Mesoscopic Regime Research Articles

Coherent neutron scattering and collective dynamics on mesoscale

By combining, and modestly extending, a variety of theoretical concepts for the dynamics of liquids in the supercooled regime, we formulate a simple analytic model for the temperature and wavevector dependent collective density fluctuation relaxation time that is measurable using coherent dynamic neutron scattering. Comparison with experiments on the ionic glass-forming liquid Ca-K-NO3 in the lightly supercooled regime suggests the model captures the key physics in both the local cage and mesoscopic regimes, including the unusual wavevector dependence of the collective structural relaxation time. The model is consistent with the idea that the decoupling between diffusion and viscosity is reflected in a different temperature dependence of the collective relaxation time at intermediate wavevectors and near the main (cage) peak of the static structure factor. More generally, our analysis provides support for the ideas that decoupling information and growing dynamic length scales can be at least qualitatively deduced by analyzing the collective relaxation time as a function of temperature and wavevector, and that there is a strong link between dynamic heterogeneity phenomena at the single and many particle level. Though very simple, the model can be applied to other systems, such as molecular liquids.

Damping of mechanical vibrations by free electrons in metallic nanoresonators

We investigate the effect of free electrons on the quality factor ($Q$) of a metallic nanomechanical resonator in the form of a thin elastic beam. The flexural and longitudinal modes of the beam are modeled using thin beam elasticity theory, and simple perturbation theory is used to calculate the rate at which an externally excited vibration mode decays due to its interaction with free electrons. We find that electron-phonon interaction significantly affects the $Q$ of longitudinal modes, and may also be of significance to the damping of flexural modes in otherwise high-$Q$ beams. The finite geometry of the beam is manifested in two important ways. Its finite length breaks translation invariance along the beam and introduces an imperfect momentum conservation law in place of the exact law. Its finite width imposes a quantization of the electronic states that introduces a temperature scale for which there exists a crossover from a high-temperature macroscopic regime, where electron-phonon damping behaves as if the electrons were in the bulk, to a low-temperature mesoscopic regime, where damping is dominated by just a few dissipation channels and exhibits sharp nonmonotonic changes as parameters are varied. This suggests a scheme for probing the electronic spectrum of a nanoscale device by measuring the $Q$ of its mechanical vibrations.

Exact results for the spectra of interacting bosons and fermions on the lowest Landau level

A system of N interacting bosons or fermions in a two-dimensional harmonic potential (or, equivalently, magnetic field) whose states are projected onto the lowest Landau level is considered. Generic expressions are derived for the matrix elements of any interaction, in the basis of angular momentum eigenstates. For the fermion ‘ground state’ (ν = 1 Laughlin state), this makes it possible to exactly calculate its energy all the way up to the mesoscopic regime N ∼ 1000. It is also shown that for N = 3 and Coulomb interaction, several rational low-lying values of energy exist, for bosons and fermions alike.

HIGH-ORDER PHOTON-NUMBER CORRELATIONS: A RESOURCE FOR CHARACTERIZATION AND APPLICATIONS OF QUANTUM STATES

We measure high-order correlation functions of detected-photon numbers in the mesoscopic regime by means of hybrid photodetectors. The analytical expressions for correlations are evaluated in terms of quantities that can be experimentally accessed by a selfconsistent analysis of the detectors' outputs. We demonstrate that high-order correlations can be used to characterize the nature of the optical states, for instance by better discriminating between classical and quantum behavior even in critical situations, such as multimode twin-beam state. The results are in very good agreement with the theory, both for classical states and quantum states.

A quantum dot close to Stoner instability: The role of the Berry phase

The physics of a quantum dot with electron–electron interactions is well captured by the so called “Universal Hamiltonian” if the dimensionless conductance of the dot is much higher than unity. Within this scheme interactions are represented by three spatially independent terms which describe the charging energy, the spin-exchange and the interaction in the Cooper channel. In this paper we concentrate on the exchange interaction and generalize the functional bosonization formalism developed earlier for the charging energy. This turned out to be challenging as the effective bosonic action is formulated in terms of a vector field and is non-abelian due to the non-commutativity of the spin operators. Here we develop a geometric approach which is particularly useful in the mesoscopic Stoner regime, i.e., when the strong exchange interaction renders the system close to the Stoner instability. We show that it is sufficient to sum over the adiabatic paths of the bosonic vector field and, for these paths, the crucial role is played by the Berry phase. Using these results we were able to calculate the magnetic susceptibility of the dot. The latter, in close vicinity of the Stoner instability point, matches very well with the exact solution [I.S. Burmistrov, Y. Gefen, M.N. Kiselev, JETP Lett. 92 (2010) 179].

