Dirk Witthaut

Braess's paradox in oscillator networks, desynchronization and power outage

Robust synchronization is essential to ensure the stable operation of many complex networked systems such as electric power grids. Increasing energy demands and more strongly distributing power sources raise the question of where to add new connection lines to the already existing grid. Here we study how the addition of individual links impacts the emergence of synchrony in oscillator networks that model power grids on coarse scales. We reveal that adding new links may not only promote but also destroy synchrony and link this counter-intuitive phenomenon to Braesss paradox known for traffic networks. We analytically uncover its underlying mechanism in an elementary grid example, trace its origin to geometric frustration in phase oscillators, and show that it generically occurs across a wide range of systems. As an important consequence, upgrading the grid requires particular care when adding new connections because some may destabilize the synchronization of the grid—and thus induce power outages.

Photon scattering by a three-level emitter in a one-dimensional waveguide

We discuss the scattering of photons from a three-level emitter in a one-dimensional waveguide, where the transport is governed by the interference of spontaneously emitted and directly transmitted waves. The scattering problem is solved in closed form for different level structures. Several possible applications are discussed: the state of the emitter can be switched deterministically by Raman scattering, thus enabling applications in quantum computing such as a single-photon transistor. An array of emitters gives rise to a photonic band gap structure, which can be tuned by a classical driving laser. A disordered array leads to Anderson localization of photons, where the localization length can again be controlled by an external driving.

Impact of network topology on synchrony of oscillatory power grids

Replacing conventional power sources by renewable sources in current power grids drastically alters their structure and functionality. In particular, power generation in the resulting grid will be far more decentralized, with a distinctly different topology. Here, we analyze the impact of grid topologies on spontaneous synchronization, considering regular, random, and small-world topologies and focusing on the influence of decentralization. We model the consumers and sources of the power grid as second order oscillators. First, we analyze the global dynamics of the simplest non-trivial (two-node) network that exhibit a synchronous (normal operation) state, a limit cycle (power outage), and coexistence of both. Second, we estimate stability thresholds for the collective dynamics of small network motifs, in particular, star-like networks and regular grid motifs. For larger networks, we numerically investigate decentralization scenarios finding that decentralization itself may support power grids in exhibiting a stable state for lower transmission line capacities. Decentralization may thus be beneficial for power grids, regardless of the details of their resulting topology. Regular grids show a specific sharper transition not found for random or small-world grids.

Dissipation induced coherence of a two-mode Bose-Einstein condensate.

We discuss the dynamics of a Bose-Einstein condensate in a double-well trap subject to phase noise and particle loss. The phase coherence of a weakly interacting condensate as well as the response to an external driving show a pronounced stochastic resonance effect: Both quantities become maximal for a finite value of the dissipation rate matching the intrinsic time scales of the system. Even stronger effects are observed when dissipation acts in concurrence with strong interparticle interactions, restoring the purity of the condensate almost completely and increasing the phase coherence significantly.

Mean-field dynamics of a Bose-Einstein condensate in a time-dependent triple-well trap: Nonlinear eigenstates, Landau-Zener models and STIRAP

Technische Universit¨at Kaiserslautern, FB Physik, D-67653 Kaiserslautern, Ger many(Dated: February 1, 2008)We investigate the dynamics of a Bose–Einstein condensate (BEC) in a triple-well trap in athree-level approximation. The inter-atomic interactions are taken into account in a mean-fieldapproximation (Gross-Pitaevskii equation), leading toanonlinear three-levelmodel. Neweigenstatesemerge due to the nonlinearity, depending on the system parameters. Adiabaticity breaks down ifsuch a nonlinear eigenstate disappears when the parameters are varied. The dynamical implicationsof this loss of adiabaticity are analyzed for two important special cases: A three level Landau-Zener model and the STIRAP scheme. We discuss the emergence of looped levels for an equal-slope Landau-Zener model. The Zener tunneling probability does not tend to zero in the adiabaticlimit and shows pronounced oscillations as a function of the velocity of the parameter variation.Furthermore we generalize the STIRAP scheme for adiabatic coherent population transfer betweenatomic states to the nonlinear case. It is shown that STIRAPbreaks down if the nonlinearity exceedsthe detuning.

Bound and resonance states of the nonlinear Schrödinger equation in simple model systems

We study the stationary nonlinear Schrodinger equation, or Gross–Pitaevskii equation, for a single delta potential and a delta-shell potential. These model systems allow analytical solutions, and thus provide useful insight into the features of stationary bound, scattering and resonance states of the nonlinear Schrodinger equation. For the single delta potential, the influence of the potential strength and the nonlinearity is studied as well as the transition from bound to scattering states. Furthermore, the properties of resonance states in a repulsive delta-shell potential are discussed.

Decentral Smart Grid Control

Stable operation of complex flow and transportation networks requires balanced supply and demand. For the operation of electric power grids?due to their increasing fraction of renewable energy sources?a pressing challenge is to fit the fluctuations in decentralized supply to the distributed and temporally varying demands. To achieve this goal, common smart grid concepts suggest to collect consumer demand data, centrally evaluate them given current supply and send price information back to customers for them to decide about usage. Besides restrictions regarding cyber security, privacy protection and large required investments, it remains unclear how such central smart grid options guarantee overall stability. Here we propose a Decentral Smart Grid Control, where the price is directly linked to the local grid frequency at each customer. The grid frequency provides all necessary information about the current power balance such that it is sufficient to match supply and demand without the need for a centralized IT infrastructure. We analyze the performance and the dynamical stability of the power grid with such a control system. Our results suggest that the proposed Decentral Smart Grid Control is feasible independent of effective measurement delays, if frequencies are averaged over sufficiently large time intervals.

Beyond mean-field dynamics of small Bose-Hubbard systems based on the number-conserving phase-space approach

The number-conserving quantum phase space description of the Bose-Hubbard model is discussed for the illustrative case of two and three modes, as well as the generalization of the two-mode case to an open quantum system. The phase-space description based on generalized

Photon sorters and QND detectors using single photon emitters

\mathrm{SU}(M)

Exact number-conserving phase-space dynamics of the M-site Bose-Hubbard model

coherent states yields a Liouvillian flow in the macroscopic limit, which can be efficiently simulated using Monte Carlo methods even for large systems. We show that this description clearly goes beyond the common mean-field limit. In particular it resolves well-known problems where the common mean-field approach fails, such as the description of dynamical instabilities and chaotic dynamics. Moreover, it provides a valuable tool for a semiclassical approximation of many interesting quantities, which depend on higher moments of the quantum state and are therefore not accessible within the common approach. As a prominent example, we analyze the depletion and heating of the condensate. A comparison to methods ignoring the fixed particle number shows that in this case artificial number fluctuations lead to ambiguities and large deviations even for quite simple examples.