@misc{KoseskaZaikinKurthsetal.2009, author = {Koseska, Aneta and Zaikin, Alexey and Kurths, J{\"u}rgen and Garc{\´i}a-Ojalvo, Jordi}, title = {Timing cellular decision making under noise via cell-cell communication}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-45260}, year = {2009}, abstract = {Many cellular processes require decision making mechanisms, which must act reliably even in the unavoidable presence of substantial amounts of noise. However, the multistable genetic switches that underlie most decision-making processes are dominated by fluctuations that can induce random jumps between alternative cellular states. Here we show, via theoretical modeling of a population of noise-driven bistable genetic switches, that reliable timing of decision-making processes can be accomplished for large enough population sizes, as long as cells are globally coupled by chemical means. In the light of these results, we conjecture that cell proliferation, in the presence of cell-cell communication, could provide a mechanism for reliable decision making in the presence of noise, by triggering cellular transitions only when the whole cell population reaches a certain size. In other words , the summation performed by the cell population would average out the noise and reduce its detrimental impact.}, language = {en} } @misc{TodtPenaZuehlkeetal.2011, author = {Todt, Helge Tobias and Pe{\~n}a, Miriam and Z{\"u}hlke, Julia and Oskinova, Lida and Hamann, Wolf-Rainer and Gr{\"a}fener, G{\"o}tz}, title = {Weak emission line central stars of planetary nebulae}, series = {Planetary Nebulae: an Eye to the Future}, journal = {Planetary Nebulae: an Eye to the Future}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-413775}, pages = {2}, year = {2011}, abstract = {To understand the evolution and morphology of planetary nebulae, a detailed knowledge of their central stars is required. Central stars that exhibit emission lines in their spectra, indicating stellar mass-loss allow to study the evolution of planetary nebulae in action. Emission line central stars constitute about 10 \% of all central stars. Half of them are practically hydrogen-free Wolf-Rayet type central stars of the carbon sequence, [WC], that show strong emission lines of carbon and oxygen in their spectra. In this contribution we address the weak emission-lines central stars (wels). These stars are poorly analyzed and their hydrogen content is mostly unknown. We obtained optical spectra, that include the important Balmer lines of hydrogen, for four weak emission line central stars. We present the results of our analysis, provide spectral classification and discuss possible explanations for their formation and evolution.}, language = {en} } @misc{FedericiPohlRuppeletal.2011, author = {Federici, S. and Pohl, Martin and Ruppel, J. and Telezhinsky, Igor O. and Hofmann, Werner and Martinez, M. and Knapp, J.}, title = {Design concepts for the Cherenkov Telescope Array CTA}, series = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, volume = {32}, journal = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, number = {1325}, issn = {1866-8372}, doi = {10.25932/publishup-43014}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-430149}, pages = {124}, year = {2011}, abstract = {Ground-based gamma-ray astronomy has had a major breakthrough with the impressive results obtained using systems of imaging atmospheric Cherenkov telescopes. Ground-based gamma-ray astronomy has a huge potential in astrophysics, particle physics and cosmology. CTA is an international initiative to build the next generation instrument, with a factor of 5-10 improvement in sensitivity in the 100 GeV-10 TeV range and the extension to energies well below 100 GeV and above 100 TeV. CTA will consist of two arrays (one in the north, one in the south) for full sky coverage and will be operated as open observatory. The design of CTA is based on currently available technology. This document reports on the status and presents the major design concepts of CTA.}, language = {en} } @misc{BarbosaPfannesAnielskiGerhardtetal.2013, author = {Barbosa Pfannes, Eva Katharina and Anielski, Alexander and Gerhardt, Matthias and Beta, Carsten}, title = {Intracellular photoactivation of caged cGMP induces myosin II and actin responses in motile cells}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-94984}, pages = {1456 -- 1463}, year = {2013}, abstract = {Cyclic GMP (cGMP) is a ubiquitous second messenger in eukaryotic cells. It is assumed to regulate the association of myosin II with the cytoskeleton of motile cells. When cells of the social amoeba Dictyostelium discoideum are exposed to chemoattractants or to increased osmotic stress, intracellular cGMP levels rise, preceding the accumulation of myosin II in the cell cortex. To directly investigate the impact of intracellular cGMP on cytoskeletal dynamics in a living cell, we released cGMP inside the cell by laser-induced photo-cleavage of a caged precursor. With this approach, we could directly show in a live cell experiment that an increase in intracellular cGMP indeed induces myosin II to accumulate in the cortex. Unexpectedly, we observed for the first time that also the amount of filamentous actin in the cell cortex increases upon a rise in the cGMP concentration, independently of cAMP receptor activation and signaling. We discuss our results in the light of recent work on the cGMP signaling pathway and suggest possible links between cGMP signaling and the actin system.