Crossover between macroscopic and mesoscopic regimes of vortex interactions in type-II superconductors

In the present work we report the existence of a crossover between the macroscopic and mesoscopic regimes of vortex interactions in type-II superconductors. Our findings rely on a systematic procedure to determine this crossover, which is based on the influence of the surface on the vortex structure of small superconductors. An adjacent result that we have found is that near this regime transformation, the vortex lattice develops a progressive change of symmetry, from square to hexagonal, which is intimately related to the meso-to-macro crossover. Our numerical simulations have been done for a long superconducting cylinder of square cross section for a wide range of length scales and temperatures.

Mesoscopic analysis of motion and conformation of cross-bridges.

The orientation of a cross-bridge is widely used as a parameter in determining the state of muscle. The conventional measurements of orientation, such as that made by wide-field fluorescence microscopy, electron paramagnetic resonance (EPR) or X-ray diffraction or scattering, report the average orientation of 1012-109 myosin cross-bridges. Under conditions where all the cross-bridges are immobile and assume the same orientation, for example in normal skeletal muscle in rigor, it is possible to determine the average orientation from such global measurements. But in actively contracting muscle, where a parameter indicating orientation fluctuates in time, the measurements of the average value provide no information about cross-bridge kinetics. To avoid problems associated with averaging information from trillions of cross-bridges, it is necessary to decrease the number of observed cross-bridges to a mesoscopic value (i.e. the value affected by fluctuations around the average). In such mesoscopic regimes, the averaging of the signal is minimal and dynamic behavior can be examined in great detail. Examples of mesoscopic analysis on skeletal and cardiac muscle are provided.

The dispersive behavior of collective excitations in fluids: An experimental test for the generalized collective modes theory

The predictions of the generalized collective modes (GCM) theory on the non-hydrodynamic dispersion of collective excitations of liquids and supercritical fluids have been tested against previous inelastic x-ray scattering measurements on samples of increasing complexity. We observed a good agreement between experimental results and theoretical predictions within the hypothesis that sound propagation is adiabatic. Overall, the performed comparison provides an experimental validation of GCM predictions and shows that, even in the transition region between the hydrodynamic and the mesoscopic regimes, thermal fluctuations have a minor influence on the dispersion, whose non-hydrodynamic effects are mostly driven by viscoelastic phenomena.

Bethe Ansatz approach to the pairing fluctuations in the mesoscopic regime

AbstractWe review the exact treatment of the pairing correlation functions in the canonical ensemble. The key for the calculations has been provided by relating the discrete BCS model to known integrable theories corresponding to the so called Gaudin magnets with suitable boundary terms. In the present case the correlation functions can be accessed beyond the formal level, allowing the description of the cross‐over from few electrons to the thermodynamic limit. In particular, we summarize the results on the finite size scaling behavior of the canonical pairing clarifying some puzzles emerged in the past. Some recent developments and applications are outlined.

Effects of Grain Boundary Decoration on the Electrical Conduction of Nanocrystalline CeO2

In this study, we investigate the effect of decorating the grain boundaries of nanocrystalline undoped ceria on the electrical transport properties. For the decoration, different acceptors (Yb, Y, Bi) were chosen. On decoration, the conduction switches from electronic to ionic. Upon sintering the grains are characterized by a core-shell configuration, in which the core remains undoped while the shell is heavily doped as a consequence of the diffusion of the acceptors toward the grain interior. The shell dominates the overall transport properties of the nanocrystalline ceria and is found to be in the mesoscopic regime.

Distribution of zeta zeroes of Artin–Schreier covers

We study the distribution of the zeroes of the zeta functions of the family of Artin-Schreier curves over Fq when q is fixed and the genus goes to infinity. We consider both the global and the mesoscopic regimes, proving that when the genus goes to infinity, the number of zeroes with angles in a prescribed interval of [−π, π) has a standard Gaussian distribution (when properly normalized).

Distributed Multiscale Simulations of Clay-Polymer Nanocomposites

ABSTRACTThe mechanical enhancement of polymers when clay nanoparticles are dispersed within it depends on factors over various length scales; for example, the orientation of the clay platelets in the polymer matrix will affect the mechanical resistance of the composite, while at the shortest scale the molecular arrangement and the adhesion energy of the polymer molecules in the galleries and the vicinity of the clay-polymer interface will also affect the overall mechanical properties.In this paper, we address the challenge of creating a hierarchal multiscale modelling scheme to traverse a sufficiently wide range of time and length scales to simulate clay-polymer nanocomposites effectively. This scheme varies from the electronic structure (to capture the polymer – clay interactions, especially those of the reactive clay edges) through classical atomistic molecular dynamics to coarse-grained models (to capture the long length scale structure).Such a scenario is well suited to distributed computing with each level of the scheme allocated to a suitable computational resource. We describe how the e-infrastructure and tools developed by the MAPPER (Multiscale Applications on European e-Infrastructures) project facilitates our multiscale scheme. Using this new technology, we have simulated clay-polymer systems containing up to several million atoms/particles. This system size is firmly within the mesoscopic regime, containing several clay platelets with the edges of the platelets explicitly resolved. We show preliminary results of a “bottom-up” multiscale simulation of a clay platelet dispersion in poly(ethylene) glycol.

