes are included, cavity-modified phenomena can significantly change and the self-polarization, which is often neglected, has an increasingly crucial impact on the dynamics and even more so presents a potential new tool to control and change chemical reactions. To this end, we introduce the concept of self-polarization-modified Born-Oppenheimer surfaces as an instructive tool for analysis. Furthermore, in order to gain a fundamental understanding of the dynamics obtained by the mixed-quantum classical methods, we investigate the time-dependent potential energy surfaces within the exact factorization framework. Here we find on the one hand that the corresponding time-dependent potential energy surfaces for photons show significant differences to the harmonic potentials used in conventional approaches. On the other hand, analyzing the time-dependent potential energy surface driving the proton motion of a cavity-induced chemical suppression, we show how its features directly correlate to the proton dynamics, in contrast to the polaritonic surfaces. Particularly, within the mixed-quantum classical methods for photons we identify a promising route towards describing quantum effects in realistic correlated light-matter systems. Especially, combining the introduced methods with an existing ab initio electronic structure methods such as time-dependent density functional theory would provide an ab initio computationally feasible way to simulate photon-field fluctuations and correlations in realistic three-dimensional systems.Zur Analyse der Wechselwirkung von Molekülen mit nur wenigen Photonen, ist die klassische Beschreibung des elektromagnetischen Feldes unzureichend und die Quanteneigenschaften des Lichts müssen berücksichtigt werden. Darüber hinaus erfordert die Simulaton chemischer Prozesse mit starker Quantenlicht- Wechselwirkung eine genaue, flexible und rechnerisch effiziente Beschreibung von Licht-Materie-Wechselwirkung. Die vorliegende Arbeit untersucht daher Theorien der Licht-Matrie-Wechselwirkung für Resonatorquantenelektrodynamik an der Schnittstelle von Quantenoptik und Quantenchemie. Insbesondere betrachten wir die Erweiterung der gemischt quanten-klassischen Trajektorienmethoden, sowie das Konzept der zeitabhängigen Potentialenergieflächen, beides ursprünglich für Elektron-Kern Systeme entwickelt, auf die photonischen Freiheitsgrade. Wir stellen fest, dass die klassische Wigner-Dynamik für Photonen gut geeignet ist, um Quanteneffekte wie spontane Emission, Korrelationsfunktionen, gebundene Photonenzustände und resonatorinduzierte chemische Suppression des Proton-Elektron gekoppelten Ladungstransfers zu beschreiben. Hierbei berücksichtigen wir einerseits die Quantenstatistik des Vakuumfeldes und verwenden andererseits klassische/semi-klassische Trajektorien zur Beschreibung der Zeitevolution. Geht man außerdem über die üblicherweise verwendete Kopplung zu nur einer Photonenmode hinaus, verändern sich die beobachteten resonatormodifizierten Phänomene erheblich und die oft vernachlässigte Selbstpolarisation hat einen immer wichtigeren Einfluss auf die Dynamik und stellt darüber hinaus ein potenzielles neues Werkzeug zur Kontrolle und Veränderung chemischer Reaktionen dar. Zu diesem Zweck stellen wir das Konzept der selbstpolarisationsmodifizierten Born-Oppenheimer-Potentialenergieflächen als instruktives Analysewerkzeug vor. Um ein grundlegendes Verständnis der simulierten Dynamik innerhalb der gemischt quanten-klassischen Trajektorienmethoden zu erhalten, untersuchen wir weiterhin die zeitabhängigen Potentialenergieflächen. Wir stellen fest, dass sich diese für Photonen signifikant von dem üblicherweise verwendeten harmonischen Bild unterscheiden. Darüber hinaus analysieren wir die zeitabhängige Potentialenergiefläche, die die Protonenbewegung einer resonator-induzierten chemischen Suppression des Proton-Elektron gekoppelten Ladungstransfers antreibt, und zeigen wie ihre Charakteristik, im Gegensatz zu polaritonischen Potentialenergieflächen, direkt mit der Protonendynamik zusammenhängen. Wir kommen zu dem Schluss, dass die gemischt quanten-klassischen Methoden für Photonen ein vielversprechender Weg zur Beschreibung von Quanteneffekten in realistischen korrelierten Licht-Materie-Systemen darstellen. Insbesondere die Kombination der vorgestellten Methoden mit einer schon bestehenden ab initio elektronischen Strukturmethode, wie zum Beispiel der zeitabhängigen Dichtefunktionaltheorie, eröffnet die Möglichkeit sowohl Photonenfeldschwankungen als auch Photonkorrelationen in realistischen dreidimensionalen Systemen zu simulieren