}, language = {en} } @misc{PalyulinAlaNissilaMetzler2014, author = {Palyulin, Vladimir V. and Ala-Nissila, Tapio and Metzler, Ralf}, title = {Polymer translocation: the first two decades and the recent diversification}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-76287}, pages = {9016 -- 9037}, year = {2014}, abstract = {Probably no other field of statistical physics at the borderline of soft matter and biological physics has caused such a flurry of papers as polymer translocation since the 1994 landmark paper by Bezrukov, Vodyanoy, and Parsegian and the study of Kasianowicz in 1996. Experiments, simulations, and theoretical approaches are still contributing novel insights to date, while no universal consensus on the statistical understanding of polymer translocation has been reached. We here collect the published results, in particular, the famous-infamous debate on the scaling exponents governing the translocation process. We put these results into perspective and discuss where the field is going. In particular, we argue that the phenomenon of polymer translocation is non-universal and highly sensitive to the exact specifications of the models and experiments used towards its analysis.}, language = {en} } @misc{JeonChechkinMetzler2014, author = {Jeon, Jae-Hyung and Chechkin, Aleksei V. and Metzler, Ralf}, title = {Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-76302}, pages = {15811 -- 15817}, year = {2014}, abstract = {Anomalous diffusion is frequently described by scaled Brownian motion (SBM){,} a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is ?x2(t)? [similar{,} equals] 2K(t)t with K(t) [similar{,} equals] t[small alpha]-1 for 0 < [small alpha] < 2. SBM may provide a seemingly adequate description in the case of unbounded diffusion{,} for which its probability density function coincides with that of fractional Brownian motion. Here we show that free SBM is weakly non-ergodic but does not exhibit a significant amplitude scatter of the time averaged mean squared displacement. More severely{,} we demonstrate that under confinement{,} the dynamics encoded by SBM is fundamentally different from both fractional Brownian motion and continuous time random walks. SBM is highly non-stationary and cannot provide a physical description for particles in a thermalised stationary system. Our findings have direct impact on the modelling of single particle tracking experiments{,} in particular{,} under confinement inside cellular compartments or when optical tweezers tracking methods are used.}, language = {en} } @misc{GoychukKharchenkoMetzler2014, author = {Goychuk, Igor A. and Kharchenko, Vasyl O. and Metzler, Ralf}, title = {Molecular motors pulling cargos in the viscoelastic cytosol: how power strokes beat subdiffusion}, series = {Physical Chemistry Chemical Physics}, journal = {Physical Chemistry Chemical Physics}, publisher = {The Royal Society of Chemistry}, address = {Cambridge}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-76478}, pages = {16524 -- 16535}, year = {2014}, abstract = {The discovery of anomalous diffusion of larger biopolymers and submicron tracers such as endogenous granules, organelles, or virus capsids in living cells, attributed to the viscoelastic nature of the cytoplasm, provokes the question whether this complex environment equally impacts the active intracellular transport of submicron cargos by molecular motors such as kinesins: does the passive anomalous diffusion of free cargo always imply its anomalously slow active transport by motors, the mean transport distance along microtubule growing sublinearly rather than linearly in time? Here we analyze this question within the widely used two-state Brownian ratchet model of kinesin motors based on the continuous-state diffusion along microtubules driven by a flashing binding potential, where the cargo particle is elastically attached to the motor. Depending on the cargo size, the loading force, the amplitude of the binding potential, the turnover frequency of the molecular motor enzyme, and the linker stiffness we demonstrate that the motor transport may turn out either normal or anomalous, as indeed measured experimentally. We show how a highly efficient normal active transport mediated by motors may emerge despite the passive anomalous diffusion of the cargo, and study the intricate effects of the elastic linker. Under different, well specified conditions the microtubule-based motor transport becomes anomalously slow and thus significantly less efficient.