Universal nature of particle displacements close to glass and jamming transitions

We examine the structure of the distribution of single particle displacements (van Hove function) in a broad class of materials close to glass and jamming transitions. In a wide time window comprising structural relaxation, van Hove functions reflect the coexistence of slow and fast particles (dynamic heterogeneity). The tails of the distributions exhibit exponential, rather than Gaussian, decay. We argue that this behavior is universal in glassy materials and should be considered the analog, in space, of the stretched exponential decay of time correlation functions. We introduce a dynamical model that describes quantitatively numerical and experimental data in supercooled liquids, colloidal hard spheres, and granular materials. The tails of the distributions directly explain the decoupling between translational diffusion and structural relaxation observed in glassy materials.     

Maximum Entropy Analysis of Analytically Simulated Complex Fluorescence Decays

We tested a Maximum Entropy Method developed for oversampled data (SVD-MEM) on complex analytically simulated exponential decay data consisting of both noisy and noiseless multi-exponential fluorescence decay curves. We observed recovery of simulated parameters for three sets of data: a decay containing three exponential functions in both intensity and anisotropy curves, a set of intensity decays composed of 4, 5 and 6 exponential functions, and a decay characterized by a Gaussian lifetime distribution. The SVD-MEM fitting of the noiseless data returned the simulated parameters with the high accuracy. Noise added to the data affected recovery of the parameters in dependence on a data complexity. At selected realistic noise levels we obtained a good recovery of simulated parameters for all tested data sets. Decay parameters recovered from decays containing discrete lifetime components were almost independent of the value of the entropy scaling parameter γ used in the maximization procedure when it changed across the main peak of its posterior probability. A correct recovery of the Gaussian shaped lifetime distribution required selection of the γ-factor which was by several orders of magnitude larger than its most probable value to avoid a band splitting.     

A Langevin approach to the Log–Gauss–Pareto composite statistical structure

The distribution of wealth in human populations displays a Log–Gauss–Pareto composite statistical structure: its density is Log–Gauss in its central body, and follows power-law decay in its tails. This composite statistical structure is further observed in other complex systems, and on a logarithmic scale it displays a Gauss-Exponential structure: its density is Gauss in its central body, and follows exponential decay in its tails. In this paper we establish an equilibrium Langevin explanation for this statistical phenomenon, and show that: (i) the stationary distributions of Langevin dynamics with sigmoidal force functions display a Gauss-Exponential composite statistical structure; (ii) the stationary distributions of geometric Langevin dynamics with sigmoidal force functions display a Log–Gauss–Pareto composite statistical structure. This equilibrium Langevin explanation is universal — as it is invariant with respect to the specific details of the sigmoidal force functions applied, and as it is invariant with respect to the specific statistics of the underlying noise.     

Asymptotic behavior of correlation functions for electric potential and field fluctuations in a classical one- component plasma

The correlations of the electric potential fluctuations in a classical one-component plasma are studied for large distances between the observation points. The two-point correlation function for these fluctuations is known to decay slowly for large distances, even if exponential clustering holds for the charge correlation functions. In this paper the asymptotic behavior of the generalk-point electric potential correlation functions is analyzed. Each of these correlation functions can be split into a reducible part, which is given by a sum of products of lower-order correlation functions, and a remaining irreducible part. It is shown, on the basis of an exponential clustering hypothesis for the charge correlation functions, that for allk3 the irreducible parts of the electric potential correlation functions decay faster than any inverse power of the distance, if one or more of the observation points move far away from the others. Hence, the two-point electric potential correlation function is the only one with a slow algebraic decay. The same statement holds for the correlation functions of the electric field fluctuations.     

Untersuchung der Lumineszenzabklingung von Wolframatleuchtstoffen nach Anregung mit UV-Licht und Elektronen

The decay of the luminescence of CaWO₄, CdWO₄, MgWO₄, and ZnWO₄ after excitation with short pulses of light and electron beams has been investigated at different temperatures. Excitation with UV-light yields an exponential decay, and from the temperature dependence of the decay time it can be concluded that at high temperatures non-radiative transitions are prevalent. After excitation with electrons, there are additional effects by the heating up of the “excitation channel”. In this case the decay is not purely exponential and thermoluminescence is observed. This indicates the existence of traps, which are assumed to be located in the centers of the luminescence.     

Heterogeneous relaxation patterns in supercooled liquids studied by solvation dynamics

We have measured the solvation dynamics of a dipolar supercooled liquid near its glass transition in a temperature range in which the average structural relaxation time varies more than four orders of magnitude. The analysis of the time dependent average emission energy and the inhomogeneous linewidth of the S0<--T1(0-0) transition reveals that the orientation correlation decay pattern intrinsic in each relaxing unit is associated with a stretching exponent beta(intr)=1.00+/-0.08 in the entire range T(g)(KWW) the individual time constants remain correlated to their initial values at t=0.     

A two-dimensional isotropic quantum antiferromagnet with unique disordered ground state

We continue the study of valence-bond solid antiferromagnetic quantum Hamiltonians. These Hamiltonians are invariant under rotations in spin space. We prove that a particular two-dimensional model from this class (the spin-3/2 model on the hexagonal lattice) has a unique ground state in the infinite-volume limit and hence no Néel order. Moreover, all truncated correlation functions decay exponentially in this ground state. We also characterize all the finite-volume ground states of these models (in every dimension), and prove that the two-point correlation function of the spin-2 square lattice model with periodic boundary conditions has exponential decay.     

