Table of contents

We use molecular dynamics to investigate the glass transition occurring at large volume fraction, φ, and low temperature, T, in assemblies of soft repulsive particles. We find that equilibrium dynamics in the (φ, T)-plane obey a form of dynamic scaling in the proximity of a critical point at T=0 and φ=φ₀, which should correspond to the ideal glass transition of hard spheres. This glass point, "point G", is distinct from athermal jamming thresholds. A remarkable consequence of scaling behaviour is that the dynamics at fixed φ passes smoothly from that of a strong glass to that of a very fragile glass as φ increases beyond φ₀. Correlations between fragility and various physical properties are explored.

Fluctuations of the number of condensed atoms in a finite-size, weakly interacting Bose gas confined in a box potential are investigated for temperatures up to the critical region. The canonical partition functions are evaluated using a recursive scheme for smaller systems, and a saddle-point approximation for larger samples that allows to treat realistic size systems containing up to N∼10⁵ particles. We point out the importance of particle-number constraint and interactions between out of condensate atoms for the statistics near the critical region. For sufficiently large systems, the crossover from the anomalous to normal scaling of the fluctuations is observed. The excitations are described in a self-consistent way within the Bogoliubov-Popov approximation, and the interactions between thermal atoms are described by means of the Hartree-Fock method.

In connection with the recent discussion of topological order and topological phase transitions in quantum systems, we reexamine the circumstances that lead to the appearance of a topological glass in certain classical lattice spin models. Local bonding enforces constraints on low-energy states that organize themselves into topologically distinct classes that break ergodicity but not any apparent symmetry as in the usual Landau theory of phase transitions. Various properties of such a topological glass are demonstrated using two classical Ising-like models.

The calculation of the heating rate of cold atoms in vibrating traps requires a theory that goes beyond the Kubo linear response formulation. If a strong "quantum chaos" assumption does not hold, the analysis of transitions shows similarities with a percolation problem in energy space. We show how the texture and the sparsity of the perturbation matrix, as determined by the geometry of the system, dictate the result. An improved sparse random matrix model is introduced: it captures the essential ingredients of the problem and leads to a generalized variable range hopping picture.

The relaxation of field-induced anisotropy in a magnetic fluid with dominant repulsion is theoretically modeled and experimentally measured by small angle neutron scattering on a sample rotating at angular velocity ω. The scattered pattern distortion scales as the Mason number Mn=ω·τ_q, τ_q being the q-dependent diffusion time of nanoparticles. The model accounts for the magnetophoretical drift in the non-homogeneous self-magnetic field of the assembly, continuously created by the thermal noise. The Mn-dependence of the pattern distortion is well described without any adjustable parameter.

Explicit determination of the mean first-passage time (MFPT) for the trapping problem on complex media is a theoretical challenge. In this paper, we study random walks on the Apollonian network with a trap fixed at a given hub node (i.e., node with the highest degree), which are simultaneously scale-free and small-world. We obtain the precise analytic expression for the MFPT that is confirmed by direct numerical calculations. In the large system size limit, the MFPT approximately grows as a power law function of the number of nodes, with the exponent much less than 1, which is significantly different from the scaling for some regular networks or fractals such as regular lattices, Sierpinski fractals, T-graph, and complete graphs. The Apollonian network is the most efficient configuration for transport by diffusion among all the previously studied structures.

We propose the extension of the spectral action principle to fermions and show that the neutrino mass terms then appear naturally as next-order corrections.

Knotted vortex lines in the spin-1 Bose-Einstein condensates are studied. The Faddeev-Niemi model is considered, and it is found that naturally there exist topological vortex line structures in the condensates. We focus on the knotted vortex lines and examine their Faddeev-Niemi knot quantum number. It is shown that the Faddeev-Niemi number is identical to the sum of all the (self-)linking numbers of the knots family and is preserved during the branching processes of vortex lines.

We study energy propagation in locally time-periodically driven disordered nonlinear chains. For frequencies inside the band of linear Anderson modes, three different regimes are observed with increasing driver amplitude: 1) below threshold, localized quasiperiodic oscillations and no spreading; 2) three different regimes in time close to threshold, with almost regular oscillations initially, weak chaos and slow spreading for intermediate times and finally strong diffusion; 3) immediate spreading for strong driving. The thresholds are due to simple bifurcations, obtained analytically for a single oscillator, and numerically as turning points of the nonlinear response manifold for a full chain. Generically, the threshold is nonzero also for infinite chains.