}, language = {en} } @misc{deCarvalhoMetzlerCherstvy2014, author = {de Carvalho, Sidney J. and Metzler, Ralf and Cherstvy, Andrey G.}, title = {Critical adsorption of polyelectrolytes onto charged Janus nanospheres}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-98783}, pages = {12}, year = {2014}, abstract = {Based on extensive Monte Carlo simulations and analytical considerations we study the electrostatically driven adsorption of flexible polyelectrolyte chains onto charged Janus nanospheres. These net-neutral colloids are composed of two equally but oppositely charged hemispheres. The critical binding conditions for polyelectrolyte chains are analysed as function of the radius of the Janus particle and its surface charge density, as well as the salt concentration in the ambient solution. Specifically for the adsorption of finite-length polyelectrolyte chains onto Janus nanoparticles, we demonstrate that the critical adsorption conditions drastically differ when the size of the Janus particle or the screening length of the electrolyte are varied. We compare the scaling laws obtained for the adsorption-desorption threshold to the known results for uniformly charged spherical particles, observing significant disparities. We also contrast the changes to the polyelectrolyte chain conformations close to the surface of the Janus nanoparticles as compared to those for simple spherical particles. Finally, we discuss experimentally relevant physico-chemical systems for which our simulations results may become important. In particular, we observe similar trends with polyelectrolyte complexation with oppositely but heterogeneously charged proteins.}, language = {en} } @misc{BauerGodecMetzler2014, author = {Bauer, Maximilian and Godec, Aljaž and Metzler, Ralf}, title = {Diffusion of finite-size particles in two-dimensional channels with random wall configurations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-76199}, year = {2014}, abstract = {Diffusion of chemicals or tracer molecules through complex systems containing irregularly shaped channels is important in many applications. Most theoretical studies based on the famed Fick-Jacobs equation focus on the idealised case of infinitely small particles and reflecting boundaries. In this study we use numerical simulations to consider the transport of finite-size particles through asymmetrical two-dimensional channels. Additionally, we examine transient binding of the molecules to the channel walls by applying sticky boundary conditions. We consider an ensemble of particles diffusing in independent channels, which are characterised by common structural parameters. We compare our results for the long-time effective diffusion coefficient with a recent theoretical formula obtained by Dagdug and Pineda [J. Chem. Phys., 2012, 137, 024107].}, language = {en} } @misc{LiuTkachovKomberetal.2014, author = {Liu, W. and Tkachov, R. and Komber, H. and Senkovskyy, V. and Schubert, M. and Wei, Z. and Facchetti, A. and Neher, Dieter and Kiriy, A.}, title = {Chain-growth polycondensation of perylene diimide-based copolymers}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-98724}, pages = {8}, year = {2014}, abstract = {Herein, we report the chain-growth tin-free room temperature polymerization method to synthesize n-type perylene diimide-dithiophene-based conjugated polymers (PPDIT2s) suitable for solar cell and transistor applications. The palladium/electron-rich tri-tert-butylphosphine catalyst is effective to enable the chain-growth polymerization of anion-radical monomer Br-TPDIT-Br/Zn to PPDIT2 with a molecular weight up to Mw ≈ 50 kg mol-1 and moderate polydispersity. This is the second example of the polymerization of unusual anion-radical aromatic complexes formed in a reaction of active Zn and electron-deficient diimide-based aryl halides. As such, the discovered polymerization method is not a specific reactivity feature of the naphthalene-diimide derivatives but is rather a general polymerization tool. This is an important finding, given the significantly higher maximum external quantum efficiency that can be reached with PDI-based copolymers (32-45\%) in all-polymer solar cells compared to NDI-based materials (15-30\%). Our studies revealed that PPDIT2 synthesized by the new method and the previously published polymer prepared by step-growth Stille polycondensation show similar electron mobility and all-polymer solar cell performance. At the same time, the polymerization reported herein has several technological advantages as it proceeds relatively fast at room temperature and does not involve toxic tin-based compounds. Because several chain-growth polymerization reactions are well-suited for the preparation of well-defined multi-functional polymer architectures, the next target is to explore the utility of the discovered polymerization in the synthesis of end-functionalized polymers and block copolymers. Such materials would be helpful to improve the nanoscale morphology of polymer blends in all-polymer solar cells.