An Atomistic Semiclassical Interpretation of Effective Charge in Electromigration

ABSTRACTElectromigration has gained increased prominence in recent years, as semiconductor device scaling has given way to higher current and power densities in computing interconnects and devices. The conventional understanding of electromigration has remained at an uneasy juncture between the mesoscopic semiclassical and atomistic quantum mechanical regimes. Herein, an “atomistic semiclassical” interpretation of electromigration is presented in an attempt to bridge these two perspectives at the nanoscale.

Scaling of the Magnetoelectric Effect in Chromia Thin Films

Scaling behavior of chromia (0001)-oriented films is investigated for film thicknesses ranging from the nanoscale up to the mesoscopic regime. Unusually prominent finite-size scaling of the critical point shift is observed which is accompanied by finite-size effects of magnetic response functions. We investigate the scaling of the antiferromagnetic ordering temperature by reviewing data from the literature and complementing them with our findings. Particular attention is paid to the hitherto unexplored regime of mesoscopic film thicknesses where conventionally no finite-size effects are expected. Results of previously unreported direct measurements of the magnetic susceptibility of chromia thin films grown by molecular beam epitaxy are presented. The magnetometry data reveal qualitative changes in the temperature dependence and peak value of the susceptibility in comparison with the susceptibility of a bulk single crystal. These non-trivial finite-size effects may originate from oxygen defects which accompany reactive sputtering and evaporation growth processes. Significant implications for the scaling behavior of the magnetoelectric effect and consequences for potential spintronic applications are discussed.

Methods in diffuse optical imaging

We describe some modelling and reconstruction methods for optical imaging in the macroscopic and mesoscopic regimes. Beginning with the basic model of radiative transport, we describe the diffusion approximation and its extensions. Some linear and nonlinear problems in diffuse optical imaging are outlined, together with some indications of current trends and future directions.

Angularly selective mesoscopic tomography

We report three-dimensional tomographic reconstruction of optical parameters for the mesoscopic light-scattering regime from experimentally obtained datasets by employing angularly selective data acquisition. The approach is based on the assumption that the transport coefficient of a scattering medium differs by an order of magnitude for weakly and highly scattering regions. Datasets were obtained by imaging a weakly scattering phantom, which embeds a highly scattering cylinder of two to three photons' mean path length in diameter containing light-absorbing inclusions. Reconstruction results are presented and discussed.

Quantum Transport in MesoscopicHe3Films: Experimental Study of the Interference of Bulk and Boundary Scattering

We discuss the mass transport of a degenerate Fermi liquid ^{3}He film over a rough surface, and the film momentum relaxation time, in the framework of theoretical predictions. In the mesoscopic regime, the anomalous temperature dependence of the relaxation time is explained in terms of the interference between elastic boundary scattering and inelastic quasiparticle-quasiparticle scattering within the film. We exploit a quasiclassical treatment of quantum size effects in the film in which the surface roughness, whose power spectrum is experimentally determined, is mapped into an effective disorder potential within a film of uniform thickness. Confirmation is provided by the introduction of elastic scattering centers within the film. The improved understanding of surface roughness scattering may impact on enhancing the conductivity in thin metallic films.

Resonance Clustering in Wave Turbulent Regimes: Integrable Dynamics

AbstractTwo fundamental facts of the modern wave turbulence theory are 1) existence of power energy spectra ink-space, and 2) existence of “gaps” in this spectra corresponding to the resonance clustering. Accordingly, three wave turbulent regimes are singled out:kinetic, described by wave kinetic equations and power energy spectra;discrete, characterized by resonance clustering; andmesoscopic, where both types of wave field time evolution coexist. In this review paper we present the results on integrable dynamics of resonance clusters appearing in discrete and mesoscopic wave turbulent regimes. Using a novel method based on the notion of dynamical invariant we show that some of the frequently met clusters are integrable in quadratures for arbitrary initial conditions and some others-only for particular initial conditions. We also identify chaotic behaviour in some cases. Physical implications of the results obtained are discussed.

Phonon Transport Across Mesoscopic Constrictions

Phonon transport across constrictions formed by a nanowire or a nanoparticle on a substrate is studied by a numerical solution of the gray Boltzmann transport equation (BTE) resolving the effects of two length scales that govern problems of practical importance. Predictions of total thermal resistance for wire/substrate and particle/substrate combinations are made for the entire range of Knudsen number, with an emphasis on resolving transport in the mesoscopic regime where ballistic-diffusive mechanisms operate and analytical expressions are not available. The relative magnitudes of bulk and constriction resistance are established, and a correlation for overall thermal resistance spanning the range of practical Knudsen numbers is provided.

Scaling the Chirality in Porphyrin J-Nanoaggregates

Chiral porphyrin J-aggregates are confined into microemulsions, achieving a fine control of their size and optical properties. The quality of the circular dichroism signal exhibits a remarkable scaling on the dimension from the nano- up to mesoscopic regime.