Table of contents

We investigate velocity probability distribution functions (PDF) of sheared hard-sphere suspensions. As observed in our Stokes flow simulations and explained by our single-particle theory, these PDFs can show pronounced deviations from a Maxwell-Boltzmann distribution. The PDFs are symmetric around zero velocity and show a Gaussian core and exponential tails over more than six orders of magnitude of probability. Following the excellent agreement of our theory and simulation data, we demonstrate that the distribution functions scale with the shear rate, the particle volume concentration, as well as the fluid viscosity.

We show that for Hamiltonian of the form, H=c(t)∂_x∂_x+V(x,t), the general potential V(x, t) for which Airy packets remain nonspreading under time evolution can only be of the form V(x,t)=p(t)x+q(t), where p(t) and q(t) are real functions. We derive rules for constructing nonspreading Airy packets from this general potential. We also consider normalizable packets obtained from Airy packet times a converging factor, such as e^βx, with β> 0. We show that there is no potential which sustains nonspreading wave packets of this kind.

We investigate the statistics of volumes of shares traded in stock markets. We show that the stochastic process of trading volumes can be understood on the basis of a mixed Poisson process at the microscopic time level. The beta distribution of the second kind (also known as q-gamma distribution), that has been proposed to describe empirical volume histograms, naturally results from our analysis. In particular, the shape of the distribution at small volumes is governed by the degree of granularity in the trading process, while the exponent controlling the tail is a measure of the inhomogeneities in market activity. Furthermore, the present case furnishes empirical evidence of how power law probability distributions can arise as a consequence of a fluctuating intrinsic parameter.

We introduce the concept of quantum supermap, describing the most general transformation that maps an input quantum operation into an output quantum operation. Since quantum operations include as special cases quantum states, effects, and measurements, quantum supermaps describe all possible transformations between elementary quantum objects (quantum systems as well as quantum devices). After giving the axiomatic definition of supermap, we prove a realization theorem, which shows that any supermap can be physically implemented as a simple quantum circuit. Applications to quantum programming, cloning, discrimination, estimation, information-disturbance trade-off, and tomography of channels are outlined.

Molecular motors transduce chemical energy obtained from hydrolizing ATP into mechanical work exerted against an external force. We calculate their efficiency at maximum power output for two simple generic models and show that the qualitative behaviour depends crucially on the position of the transition state or, equivalently, on the load distribution factor. Specifically, we find a transition state near the initial state (sometimes characterized as a "power stroke") to be most favorable with respect to both high power output and high efficiency at maximum power. In this regime, driving the motor further out of equilibrium by applying higher chemical potential differences can even, counterintuitively, increase the efficiency.

We present exact results for the spectrum of the fractional Laplacian in a bounded domain and apply them to First-Passage–Time (FPT) statistics of Lévy flights. We specifically show that the average is insufficient to describe the distribution of the FPT, although it is the only quantity available in the existing literature. In particular, we show that the FPT distribution is not peaked around the average, and that knowledge of the whole distribution is necessary to describe this phenomenon. For this purpose, we provide an efficient method to calculate higher-order cumulants and the whole distribution.

Strongly interacting bosonic particles in a tight-binding periodic potential superimposed by a weak parabolic trap is a paradigm for many cold atom experiments. Here, after revisiting the single-particle problem, we study interaction-bound dimers of bosonic atoms in the combined lattice and parabolic potential. We consider both repulsively and attractively bound dimers and find pronounced differences in their behaviour. We identify conditions under which attractive and repulsive dimers exhibit analogous dynamics. Our studies reveal that coherent transport and periodic oscillations of appropriately prepared one- and two-atom wave packets can be achieved, which may facilitate information transfer in optical-lattice–based quantum computation schemes.

By computing the local energy expectation values with respect to some local measurement basis we show that for any quantum system there are two fundamentally different contributions: changes in energy that do not alter the local von Neumann entropy and changes that do. We identify the former as work and the latter as heat. Since our derivation makes no assumptions on the system Hamiltonian or its state, the result is valid even for states arbitrarily far from equilibrium. Examples are discussed ranging from the classical limit to purely quantum-mechanical scenarios, i.e. where the Hamiltonian and the density operator do not commute.