}, language = {en} } @misc{MetzlerBauerRasmussenetal.2015, author = {Metzler, Ralf and Bauer, Maximilian and Rasmussen, Emil S. and Lomholt, Michael A.}, title = {Real sequence effects on the search dynamics of transcription factors on DNA}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-79411}, year = {2015}, abstract = {Recent experiments show that transcription factors (TFs) indeed use the facilitated diffusion mechanism to locate their target sequences on DNA in living bacteria cells: TFs alternate between sliding motion along DNA and relocation events through the cytoplasm. From simulations and theoretical analysis we study the TF-sliding motion for a large section of the DNA-sequence of a common E. coli strain, based on the two-state TF-model with a fast-sliding search state and a recognition state enabling target detection. For the probability to detect the target before dissociating from DNA the TF-search times self-consistently depend heavily on whether or not an auxiliary operator (an accessible sequence similar to the main operator) is present in the genome section. Importantly, within our model the extent to which the interconversion rates between search and recognition states depend on the underlying nucleotide sequence is varied. A moderate dependence maximises the capability to distinguish between the main operator and similar sequences. Moreover, these auxiliary operators serve as starting points for DNA looping with the main operator, yielding a spectrum of target detection times spanning several orders of magnitude. Auxiliary operators are shown to act as funnels facilitating target detection by TFs.}, language = {en} } @misc{PulkkinenMetzler2015, author = {Pulkkinen, Otto and Metzler, Ralf}, title = {Variance-corrected Michaelis-Menten equation predicts transient rates of single-enzyme reactions and response times in bacterial gene-regulation}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-86632}, year = {2015}, abstract = {Many chemical reactions in biological cells occur at very low concentrations of constituent molecules. Thus, transcriptional gene-regulation is often controlled by poorly expressed transcription-factors, such as E.coli lac repressor with few tens of copies. Here we study the effects of inherent concentration fluctuations of substrate-molecules on the seminal Michaelis-Menten scheme of biochemical reactions. We present a universal correction to the Michaelis-Menten equation for the reaction-rates. The relevance and validity of this correction for enzymatic reactions and intracellular gene-regulation is demonstrated. Our analytical theory and simulation results confirm that the proposed variance-corrected Michaelis-Menten equation predicts the rate of reactions with remarkable accuracy even in the presence of large non-equilibrium concentration fluctuations. The major advantage of our approach is that it involves only the mean and variance of the substrate-molecule concentration. Our theory is therefore accessible to experiments and not specific to the exact source of the concentration fluctuations.}, language = {en} } @misc{MetzlerCherstvyChechkinetal.2015, author = {Metzler, Ralf and Cherstvy, Andrey G. and Chechkin, Aleksei V. and Bodrova, Anna S.}, title = {Ultraslow scaled Brownian motion}, series = {New journal of physics : the open-access journal for physics}, journal = {New journal of physics : the open-access journal for physics}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-78618}, year = {2015}, abstract = {We define and study in detail utraslow scaled Brownian motion (USBM) characterized by a time dependent diffusion coefficient of the form . For unconfined motion the mean squared displacement (MSD) of USBM exhibits an ultraslow, logarithmic growth as function of time, in contrast to the conventional scaled Brownian motion. In a harmonic potential the MSD of USBM does not saturate but asymptotically decays inverse-proportionally to time, reflecting the highly non-stationary character of the process. We show that the process is weakly non-ergodic in the sense that the time averaged MSD does not converge to the regular MSD even at long times, and for unconfined motion combines a linear lag time dependence with a logarithmic term. The weakly non-ergodic behaviour is quantified in terms of the ergodicity breaking parameter. The USBM process is also shown to be ageing: observables of the system depend on the time gap between initiation of the test particle and start of the measurement of its motion. Our analytical results are shown to agree excellently with extensive computer simulations.