Scattering fingerprints of two-state dynamics

Particle transport in complex environments such as the interior of living cells is often (transiently) non-Fickian or anomalous, that is, it deviates from the laws of Brownian motion. Such anomalies may be the result of small-scale spatio-temporal heterogeneities in, or viscoelastic properties of, the medium, molecular crowding, etc. Often the observed dynamics displays multi-state characteristics, i.e. distinct modes of transport dynamically interconverting between each other in a stochastic manner. Reliably distinguishing between single- and multi-state dynamics is challenging and requires a combination of distinct approaches. To complement the existing methods relying on the analysis of the particle's mean squared displacement, position- or displacement-autocorrelation function, and propagators, we here focus on 'scattering fingerprints' of multi-state dynamics. We develop a theoretical framework for two-state scattering signatures—the intermediate scattering function and dynamic structure factor—and apply it to the analysis of simple model systems as well as particle-tracking experiments in living cells. We consider inert tracer-particle motion as well as systems with an internal structure and dynamics. Our results may generally be relevant for the interpretation of state-of-the-art differential dynamic microscopy experiments on complex particulate systems, as well as inelastic or quasielastic neutron (incl. spin-echo) and x-ray scattering probing structural and dynamical properties of macromolecules, when the underlying dynamics displays two-state transport

Singular electrostatic energy of nanoparticle clusters

The binding of clusters of metal nanoparticles is partly electrostatic. We address difficulties in calculating the electrostatic energy when high charging energies limit the total charge to a single quantum, entailing unequal potentials on the particles. We show that the energy at small separation $h$ has a strong logarithmic dependence on $h$. We give a general law for the strength of this logarithmic correction in terms of a) the energy at contact ignoring the charge quantization effects and b) an adjacency matrix specifying which spheres of the cluster are in contact and which is charged. We verify the theory by comparing the predicted energies for a tetrahedral cluster with an explicit numerical calculation.Comment: 17 pages, 3 figures. Submitted to Phys Rev

Unusual electronic ground state of a prototype cuprate: band splitting of single CuO_2-plane Bi_2 Sr_(2-x) La_x CuO_(6+delta)

By in-situ change of polarization a small splitting of the Zhang-Rice singlet state band near the Fermi level has been resolved for optimum doped (x=0.4) Bi$_{2}$Sr$_{2-x}$La$_{x}$CuO$_{6+\delta}$ at the (pi,0)-point (R.Manzke et al. PRB 63, R100504 (2001). Here we treat the momentum dependence and lineshape of the split band by photoemission in the EDC-mode with very high angular and energy resolution. The splitting into two destinct emissions could also be observed over a large portion of the major symmetry line $\Gamma$M, giving the dispersion for the individual contributions. Since bi-layer effects can not be present in this single-layer material the results have to be discussed in the context of one-particle removal spectral functions derived from current theoretical models. The most prominent are microscopic phase separation including striped phase formation, coexisting antiferromagnetic and incommensurate charge-density-wave critical fluctuations coupled to electrons (hot spots) or even spin charge separation within the Luttinger liquid picture, all leading to non-Fermi liquid like behavior in the normal state and having severe consequences on the way the superconducting state forms. Especially the possibilty of observing spinon and holon excitations is discussed.Comment: 5 pages, 4 figure

The Non-Trapping Degree of Scattering

We consider classical potential scattering. If no orbit is trapped at energy E, the Hamiltonian dynamics defines an integer-valued topological degree. This can be calculated explicitly and be used for symbolic dynamics of multi-obstacle scattering. If the potential is bounded, then in the non-trapping case the boundary of Hill's Region is empty or homeomorphic to a sphere. We consider classical potential scattering. If at energy E no orbit is trapped, the Hamiltonian dynamics defines an integer-valued topological degree deg(E) < 2. This is calculated explicitly for all potentials, and exactly the integers < 2 are shown to occur for suitable potentials. The non-trapping condition is restrictive in the sense that for a bounded potential it is shown to imply that the boundary of Hill's Region in configuration space is either empty or homeomorphic to a sphere. However, in many situations one can decompose a potential into a sum of non-trapping potentials with non-trivial degree and embed symbolic dynamics of multi-obstacle scattering. This comprises a large number of earlier results, obtained by different authors on multi-obstacle scattering.Comment: 25 pages, 1 figure Revised and enlarged version, containing more detailed proofs and remark