Entanglement is very susceptible to decoherence and can rapidly decay or even completely disappear in finite time. A universal dynamical control of the disentanglement approach is presented, whereby one locally modulates entangled systems weakly coupled to thermal baths. We show that these local modulations can reduce the entanglement's decay rate and may facilitate controlled oscillations of entanglement that result in entanglement partial resuscitation. In the case of separate systems, we show that controlling the asymmetry between the systems' decoherence rates may result in partial resuscitation in non-Markovian time scales. Furthermore, controlling the time-dependent cross-decoherence of systems coupled to the same bath may exhibit partial resuscitation on longer time scales, dictated by the local modulations.

We study the dynamics of rotating scroll waves in three-dimensional excitable systems. Experiments are carried out with the 1,4-cyclohexanedione Belousov-Zhabotinsky reaction and wave patterns are measured using optical tomography. We create twisted scroll rings for which the rotation phase varies along their circular rotation backbone and measure the untwisting dynamics of the collapsing structures. Experimental data reveal the formation of an asymmetric, plateau-like phase profile with a growing region of leading phase and a shrinking region of lagging phase. The experimental data support a quantitative description in terms of a nonlinear diffusion equation.

In this letter we discuss the validity of the ergodicity hypothesis in theories of violent relaxation in long-range interacting systems. We base our reasoning on the Hamiltonian mean-field model and show that the lifetime of quasi-stationary states resulting from the violent relaxation does not allow the system to reach a complete mixed state. We also discuss the applicability of a generalization of the central-limit theorem. In this context, we show that no attractor exists in distribution space for the sum of velocities of a particle other than the Gaussian distribution. The long-range nature of the interaction leads in fact to a new instance of sluggish convergence to a Gaussian distribution.

We demonstrate the possibility of existence of meta-stable N-body Efimov states in trapped Bose systems with large scattering length. We calculate spectra of trapped systems of N=3, 4, 5, 6, and 7 bosons using a stochastic variational method with a restricted correlated Gaussian basis. For each system the calculations reveal a series of Efimov states where the energy and the r.m.s. radius exhibit the characteristic exponential dependence upon the state number. We also estimate the contribution of these states to the recombination rate of Bose-Einstein condensates.

The radial Schrödinger equation with a central potential is discussed and the pertinent WKB integral is cast in a more convenient form to extract closed formulae for the eigenvalues. These can be deduced in several interesting cases and are of asymptotic nature, i.e. they hold when one of the two quantum numbers appearing in the equation tends to infinity.

The large body of experimental data on nuclear fission is analyzed with a semi-empirical ordering scheme based on the macro-microscopic approach and the separability of compound-nucleus and fragment properties on the fission path. We apply the statistical model to the non-equilibrium descent from saddle to scission, taking the influence of dynamics into account by an early freeze-out. The present approach reveals a large portion of common features behind the variety of the complex observations made for the different systems.

We study the spectral properties of the advection-diffusion operator associated with a non-chaotic 3d Stokes flow defined in the annular region between counter-rotating cylinders of finite length. The focus is on the dependence of the eigenvalue-eigenfunction spectrum on the Peclet number Pe. Several convection-enhanced mixing regimes are identified, each characterized by a power law scaling, -μ_d∼Pe^-γ (γ<1) of the real part of the dominant eigenvalue, -μ_d, vs.Pe. Among these regimes, a Pe-independent scaling -μ_d=const (i.e., γ=0), qualitatively similar to the asymptotic regime of globally chaotic flows, is observed. This regime arises as the consequence of different eigenvalues branches interchanging dominance at increasing Pe. A combination of perturbation analysis and functional-theoretical arguments is used to explain the occurrence and the range of existence of each regime.