Stress-stress correlation functions in lattice gases beyond Boltzmann's approximation

The complete time dependence of the stress-stress correlation functions in lattice gas cellular automata is calculated from the ring kinetic theory using numerical and analytical methods. This provides corrections, typically of 10–20%, to the usual molecular chaos calculations, where correlation functions decay exponentially. The resulting correlation function crosses over from an initial exponential decay to the long-time behavior calculated from mode coupling theory. The present theory, applied to the viscosity, accounts for a substantial part of the observed difference between the Boltzmann theory and simulations.     

A Combinatorial Proof of Tree Decay of Semi-Invariants

We consider finite range Gibbs fields and provide a purely combinatorial proof of the exponential tree decay of semi-invariants, supposing that the logarithm of the partition function can be expressed as a sum of suitable local functions of the boundary conditions. This hypothesis holds for completely analytical Gibbs fields; in this context the tree decay of semi-invariants has been proven via analyticity arguments. However the combinatorial proof given here can be applied also to the more complicated case of disordered systems in the so-called Griffiths' phase when analyticity arguments fail.     

Evidence for light-induced hole polarons in LiNbO3

Transient light-induced absorption in LiNbO3 is observed in the blue-green spectral range after pulsed illumination with 532 nm. Its buildup and decay in Fe-doped LiNbO3 is satisfactorily described by a sum of two stretched exponential functions. For undoped LiNbO3, however, only one stretched exponential decay is observed. These experimental results are explained by the formation of both small Nb(Li)4+ electron polarons and O- hole polarons. The mechanism is discussed on the basis of a proposed band scheme.     

Emission spectra in orthorhombic PbCl2 at low temperature

The emission spectra and its time decay in PbCl₂ at low temperature are reported. Three emission bands lying at 3.81 (uv), 2.93 (blue) and 2.60 eV are found for the photo-excitation in the intrinsic absorption region, at 4.2 K. An exponential decay with decay time of 11.4 μs is observed for the uv emission. For the blue emission two kinds of time decay spectra are observed: a second order process below 10 K and an exponential decay above 14 K. The mechanisms of these emission are discussed by taking into account the above results.     

Zur Begründung eines Variationsprinzipes für zerfallende Systeme

Taking into account the circumstance that the decay of an unstable microscopic system into two fragments is established by the counting of one of the decay products in a detector, the observed exponential decay law then asserts only knowledge of the spatiotemporal behaviour of the probability density (and therewith knowledge of the decaying state) at a large finite distance from the site of decay. We therefore formulate a variational principle, of which stationary functions show this decay behaviour. In addition to the resonant wave functions there are also solutions of the variational principle, which decrease exponentially with increasing distance, i.e., functions which could be used to describe the bound states. As the time-dependent treatment shows, the decaying states cannot occur in isolation in a scattering process. The mathematical characterisation of the decaying states via a variational principle is incorporated in a theory of open physical systems. In contradiction to the variational principle of Schrödinger our principle does not provide complete knowledge of the quantum states, but this is not needed in order to describe the decay.     

Decay of Determinantal and Pfaffian Correlation Functionals in One-Dimensional Lattices

We establish bounds on the decay of time-dependent multipoint correlation functionals of one-dimensional quasi-free fermions in terms of the decay properties of their two-point function. At a technical level, this is done with the help of bounds on certain bordered determinants and pfaffians. These bounds, which we prove, go beyond the well-known Hadamard estimates. Our main application of these results is a proof of strong (exponential) dynamical localization of spin-correlation functions in disordered XY-spin chains.     

Resonance-assisted tunneling in near-integrable systems

Dynamical tunneling between symmetry related invariant tori is studied in the near-integrable regime. Using the kicked Harper model as an illustration, we show that the exponential decay of the wave functions in the classically forbidden region is modified due to coupling processes that are mediated by classical resonances. This mechanism leads to a substantial deviation of the splitting between quasidegenerate eigenvalues from the purely exponential decrease with 1/Planck's over 2pi obtained for the integrable system. A simple semiclassical framework, which takes into account the effect of the resonance substructure on the invariant tori, allows one to quantitatively reproduce the behavior of the eigenvalue splittings.     

Correlation decay for an intermittent area-preserving map

We consider an area-preserving map which is almost everywhere hyperbolic, with a single marginal fixed point. Correlation decay is studied both by direct simulation of autocorrelations of smooth observables and by recurrence statistics on longer time scales. While on the time scale on which correlations are observed directly results are consistent with exponential relaxation, a transition to power-law is observed in the “sticking” times statistics.     

A correlation decay theorem at high temperature

We derive a theorem of exponential decay of correlation functions at high temperature for a general statistical mechanical system following the approach introduced by L. Gross. The theorem is formulated so as to be useful for locality problems in lattice quantum gravity.     

Anomalous scaling of a passive scalar in turbulence and in equilibrium

We analyze the multipoint correlation functions of a tracer in an incompressible flow at scales far exceeding the scale L at which fluctuations are generated (quasiequilibrium domain) and compare them with the correlation functions at scales smaller than L (turbulence domain). We demonstrate that scale invariance can be broken in the equilibrium domain and trace this breakdown to the statistical integrals of motion (zero modes) as has been done before for turbulence. Employing the Kraichnan model of short-correlated velocity we identify the new type of zero modes, which break scale invariance and determine an anomalously slow decay of correlations at large scales.     

Velocity correlation functions for finite one-dimensional systems

Certain systems consisting of a one-dimensional gas of a finite number of point particles interacting with a “hard-core” potential are considered.We use the technique developed by Jepsen to calculate exactly the velocity correlation functions for these systems. We discover that after a slow decay for times of the order of the relaxation time, there is a “fast” decay to the equilibrium value on a macroscopic time scale characterized by L/v_TH (L is the length of the container and v_TH the thermal velocity).The dependence of the velocity correlation functions on the initial position of the specified particle is also considered. In particular, the behaviour approaching the boundary of the container is analyzed. These considerations are generalized to systems of higher spatial dimension.