Leveraging large-deviation statistics to decipher the stochastic properties of measured trajectories

Extensive time-series encoding the position of particles such as viruses, vesicles, or individual proteins are routinely garnered in single-particle tracking experiments or supercomputing studies. They contain vital clues on how viruses spread or drugs may be delivered in biological cells. Similar time-series are being recorded of stock values in financial markets and of climate data. Such time-series are most typically evaluated in terms of time-averaged mean-squared displacements (TAMSDs), which remain random variables for finite measurement times. Their statistical properties are different for different physical stochastic processes, thus allowing us to extract valuable information on the stochastic process itself. To exploit the full potential of the statistical information encoded in measured time-series we here propose an easy-to-implement and computationally inexpensive new methodology, based on deviations of the TAMSD from its ensemble average counterpart. Specifically, we use the upper bound of these deviations for Brownian motion (BM) to check the applicability of this approach to simulated and real data sets. By comparing the probability of deviations for different data sets, we demonstrate how the theoretical bound for BM reveals additional information about observed stochastic processes. We apply the large-deviation method to data sets of tracer beads tracked in aqueous solution, tracer beads measured in mucin hydrogels, and of geographic surface temperature anomalies. Our analysis shows how the large-deviation properties can be efficiently used as a simple yet effective routine test to reject the BM hypothesis and unveil relevant information on statistical properties such as ergodicity breaking and short-time correlations. Video Abstract Video Abstract: Leveraging large-deviation statistics to decipher the stochastic properties of measured trajectorie

Size of Cell-Surface Kv2.1 Domains is Governed by Growth Fluctuations

AbstractThe Kv2.1 voltage-gated potassium channel forms stable clusters on the surface of different mammalian cells. Even though these cell-surface structures have been observed for almost a decade, little is known about the mechanism by which cells maintain them. We measure the distribution of domain sizes to study the kinetics of their growth. Using a Fokker-Planck formalism, we find no evidence for a feedback mechanism present to maintain specific domain radii. Instead, the size of Kv2.1 clusters is consistent with a model where domain size is established by fluctuations in the trafficking machinery. These results are further validated using likelihood and Akaike weights to select the best model for the kinetics of domain growth consistent with our experimental data

A New Type of Electron Nuclear-Spin Interaction from Resistively Detected NMR in the Fractional Quantum Hall Effect Regime

Two dimensional electron gases in narrow GaAs quantum wells show huge longitudinal resistance (HLR) values at certain fractional filling factors. Applying an RF field with frequencies corresponding to the nuclear spin splittings of {69}Ga, {71}Ga and {75}As leads to a substantial decreases of the HLR establishing a novel type of resistively detected NMR. These resonances are split into four sub lines each. Neither the number of sub lines nor the size of the splitting can be explained by established interaction mechanisms.Comment: 4 pages, 3 figure

Spectral content of a single non-Brownian trajectory

Time-dependent processes are often analysed using the power spectral density (PSD), calculated by taking an appropriate Fourier transform of individual trajectories and finding the associated ensemble-average. Frequently, the available experimental data sets are too small for such ensemble averages, and hence it is of a great conceptual and practical importance to understand to which extent relevant information can be gained from $S(f,T)$, the PSD of a single trajectory. Here we focus on the behavior of this random, realization-dependent variable, parametrized by frequency $f$ and observation-time $T$, for a broad family of anomalous diffusions---fractional Brownian motion (fBm) with Hurst-index $H$---and derive exactly its probability density function. We show that $S(f,T)$ is proportional---up to a random numerical factor whose universal distribution we determine---to the ensemble-averaged PSD. For subdiffusion ($H<1/2$) we find that $S(f,T)\sim A/f^{2H+1}$ with random-amplitude $A$. In sharp contrast, for superdiffusion $(H>1/2)$ $S(f,T)\sim BT^{2H-1}/f^2$ with random amplitude $B$. Remarkably, for $H>1/2$ the PSD exhibits the same frequency-dependence as Brownian motion, a deceptive property that may lead to false conclusions when interpreting experimental data. Notably, for $H>1/2$ the PSD is ageing and is dependent on $T$. Our predictions for both sub- and superdiffusion are confirmed by experiments in live cells and in agarose hydrogels, and by extensive simulations.Comment: 13 pages, 5 figures, Supplemental Material can be found at https://journals.aps.org/prx/supplemental/10.1103/PhysRevX.9.011019/prx_SM_final.pd