We experimentally study the deformations of liquid-liquid interfaces induced by a high-intensity focused ultrasonic beam. We quantitatively verify that small-amplitude deformations of a transparent chloroform-water interface are well described by the theory of Langevin acoustic radiation pressure, in both static and dynamic regimes. The large-amplitude deformations depend on the direction of propagation of the beam and are qualitatively similar to those induced by electromagnetic radiation pressure.

We report on normal stress field measurements at the multicontact interface between a rough elastomeric film and a smooth glass sphere under normal load, using an original MEMS-based stress-sensing device. These measurements are compared to Finite-Elements Method (FEM) calculations with boundary conditions obeying locally Amontons' rigid-plastic–like friction law with a uniform friction coefficient. In dry contact conditions, significant deviations are observed which decrease with increasing load. In lubricated conditions, the measured profile recovers almost perfectly the predicted profile. These results are interpreted as a consequence of the finite compliance of the multicontact interface, a mechanism which is not taken into account in Amontons' law.

We report a lattice-Boltzmann scheme to compute the dispersion of charged tracers in charged porous media under the combined effect of advection, diffusion and electro-migration. To this end, we extend the moment propagation approach, introduced to study the dispersion of neutral tracers (Lowe C. and Frenkel D., Phys. Rev. Lett., 77 (1996) 4552), to include the effect of electrostatic forces. This method allows us to compute the velocity autocorrelation function of the charged tracers with high accuracy. The algorithm is validated studying the dispersion coefficient in the case of electro-osmotic flow in a slit without added salt. We find excellent agreement between the numerical and analytical results. This method also provides the full time dependence of the diffusion coefficient, including for charged tracers. We illustrate on the slit case how D(t), which is measured by NMR to probe the geometry of porous media, reflects how the porosity explored by tracers depends on their charge.

We present experimental results concerning the advancing motion of drops of polymer solutions in the presence of controlled evaporation. We find that at high advancing velocities the classical Cox-Voinov law is verified, i.e. the advancing contact angle varies linearly with the capillary number. Below a critical velocity the contact angle increases as the advancing velocity is reduced. These results can be explained by taking into account the divergence of the rate of evaporation close to the contact line leading to an accumulation of polymer close to the edge of the drop. The induced local increase of the viscosity explains the increase of the contact angle. We show that the accumulation of polymer over a few nanometers is sufficient to slow down the contact line.

We investigate the way in which oscillating dumb-bells, a simple microscopic model of apolar swimmers, move at low Reynold's number. In accordance with Purcell's Scallop Theorem a single dumb-bell cannot swim because its stroke is reciprocal in time. However the motion of two or more dumb-bells, with mutual phase differences, is not time reversal invariant, and hence swimming is possible. We use analytical and numerical solutions of the Stokes equations to calculate the hydrodynamic interaction between two dumb-bell swimmers and to discuss their relative motion. The cooperative effect of interactions between swimmers is explored by considering first regular, and then random arrays of dumb-bells. We find that a square array acts as a micropump. The long-time behaviour of suspensions of dumb-bells is investigated and compared to that of model polar swimmers.

The non-equilibrium structural and dynamical properties of flexible polymers confined in a square microchannel and exposed to a Poiseuille flow are investigated by mesoscale simulations. The chain length and the flow strength are systematically varied. Two transport regimes are identified, corresponding to weak and strong confinement. For strong confinement, the transport properties are independent of the polymer length. For weak confinement or sufficiently strong flow and far from the channel center, the local stretching is similar to that of a polymer in simple shear flow, but in the central part the polymer exhibits a different behavior. The analysis of the long-time tumbling dynamics of short polymers yields a non-periodic motion with a sublinear dependence on the flow strength.

We report on a new implementation of the factorisation of numbers using Gauss sums which improves tremendously the efficiency to eliminate all "ghost" factors. We show that by choosing randomly the terms in the Gauss sum, the required number of terms varies as lnN instead of . As an illustration, we present experimental results obtained by interfering thirty ultrashort laser pulses where we factorise 1340333404807. This new approach is totally general and can be implemented for all the experiments based on the Gauss sum.