Mixed Quantum-Classical Dynamics in Cavity Quantum Electrodynamics

Considering the ultimate limit of molecules interacting with a few photons, the classical description of the electromagnetic field does not suffice anymore and the quantum nature of light needs to be taken into account. Moreover, to describe chemical processes mediated by quantum light, an accurate, flexible and computationally efficient treatment of light-matter interactions is required. Therefore the present work focuses on the theoretical approaches of light-matter interaction in cavity quantum electrodynamics. In particular, we investigate the extension of mixed-quantum classical trajectory methods as well as the concept of time-dependent potential energy surfaces, both traditionally introduced for electron-nuclear problems, to the photonic degrees of freedom. The goal is to pave the way for a full ab initio and computationally feasible description of quantum effects in strongly correlated light-matter systems. We find, that classical Wigner dynamics for photons can be used to describe quantum effects such as spontaneous emission, correlation functions, bound photon states and cavity-induced suppression of proton-coupled electron transfer by properly accounting for the quantum statistics of the vacuum field while using classical/semi-classical trajectories to describe the time-evolution. Additionally, this classical Wigner treatment for the photons allows us to go beyond the usual single-mode picture, and to include the many photon modes supported in most realistic cavities, in a numerically efficient way. Here, we find that as more photon modes are included, cavity-modified phenomena can significantly change and the self-polarization, which is often neglected, has an increasingly crucial impact on the dynamics and even more so presents a potential new tool to control and change chemical reactions. To this end, we introduce the concept of self-polarization-modified Born-Oppenheimer surfaces as an instructive tool for analysis. Furthermore, in order to gain a fundamental understanding of the dynamics obtained by the mixed-quantum classical methods, we investigate the time-dependent potential energy surfaces within the exact factorization framework. Here we find on the one hand that the corresponding time-dependent potential energy surfaces for photons show significant differences to the harmonic potentials used in conventional approaches. On the other hand, analyzing the time-dependent potential energy surface driving the proton motion of a cavity-induced chemical suppression, we show how its features directly correlate to the proton dynamics, in contrast to the polaritonic surfaces. Particularly, within the mixed-quantum classical methods for photons we identify a promising route towards describing quantum effects in realistic correlated light-matter systems. Especially, combining the introduced methods with an existing ab initio electronic structure methods such as time-dependent density functional theory would provide an ab initio computationally feasible way to simulate photon-field fluctuations and correlations in realistic three-dimensional systems.Zur Analyse der Wechselwirkung von Molekülen mit nur wenigen Photonen, ist die klassische Beschreibung des elektromagnetischen Feldes unzureichend und die Quanteneigenschaften des Lichts müssen berücksichtigt werden. Darüber hinaus erfordert die Simulaton chemischer Prozesse mit starker Quantenlicht- Wechselwirkung eine genaue, flexible und rechnerisch effiziente Beschreibung von Licht-Materie-Wechselwirkung. Die vorliegende Arbeit untersucht daher Theorien der Licht-Matrie-Wechselwirkung für Resonatorquantenelektrodynamik an der Schnittstelle von Quantenoptik und Quantenchemie. Insbesondere betrachten wir die Erweiterung der gemischt quanten-klassischen Trajektorienmethoden, sowie das Konzept der zeitabhängigen Potentialenergieflächen, beides ursprünglich für Elektron-Kern Systeme entwickelt, auf die photonischen Freiheitsgrade. Wir stellen fest, dass die klassische Wigner-Dynamik für Photonen gut geeignet ist, um Quanteneffekte wie spontane Emission, Korrelationsfunktionen, gebundene Photonenzustände und resonatorinduzierte chemische Suppression des Proton-Elektron gekoppelten Ladungstransfers zu beschreiben. Hierbei berücksichtigen wir einerseits die Quantenstatistik des Vakuumfeldes und verwenden andererseits klassische/semi-klassische Trajektorien zur Beschreibung der Zeitevolution. Geht man außerdem über die üblicherweise verwendete Kopplung zu nur einer Photonenmode hinaus, verändern sich die beobachteten resonatormodifizierten Phänomene erheblich und die oft vernachlässigte Selbstpolarisation hat einen immer wichtigeren Einfluss auf die Dynamik und stellt darüber hinaus ein potenzielles neues Werkzeug zur Kontrolle und Veränderung chemischer Reaktionen dar. Zu diesem Zweck stellen wir das Konzept der selbstpolarisationsmodifizierten Born-Oppenheimer-Potentialenergieflächen als instruktives Analysewerkzeug vor. Um ein grundlegendes Verständnis der simulierten Dynamik innerhalb der gemischt quanten-klassischen Trajektorienmethoden zu erhalten, untersuchen wir weiterhin die zeitabhängigen Potentialenergieflächen. Wir stellen fest, dass sich diese für Photonen signifikant von dem üblicherweise verwendeten harmonischen Bild unterscheiden. Darüber hinaus analysieren wir die zeitabhängige Potentialenergiefläche, die die Protonenbewegung einer resonator-induzierten chemischen Suppression des Proton-Elektron gekoppelten Ladungstransfers antreibt, und zeigen wie ihre Charakteristik, im Gegensatz zu polaritonischen Potentialenergieflächen, direkt mit der Protonendynamik zusammenhängen. Wir kommen zu dem Schluss, dass die gemischt quanten-klassischen Methoden für Photonen ein vielversprechender Weg zur Beschreibung von Quanteneffekten in realistischen korrelierten Licht-Materie-Systemen darstellen. Insbesondere die Kombination der vorgestellten Methoden mit einer schon bestehenden ab initio elektronischen Strukturmethode, wie zum Beispiel der zeitabhängigen Dichtefunktionaltheorie, eröffnet die Möglichkeit sowohl Photonenfeldschwankungen als auch Photonkorrelationen in realistischen dreidimensionalen Systemen zu simulieren

