@misc{ŚlęzakMetzlerMagdziarz2019,
  author    = {Ślęzak, Jakub and Metzler, Ralf and Magdziarz, Marcin},
  title     = {Codifference can detect ergodicity breaking and non-Gaussianity},
  series = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe},
  number    = {748},
  doi       = {10.25932/publishup-43617},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-436178},
  pages     = {25},
  year      = {2019},
  abstract  = {We show that the codifference is a useful tool in studying the ergodicity breaking and non-Gaussianity properties of stochastic time series. While the codifference is a measure of dependence that was previously studied mainly in the context of stable processes, we here extend its range of applicability to random-parameter and diffusing-diffusivity models which are important in contemporary physics, biology and financial engineering. We prove that the codifference detects forms of dependence and ergodicity breaking which are not visible from analysing the covariance and correlation functions. We also discuss a related measure of dispersion, which is a nonlinear analogue of the mean squared displacement.},
  language  = {en}
}
@misc{ŚlęzakMetzlerMagdziarz2018,
  author    = {Ślęzak, Jakub and Metzler, Ralf and Magdziarz, Marcin},
  title     = {Superstatistical generalised Langevin equation},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-409315},
  pages     = {25},
  year      = {2018},
  abstract  = {Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter systems. We here formulate a stochastic model based on a generalised Langevin equation in which non-Gaussian shapes of the probability density function and normal or anomalous diffusion have a common origin, namely a random parametrisation of the stochastic force. We perform a detailed analysis demonstrating how various types of parameter distributions for the memory kernel result in exponential, power law, or power-log law tails of the memory functions. The studied system is also shown to exhibit a further unusual property: the velocity has a Gaussian one point probability density but non-Gaussian joint distributions. This behaviour is reflected in the relaxation from a Gaussian to a non-Gaussian distribution observed for the position variable. We show that our theoretical results are in excellent agreement with stochastic simulations.},
  language  = {en}
}
@article{ŚlęzakMetzlerMagdziarz2018,
  author    = {Ślęzak, Jakub and Metzler, Ralf and Magdziarz, Marcin},
  title     = {Superstatistical generalised Langevin equation},
  series = {New Journal of Physics},
  volume    = {20},
  journal   = {New Journal of Physics},
  number    = {023026},
  publisher = {Deutsche Physikalische Gesellschaft / Institute of Physics},
  address   = {Bad Honnef und London},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/aaa3d4},
  pages     = {1 -- 25},
  year      = {2018},
  abstract  = {Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter systems. We here formulate a stochastic model based on a generalised Langevin equation in which non-Gaussian shapes of the probability density function and normal or anomalous diffusion have a common origin, namely a random parametrisation of the stochastic force. We perform a detailed analysis demonstrating how various types of parameter distributions for the memory kernel result in exponential, power law, or power-log law tails of the memory functions. The studied system is also shown to exhibit a further unusual property: the velocity has a Gaussian one point probability density but non-Gaussian joint distributions. This behaviour is reflected in the relaxation from a Gaussian to a non-Gaussian distribution observed for the position variable. We show that our theoretical results are in excellent agreement with stochastic simulations.},
  language  = {en}
}
@article{ŚlęzakMetzlerMagdziarz2019,
  author    = {Ślęzak, Jakub and Metzler, Ralf and Magdziarz, Marcin},
  title     = {Codifference can detect ergodicity breaking and non-Gaussianity},
  series = {New Journal of Physics},
  volume    = {21},
  journal   = {New Journal of Physics},
  publisher = {Deutsche Physikalische Gesellschaft},
  address   = {Bad Honnef},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/ab13f3},
  pages     = {25},
  year      = {2019},
  abstract  = {We show that the codifference is a useful tool in studying the ergodicity breaking and non-Gaussianity properties of stochastic time series. While the codifference is a measure of dependence that was previously studied mainly in the context of stable processes, we here extend its range of applicability to random-parameter and diffusing-diffusivity models which are important in contemporary physics, biology and financial engineering. We prove that the codifference detects forms of dependence and ergodicity breaking which are not visible from analysing the covariance and correlation functions. We also discuss a related measure of dispersion, which is a nonlinear analogue of the mean squared displacement.},
  language  = {en}
}
@misc{ŚlęzakBurneckiMetzler2019,
  author    = {Ślęzak, Jakub and Burnecki, Krzysztof and Metzler, Ralf},
  title     = {Random coefficient autoregressive processes describe Brownian yet non-Gaussian diffusion in heterogeneous systems},
  series = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe},
  number    = {765},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-43792},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-437923},
  pages     = {18},