Geodesic acoustic modes (GAM) are shown to constitute a continuous spectrum due to radial inhomogeneities. The importance and theoretical as well as experimental implications of this fact are discussed in this work. The existence of a singular layer causes GAM to mode convert to short-wavelength kinetic GAM (KGAM) via finite ion Larmor radii; analogous to kinetic Alfvén waves (KAW). Furthermore, it is shown that KGAM can be nonlinearly excited by drift-wave (DW) turbulence via 3-wave parametric interactions, and the resultant driven-dissipative nonlinear system exhibits typical prey-predator self-regulatory dynamics, consistent with recent experimental observations on HL-2A. The degeneracy of GAM/KGAM with beta-induced Alfvén eigenmodes (BAE) is demonstrated and discussed, with emphasis on its important role in the complex self-organized behaviors of burning plasmas.

The nonlinear response theory approach is developed to study the nonlinear phenomena in non-ideal Coulomb systems. The nonlinear phenomena such as plasma wave echo and waves transformation have been investigated under non-ideal Coulomb system conditions based on a variant of the nonlinear response theory. Some general restrictions on the values of nonlinear response functions are considered. The model for the determination of quadratic response functions is presented. The conditions for experimental realization of the mentioned phenomena in non-ideal plasma are examined. It is shown that ultra-short field pulses can induce these phenomena.

By X-ray photon correlation spectroscopy we quantify the influence of elasticity and viscosity on the capillary wave (CW) surface dynamics of a supercooled liquid. To fit the data a novel model combining Maxwell-Debye and Voigt-Kelvin viscoelasticity is derived yielding a saturation of relaxation rates at high q as well as an offset in the CW dispersion relation. Diffuse X-ray scattering confirms the result and data taken on the surface of supercooled polypropylene glycol (PPG-4000) evidence a low-frequency elastic plateau of the storage modulus. A possible connection between the observed solid-like response and the supercooled state is discussed.

Electric-current–induced voltage oscillation at 600–740 kHz was observed in the current-voltage curves of nanoscopic size tunnel junctions arranged in a low-capacitance, multiple-junction configuration of ((Ni₆₀Nb₄₀)_100-xZr_x)_100-y D_y (x=30, 35, 40 and 45, 9.1⩽y⩽14.8) glassy alloys in the temperature range of 373 K to 6 K. This behavior appeared to be derived from Coulomb oscillation resulting from the tunneling of individual deuteron charging and discharging the vacancy capacitance of Zr-D-□-D-Zr atomic bond arrays among Zr-tetrahedral clusters, where □ is the vacancy barrier between clusters.

We consider the effective electric polarizability and electric-field–induced birefringence of a dilute solution of rod-like semiflexible charged polymers using hydrodynamic simulations and scaling arguments. We investigate the influence of polymer length, salt concentration, electric field strength and polyion concentration. We show that the polarizabilty is drastically reduced not only for high but also for very low salt concentrations, i.e. when the ionic clouds of neighboring rods start to overlap. As the electric polarizability (favoring rod orientation parallel to the electric field) decreases, the elasto-hydrodynamic orientation due to rod bending (favoring perpendicular alignment) can take over for not too stiff rods. This furnishes a generic mechanism for the experimentally well-known birefringence anomaly of a wide class of charged rod-like systems.

Stacks of TCNQ^- radical ions in 1 : 1 alkali salts are shown to be near the charge-density-wave (CDW) boundary, where charge degrees of freedom induce strong dimerization δ. Charge-transfer absorption and δ(V) are obtained for a one-dimensional (1D) Hubbard model with long-range Coulomb interactions V that ranges from spin-Peierls at V=0 to the CDW boundary at V_c and beyond. Cation dimerization lifts the degeneracy of Peierls systems and confers 3D contributions to the dimerization transition of alkali-TCNQ salts.