}, language = {en} } @misc{DasPradhan2015, author = {Das, Samir and Pradhan, Basudev}, title = {Photophysical and photochemical properties of a family of isoelectronic tris chelated ruthenium(II) aza-/azo-aromatic complexes}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-102320}, pages = {73726 -- 73731}, year = {2015}, abstract = {We have investigated the electrochemical, spectroscopic and electroluminescent properties of a family of aza-aromatic complexes of ruthenium of type [RuII(bpy/phen)2(L)]2+ (4d6) with three isomeric L ligands, where, bpy = 2,2′-bipyridine, phen = 1,10-phenanthroline and the L ligands are 3-(2-pyridyl)[1,2,4]triazolo[1,5-a]pyridine (L1), 3-(2-pyridyl[1,2,3])triazolo[1,5-a]pyridine (L2) and 2-(2-pyridyl)[1,2,4]triazolo[1,5-a]pyridine (L3). The complexes display two bands in the visible region near 410-420 and 440-450 nm. The complexes are diamagnetic and show well defined 1H NMR lines. They are electroactive in acetonitrile solution and exhibit a well defined RuII/RuIII couple near 1.20 to 1.30 V and -1.40 to -1.50 V due to ligand reduction versus Saturated Calomel Electrode (SCE). The solutions are also luminescent, with peaks are near 600 nm. All the complexes are electroluminescent in nature with peaks lying near 580 nm. L1 and L3 ligated complexes with two bpy co-ligands show weak photoluminescence (PL) but stronger electroluminescence (EL) compared to corresponding L2 ligated analogues.}, language = {en} } @misc{GoychukGoychuk2015, author = {Goychuk, Igor and Goychuk, Andriy}, title = {Stochastic Wilson}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-77814}, year = {2015}, abstract = {We consider a simple Markovian class of the stochastic Wilson-Cowan type models of neuronal network dynamics, which incorporates stochastic delay caused by the existence of a refractory period of neurons. From the point of view of the dynamics of the individual elements, we are dealing with a network of non-Markovian stochastic two-state oscillators with memory, which are coupled globally in a mean-field fashion. This interrelation of a higher-dimensional Markovian and lower-dimensional non-Markovian dynamics is discussed in its relevance to the general problem of the network dynamics of complex elements possessing memory. The simplest model of this class is provided by a three-state Markovian neuron with one refractory state, which causes firing delay with an exponentially decaying memory within the two-state reduced model. This basic model is used to study critical avalanche dynamics (the noise sustained criticality) in a balanced feedforward network consisting of the excitatory and inhibitory neurons. Such avalanches emerge due to the network size dependent noise (mesoscopic noise). Numerical simulations reveal an intermediate power law in the distribution of avalanche sizes with the critical exponent around -1.16. We show that this power law is robust upon a variation of the refractory time over several orders of magnitude. However, the avalanche time distribution is biexponential. It does not reflect any genuine power law dependence.}, language = {en} } @misc{MitzscherlingCuiKoopmanetal.2015, author = {Mitzscherling, Steffen and Cui, Qianling and Koopman, Wouter-Willem Adriaan and Bargheer, Matias}, title = {Dielectric function of two-phase colloid-polymer nanocomposite}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-102695}, pages = {29465 -- 29474}, year = {2015}, abstract = {The plasmon resonance of metal nanoparticles determines their optical response in the visible spectral range. Many details such as the electronic properties of gold near the particle surface and the local environment of the particles influence the spectra. We show how the cheap but highly precise fabrication of composite nanolayers by spin-assisted layer-by-layer deposition of polyelectrolytes can be used to investigate the spectral response of gold nanospheres (GNS) and gold nanorods (GNR) in a self-consistent way, using the established Maxwell-Garnett effective medium (MGEM) theory beyond the limit of homogeneous media. We show that the dielectric function of gold nanoparticles differs from the bulk value and experimentally characterize the shape and the surrounding of the particles thoroughly by SEM, AFM and ellipsometry. Averaging the dielectric functions of the layered surrounding by an appropriate weighting with the electric field intensity yields excellent agreement for the spectra of several nanoparticles and nanorods with various cover-layer thicknesses.