Multistability and localization in forced cyclic symmetric structures modelled by weakly-coupled Duffing oscillators

Many engineering structures are composed of weakly coupled sectors assembled in a cyclic and ideally symmetric configuration, which can be simplified as forced Duffing oscillators. In this paper, we study the emergence of localized states in the weakly nonlinear regime. We show that multiple spatially localized solutions may exist, and the resulting bifurcation diagram strongly resembles the snaking pattern observed in a variety of fields in physics, such as optics and fluid dynamics. Moreover, in the transition from the linear to the nonlinear behaviour isolated branches of solutions are identified. Localization is caused by the hardening effect introduced by the nonlinear stiffness, and occurs at large excitation levels. Contrary to the case of mistuning, the presented localization mechanism is triggered by the nonlinearities and arises in perfectly homogeneous systems

Super rogue waves in simulations based on weakly nonlinear and fully nonlinear hydrodynamic equations

The rogue wave solutions (rational multi-breathers) of the nonlinear Schrodinger equation (NLS) are tested in numerical simulations of weakly nonlinear and fully nonlinear hydrodynamic equations. Only the lowest order solutions from 1 to 5 are considered. A higher accuracy of wave propagation in space is reached using the modified NLS equation (MNLS) also known as the Dysthe equation. This numerical modelling allowed us to directly compare simulations with recent results of laboratory measurements in \cite{Chabchoub2012c}. In order to achieve even higher physical accuracy, we employed fully nonlinear simulations of potential Euler equations. These simulations provided us with basic characteristics of long time evolution of rational solutions of the NLS equation in the case of near breaking conditions. The analytic NLS solutions are found to describe the actual wave dynamics of steep waves reasonably well.Comment: under revision in Physical Review

Partial Clustering in Binary Two-Dimensional Colloidal Suspensions

Strongly interacting binary mixtures of superparamagnetic colloidal particles confined to a two-dimensional water-air interface are examined by theory, computer simulation and experiment. The mixture exhibits a partial clustering in equilibrium: in the voids of the matrix of unclustered big particles, the small particles form subclusters with a sponge-like topology which is accompanied by a characteristic small-wave vector peak in the small-small structure factor. This partial clustering is a general phenomenon occurring for strongly coupled negatively non-additive mixtures.Comment: 12 pages, 5 figures, submitted 200