We have carried out optical-absorption and reflectance measurements at room temperature in single crystals of AWO₄ tungstates (A=Ba, Ca, Cd, Cu, Pb, Sr, and Zn). From the experimental results their band-gap energy has been determined to be 5.26 eV (BaWO₄), 5.08 eV (SrWO₄), 4.94 eV (CaWO₄), 4.15 eV (CdWO₄), 3.9–4.4 eV (ZnWO₄), 3.8–4.2 eV (PbWO₄), and 2.3 eV (CuWO₄). The results are discussed in terms of the electronic structure of the studied tungstates. It has been found that those compounds where only the s electron states of the A²⁺ cation hybridize with the O 2p and W 5d states (e.g., BaWO₄) have larger band-gap energies than those where also p, d, and f states of the A²⁺ cation contribute to the top of the valence band and the bottom of the conduction band (e.g., PbWO₄). The results are of importance in view of the large discrepancies existent in prevoiusly published data.

Point contacts (PC) Andreev reflection dV/dI spectra for the antiferromagnetic (T_N≃6 K) superconductor (T_c≃11 K) ErNi₂B₂C have been measured for the two main crystallographic directions. The observed retention of the Andreev reflection minima in dV/dI up to T_c directly points to an unusual superconducting order parameter (OP) vanishing at T_c. The temperature dependence of the OP was obtained from dV/dI using the recent theory of Andreev reflection including the pair-breaking effect. For the first time the existence of two superconducting OPs in ErNi₂B₂C is shown. A distinct decrease of both OPs as temperature is lowered below T_N is observed.

We show that the presence of free carriers in a substance can generate the multiferroic behavior. Namely, if the substance has mixed-valence ions, which can supply free carriers and have electric dipole and spin moments, all three types of long-range order (ferromagnetic, ferroelectric and magnetoelectric (ME)) can occur at low temperature. The physical origin of the effect is that charge carriers can mediate the multiferroic behavior via spin-spin (RKKY), dipole-dipole and dipole-spin interactions. Our estimate of the interaction magnitude shows that there exist an optimal carrier concentration, at which the strength of ME interaction is maximal and comparable to that of spin-spin RKKY interaction. This permits to conclude that in substances, where RKKY interaction between local spins is not small, a substantial value of free-carriers–mediated ME interaction can occur. Our analysis shows that disorder in the above substances does not suppress multiferroic effects.

We report on the observation of self-organized stripe-like structures on the as-grown surface and in the bulk of (Nd,Eu,Gd)Ba₂Cu₃O_y single crystals. The periodicity of the stripes on the surface lies between 500–800 nm. These are possibly the growth steps of the crystal. Transmission electron microscopy investigations revealed stripes of periodicity in the range of 20–40 nm in the bulk. From electron back scattered diffraction investigations, no crystallographic misorientation due to the nanostripes has been found. Scanning tunneling spectroscopic experiments revealed nonsuperconducting regions, running along twin directions, which presumably constitute strong pinning sites.

Spin relaxation between the two lowest-lying spin-states has been studied in the S=4 single-molecule magnet Ni₄ under steady-state conditions of low amplitude and continuous microwave irradiation. The relaxation rate was determined as a function of temperature at two frequencies, 10 and 27.8 GHz, by simultaneously measuring the magnetization and the absorbed microwave power. A strong temperature dependence is observed below 1.5 K, which is not consistent with a direct single-spin-phonon relaxation process. The data instead suggest that the spin relaxation is dominated by a phonon bottleneck at low temperatures and occurs by an Orbach mechanism involving excited spin-levels at higher temperatures. Experimental results are compared with detailed calculations of the relaxation rate using the universal density matrix equation.

Quantum spin transport is studied in an interacting quantum dot. It is found that a conductance "plateau" emerges in the non-linear charge conductance by a spin bias in the Kondo regime. The conductance plateau, as a complementary to the Kondo peak, originates from the strong electron correlation and exchange processes in the quantum dot, and can be regarded as one of the characteristics in quantum spin transport.

We develop an ab initio density functional theory incorporating with Gutzwiller variational approach, which is equally applicable to the ground state of systems ranging from weakly correlated metals to strongly correlated insulators with long-range ordering. We have applied this theory to calculate the electronic structures of three different systems: non-magnetic metal SrVO₃, ferromagnetic metals Fe and Ni, and antiferromagnetic insulator NiO. Ground-state properties are all obtained in good agreement with experiments within the same approach.