}, language = {en} } @misc{Guehr2016, author = {G{\"u}hr, Markus}, title = {Ultrafast Soft X-ray Probing of Gas Phase Molecular Dynamics}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-97215}, year = {2016}, abstract = {The molecular ability to selectively and efficiently convert sunlight into other forms of energy like heat, bond change, or charge separation is truly remarkable. The decisive steps in these transformations often happen on a femtosecond timescale and require transitions among different electronic states that violate the Born-Oppenheimer approximation (BOA). Non-BOA transitions pose challenges to both theory and experiment. From a theoretical point of view, excited state dynamics and nonadiabatic transitions both are difficult problems (see Figure 1(a)). However, the theory on non-BOA dynamics has advanced significantly over the last two decades. Full dynamical simulations for molecules of the size of nucleobases have been possible for a couple of years and allow predictions of experimental observables like photoelectron energy or ion yield. The availability of these calculations for isolated molecules has spurred new experimental efforts to develop methods that are sufficiently different from all optical techniques. For determination of transient molecular structure, femtosecond X-ray diffraction and electron diffraction have been implemented on optically excited molecules.}, language = {en} } @misc{GhoshCherstvyPetrovetal.2016, author = {Ghosh, Surya K. and Cherstvy, Andrey G. and Petrov, Eugene P. and Metzler, Ralf}, title = {Interactions of rod-like particles on responsive elastic sheets}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-95882}, year = {2016}, abstract = {What are the physical laws of the mutual interactions of objects bound to cell membranes, such as various membrane proteins or elongated virus particles? To rationalise this, we here investigate by extensive computer simulations mutual interactions of rod-like particles adsorbed on the surface of responsive elastic two-dimensional sheets. Specifically, we quantify sheet deformations as a response to adhesion of such filamentous particles. We demonstrate that tip-to-tip contacts of rods are favoured for relatively soft sheets, while side-by-side contacts are preferred for stiffer elastic substrates. These attractive orientation-dependent substrate-mediated interactions between the rod-like particles on responsive sheets can drive their aggregation and self-assembly. The optimal orientation of the membrane-bound rods is established via responding to the elastic energy profiles created around the particles. We unveil the phase diagramme of attractive-repulsive rod-rod interactions in the plane of their separation and mutual orientation. Applications of our results to other systems featuring membrane-associated particles are also discussed.}, language = {en} } @misc{CherstvyMetzler2016, author = {Cherstvy, Andrey G. and Metzler, Ralf}, title = {Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-95901}, pages = {23840 -- 23852}, year = {2016}, abstract = {We investigate the ensemble and time averaged mean squared displacements for particle diffusion in a simple model for disordered media by assuming that the local diffusivity is both fluctuating in time and has a deterministic average growth or decay in time. In this study we compare computer simulations of the stochastic Langevin equation for this random diffusion process with analytical results. We explore the regimes of normal Brownian motion as well as anomalous diffusion in the sub- and superdiffusive regimes. We also consider effects of the inertial term on the particle motion. The investigation of the resulting diffusion is performed for unconfined and confined motion.}, language = {en} } @misc{Goychuk2016, author = {Goychuk, Igor}, title = {Quantum ergodicity breaking in semi-classical electron transfer dynamics}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-102264}, pages = {11}, year = {2016}, abstract = {Can the statistical properties of single-electron transfer events be correctly predicted within a common equilibrium ensemble description? This fundamental in nanoworld question of ergodic behavior is scrutinized within a very basic semi-classical curve-crossing problem. It is shown that in the limit of non-adiabatic electron transfer (weak tunneling) well-described by the Marcus-Levich-Dogonadze(MLD) rate the answer is yes. However, in the limit of the so-called solvent-controlled adiabatic electron transfer, a profound breaking of ergodicity occurs. Namely, a common description based on the ensemble reduced density matrix with an initial equilibrium distribution of the reaction coordinate is not able to reproduce the statistics of single-trajectory events in this seemingly classical regime. For sufficiently large activation barriers, the ensemble survival probability in a state remains nearly exponential with the inverse rate given by the sum of the adiabatic curve crossing (Kramers) time and the inverse MLD rate. In contrast, near to the adiabatic regime, the single-electron survival probability is clearly non-exponential, even though it possesses an exponential tail which agrees well with the ensemble description. Initially, it is well described by a Mittag-Leffler distribution with a fractional rate. Paradoxically, the mean transfer time in this classical on the ensemble level regime is well described by the inverse of the nonadiabatic quantum tunneling rate on a single particle level. An analytical theory is developed which perfectly agrees with stochastic simulations and explains our findings.}, language = {en} }