  year      = {2019},
  abstract  = {Many studies on biological and soft matter systems report the joint presence of a linear mean-squared displacement and a non-Gaussian probability density exhibiting, for instance, exponential or stretched-Gaussian tails. This phenomenon is ascribed to the heterogeneity of the medium and is captured by random parameter models such as 'superstatistics' or 'diffusing diffusivity'. Independently, scientists working in the area of time series analysis and statistics have studied a class of discrete-time processes with similar properties, namely, random coefficient autoregressive models. In this work we try to reconcile these two approaches and thus provide a bridge between physical stochastic processes and autoregressive models.Westart from the basic Langevin equation of motion with time-varying damping or diffusion coefficients and establish the link to random coefficient autoregressive processes. By exploring that link we gain access to efficient statistical methods which can help to identify data exhibiting Brownian yet non-Gaussian diffusion.},
  language  = {en}
}
@article{ŚlęzakBurneckiMetzler2019,
  author    = {Ślęzak, Jakub and Burnecki, Krzysztof and Metzler, Ralf},
  title     = {Random coefficient autoregressive processes describe Brownian yet non-Gaussian diffusion in heterogeneous systems},
  series = {New Journal of Physics},
  volume    = {21},
  journal   = {New Journal of Physics},
  publisher = {Deutsche Physikalische Gesellschaft ; IOP, Institute of Physics},
  address   = {Bad Honnef und London},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/ab3366},
  pages     = {18},
  year      = {2019},
  abstract  = {Many studies on biological and soft matter systems report the joint presence of a linear mean-squared displacement and a non-Gaussian probability density exhibiting, for instance, exponential or stretched-Gaussian tails. This phenomenon is ascribed to the heterogeneity of the medium and is captured by random parameter models such as 'superstatistics' or 'diffusing diffusivity'. Independently, scientists working in the area of time series analysis and statistics have studied a class of discrete-time processes with similar properties, namely, random coefficient autoregressive models. In this work we try to reconcile these two approaches and thus provide a bridge between physical stochastic processes and autoregressive models.Westart from the basic Langevin equation of motion with time-varying damping or diffusion coefficients and establish the link to random coefficient autoregressive processes. By exploring that link we gain access to efficient statistical methods which can help to identify data exhibiting Brownian yet non-Gaussian diffusion.},
  language  = {en}
}
@phdthesis{Zoeller2005,
  author    = {Z{\"o}ller, Gert},
  title     = {Critical states of seismicity : modeling and data analysis},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-7427},
  school      = {Universit{\"a}t Potsdam},
  year      = {2005},
  abstract  = {The occurrence of earthquakes is characterized by a high degree of spatiotemporal complexity. Although numerous patterns, e.g. fore- and aftershock sequences, are well-known, the underlying mechanisms are not observable and thus not understood. Because the recurrence times of large earthquakes are usually decades or centuries, the number of such events in corresponding data sets is too small to draw conclusions with reasonable statistical significance. Therefore, the present study combines both, numerical modeling and analysis of real data in order to unveil the relationships between physical mechanisms and observational quantities. The key hypothesis is the validity of the so-called "critical point concept" for earthquakes, which assumes large earthquakes to occur as phase transitions in a spatially extended many-particle system, similar to percolation models. New concepts are developed to detect critical states in simulated and in natural data sets. The results indicate that important features of seismicity like the frequency-size distribution and the temporal clustering of earthquakes depend on frictional and structural fault parameters. In particular, the degree of quenched spatial disorder (the "roughness") of a fault zone determines whether large earthquakes occur quasiperiodically or more clustered. This illustrates the power of numerical models in order to identify regions in parameter space, which are relevant for natural seismicity. The critical point concept is verified for both, synthetic and natural seismicity, in terms of a critical state which precedes a large earthquake: a gradual roughening of the (unobservable) stress field leads to a scale-free (observable) frequency-size distribution. Furthermore, the growth of the spatial correlation length and the acceleration of the seismic energy release prior to large events is found. The predictive power of these precursors is, however, limited. Instead of forecasting time, location, and magnitude of individual events, a contribution to a broad multiparameter approach is encouraging.},
  subject      = {Seismizit{\"a}t},
  language  = {en}
}
@phdthesis{Zoeller1999,
  author    = {Z{\"o}ller, Gert},
  title     = {Analyse raumzeitlicher Muster in Erdbebendaten},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-0000122},
  school      = {Universit{\"a}t Potsdam},
  year      = {1999},