Using the exact two-propagating-modes solutions for electrons in a quasi-2D semiconductor wave guide under sectionally constant magnetic fields and spin-orbit interactions, it is explicitly shown that the Fano-like resonances and antiresonances lead to sudden suppressions and enhancements of the spin-dependent transmission probabilities. Our calculations show that when the magnetic-field-tilting angle θ_H is increased, the spin-field interaction becomes the most significant mechanism for the spin transitions in magnetic superlattices. Taking advantage of these spin-transport effects, simple and efficient spin-inverter devices are proposed. To better visualize the relative influence of the specific semiconductor properties on the device performance and device characteristics, we consider two magnetic superlattices based on semiconductors having entirely different Landè g-factor: GaAs and InSb. Although slightly more efficient spin-inversion devices are obtained for the GaAs semiconductor, InSb requires lower magnetic fields and its efficiency can be close to 80%.

We have investigated the photon-assisted tunneling through an ultra-small quantum dot (QD) embedded Aharonov-Bohm (AB) interferometer under the perturbation of external microwave fields (MWFs). The tunneling current is derived by using nonequilibrium Green's function technique. The local density of state at finite Coulomb interaction, the differential conductance resonance, current oscillation with respect to AB flux influenced by the nature of the QD and bridge channel have been studied. The MWFs generate novel resonant and Fano structures, which are sensitively dependent on the irradiation approach of MWFs. Novel Kondo peaks can be seen due to the photon-assisted tunneling, and the asymmetric Fano structure also exhibits itself in the photon-assisted satellite peaks and valleys. Our system can be employed as an interferometer to produce novel output signals by controlling the applied MWFs.

Discs of solid material have been forward transferred from thin films on transparent carrier substrates using femtosecond Ti:sapphire laser-induced forward transfer (fs-LIFT) with a triazene polymer dynamic release layer (DRL). The fluence threshold for fs-LIFT was found to be only ≈20% of the DRL ablation threshold at the laser wavelength. This decrease is attributed to ultrafast shock-wave generation in the constrained polymer layer under femtosecond irradiation being the driving force for fs-LIFT with the polymer DRL. The result is very different from the nanosecond regime, where the LIFT threshold is observed to be slightly above the polymer ablation threshold. White-light continuum generation in a carrier substrate is observed and its influence on the fs-LIFT process is discussed.

The dynamical and conformational properties of short polyelectrolytes are studied in salt-free solution exposed to an external electric field taking hydrodynamic interactions into account by a mesoscale simulation technique. As a function of polymer length, we find a non-monotonic electrophoretic mobility, in agreement with experiments, and diffusion coefficients, which are well described by the expression of rodlike objects, both aspects reflect the importance of hydrodynamic interactions. Strong electric fields lead to particular polymer conformations, which are illustrated in a schematic diagram.

Shock-wave experiments of Al₂O₃ indicated the onset of an increase in electrical conductivity and observed the optical transparency loss at ∼130 GPa. Here, based on first-principles calculations, we determine the pressure dependence of the band gap of perfect Al₂O₃ to 220 GPa, and investigate the optical absorption of Al₂O₃ without and with oxygen and aluminum vacancies within 220 GPa. Our results indicate that: 1) the onset of the conductivity increase is attributed to a band-gap decrease due to the Rh₂O₃(II)-CaIrO₃ transition at ∼130 GPa and ∼1500 K; 2) this transition is not responsible for the transparency loss, but heterogeneous absorption in the visible-light region, induced by the +2 charge oxygen vacancy, should be a source of this phenomenon. The calculations of perfect MgSiO₃, a material analogous to Al₂O₃, suggest that a perovskite to post-povskite transition in MgSiO₃ at ∼125 GPa and ∼2500 K also yields a band-gap reduction. This causes an increase in electrical conductivity in MgSiO₃ at pressure-temperature conditions of the Earth's D'' layer.