  abstract  = {Die vorliegende Arbeit besch{\"a}ftigt sich mit der Charakterisierung von Seismizit{\"a}t anhand von Erdbebenkatalogen. Es werden neue Verfahren der Datenanalyse entwickelt, die Aufschluss dar{\"u}ber geben sollen, ob der seismischen Dynamik ein stochastischer oder ein deterministischer Prozess zugrunde liegt und was daraus f{\"u}r die Vorhersagbarkeit starker Erdbeben folgt. Es wird gezeigt, dass seismisch aktive Regionen h{\"a}ufig durch nichtlinearen Determinismus gekennzeichent sind. Dies schließt zumindest die M{\"o}glichkeit einer Kurzzeitvorhersage ein. Das Auftreten seismischer Ruhe wird h{\"a}ufig als Vorl{\"a}uferphaenomen f{\"u}r starke Erdbeben gedeutet. Es wird eine neue Methode pr{\"a}sentiert, die eine systematische raumzeitliche Kartierung seismischer Ruhephasen erm{\"o}glicht. Die statistische Signifikanz wird mit Hilfe des Konzeptes der Ersatzdaten bestimmt. Als Resultat erh{\"a}lt man deutliche Korrelationen zwischen seismischen Ruheperioden und starken Erdbeben. Gleichwohl ist die Signifikanz daf{\"u}r nicht hoch genug, um eine Vorhersage im Sinne einer Aussage {\"u}ber den Ort, die Zeit und die St{\"a}rke eines zu erwartenden Hauptbebens zu erm{\"o}glichen.},
  language  = {en}
}
@article{ZuoShoaeeKemerinketal.2021,
  author    = {Zuo, Guangzheng and Shoaee, Safa and Kemerink, Martijn and Neher, Dieter},
  title     = {General rules for the impact of energetic disorder and mobility on nongeminate recombination in phase-separated organic solar cells},
  series = {Physical review applied},
  volume    = {16},
  journal   = {Physical review applied},
  number    = {3},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {2331-7019},
  doi       = {10.1103/PhysRevApplied.16.034027},
  pages     = {19},
  year      = {2021},
  abstract  = {State-of-the-art organic solar cells exhibit power conversion efficiencies of 18\% and above. These devices benefit from the suppression of free charge recombination with regard to the Langevin limit of charge encounter in a homogeneous medium. It is recognized that the main cause of suppressed free charge recombination is the reformation and resplitting of charge-transfer (CT) states at the interface between donor and acceptor domains. Here, we use kinetic Monte Carlo simulations to understand the interplay between free charge motion and recombination in an energetically disordered phase-separated donor-acceptor blend. We identify conditions for encounter-dominated and resplitting-dominated recombination. In the former regime, recombination is proportional to mobility for all parameters tested and only slightly reduced with respect to the Langevin limit. In contrast, mobility is not the decisive parameter that determines the nongeminate recombination coefficient, k(2), in the latter case, where k2 is a sole function of the morphology, CT and charge-separated (CS) energetics, and CT-state decay properties. Our simulations also show that free charge encounter in the phase-separated disordered blend is determined by the average mobility of all carriers, while CT reformation and resplitting involves mostly states near the transport energy. Therefore, charge encounter is more affected by increased disorder than the resplitting of the CT state. As a consequence, for a given mobility, larger energetic disorder, in combination with a higher hopping rate, is preferred. These findings have implications for the understanding of suppressed recombination in solar cells with nonfullerene acceptors, which are known to exhibit lower energetic disorder than that of fullerenes.},
  language  = {en}
}
@article{ZuWolffRalaiarisoaetal.2019,
  author    = {Zu, Fengshuo and Wolff, Christian Michael and Ralaiarisoa, Maryline and Amsalem, Patrick and Neher, Dieter and Koch, Norbert},
  title     = {Unraveling the Electronic Properties of Lead Halide Perovskites with Surface Photovoltage in Photoemission Studies},
  series = {ACS applied materials \& interfaces},
  volume    = {11},
  journal   = {ACS applied materials \& interfaces},
  number    = {24},
  publisher = {American Chemical Society},
  address   = {Washington},
  issn      = {1944-8244},
  doi       = {10.1021/acsami.9b05293},
  pages     = {21578 -- 21583},
  year      = {2019},
  abstract  = {The tremendous success of metal-halide perovskites, especially in the field of photovoltaics, has triggered a substantial number of studies in understanding their optoelectronic properties. However, consensus regarding the electronic properties of these perovskites is lacking due to a huge scatter in the reported key parameters, such as work function (Φ) and valence band maximum (VBM) values. Here, we demonstrate that the surface photovoltage (SPV) is a key phenomenon occurring at the perovskite surfaces that feature a non-negligible density of surface states, which is more the rule than an exception for most materials under study. With ultraviolet photoelectron spectroscopy (UPS) and Kelvin probe, we evidence that even minute UV photon fluxes (500 times lower than that used in typical UPS experiments) are sufficient to induce SPV and shift the perovskite Φ and VBM by several 100 meV compared to dark. By combining UV and visible light, we establish flat band conditions (i.e., compensate the surface-state-induced surface band bending) at the surface of four important perovskites, and find that all are p-type in the bulk, despite a pronounced n-type surface character in the dark. The present findings highlight that SPV effects must be considered in all surface studies to fully understand perovskites' photophysical properties.},
  language  = {en}
}