Renormalizable ϕ^⋆4₄ models on Moyal space have been obtained by modifying the commutative propagator. But these models have a divergent "naive" commutative limit. We explain here how to obtain a coherent such commutative limit for a recently proposed translation-invariant model. The mechanism relies on the analysis of the ultraviolet/infrared mixing in Feynman graphs at any order in perturbation theory.

We examine the spontaneous breakdown of the matter vacuum triggered by an external force. Based on the multi-particle counting numbers, which are accessible by experiment, we present a general theoretical procedure that permits the computation of the vacuum probability for sub- and super-critical fields with arbitrary spatial and temporal profiles. When the field is supercritical, the theory leads to the expected exponentially decay of the vacuum in the long-time limit. For the special case of an infinitely extended electric force field, we establish the validity of an effective decay constant obtained by averaging the Schwinger rate over the spatial force profile.

We report on two modalities of lens-based fluorescence microscopy with diffraction-unlimited resolution relying on the depletion of the fluorophore ground state. The first version utilizes a beam with a deep intensity minimum, such as a doughnut, for intense excitation followed by mathematical deconvolution, whereas in the second version, a regularly focused beam is added for generating the image directly. In agreement with theory, the subdiffraction resolution scales with the square root of the intensity depleting the ground state. Applied to the imaging of color centers in diamond our measurements evidence a resolving power down to ≈7.6 nm, corresponding to 1/70 of the wavelength of light employed. Our study underscores the key role of exploiting (molecular) states for overcoming the diffraction barrier in far-field optical microscopy.

We report the observation of capillary wave turbulence on the surface of a fluid layer in a low-gravity environment. In such conditions, the fluid covers all the internal surface of the spherical container that is submitted to random forcing. The surface wave amplitude displays power law spectrum over two decades in frequency, corresponding to wavelength from millimeters to a few centimeters. This spectrum is found in roughly good agreement with wave turbulence theory. Such a large-scale observation without gravity waves has never been reached during ground experiments. When the forcing is periodic, two-dimensional spherical patterns are observed on the fluid surface such as subharmonic stripes or hexagons with wavelength satisfying the capillary wave dispersion relation.

We theoretically propose a light-stopping process that uses loss and gain dynamical tuning in short coupled-resonator delay lines. The structure is made of four resonators and is optimized to avoid pulse distortion in the passive regime. The loss and gain modulations allow the resonant structure to be isolated from the access waveguide and the pulse to be stored. We demonstrate via numerical simulations the pulse storing process and show that this active delay line also induces nonlinear effects leading to pulse compression. This last property could be useful for pulse dispersion tailoring.

An enthalpy-based thermal lattice Boltzmann model is introduced for simulating a class of strongly coupled thermo-hydrodynamic problems. The novelty of the model lies in the formulation of an enthalpy density distribution function to simulate the temperature field, in place of the existing internal energy density distribution function. The proposed model has a clear advantage over the earlier internal energy density distribution function based thermal lattice Boltzmann model, in a sense that it can simulate certain classes of thermofluidic transport problems without facing mathematical difficulties in handling with additional energy source terms.

We consider long-wave oscillatory convection in a layer of a binary liquid. Weakly nonlinear analysis is carried out on a hexagonal lattice. It is shown that the set of amplitude equations with cubic nonlinearity is degenerate. In order to investigate the pattern formation it is necessary to proceed to the fifth order in terms of the amplitude of convective motion. The resulting set of equations demonstrates the emergence of a heteroclinic cycle: The system wanders between three unstable limit cycles, being alternately attracted to and then repelled from each of them. The heteroclinic cycle is found to be stable.

We demonstrate the specific non-Boussinesq roles played by various fluid properties in thermal convection by allowing each of them to possess, one at a time, a temperature dependence that could be either positive or negative. The negative temperature dependence of the coefficient of thermal expansion hinders effective thermal convection and reduces the Nusselt number, whereas the negative dependence of fluid density enhances the Nusselt number. Viscosity merely smears plume generation and has a marginal effect on heat transport, whether it increases or decreases with temperature. At the moderate Rayleigh number examined here, the specific heat capacity shows no appreciable effect. On the other hand, the conductivity of the fluid near the hot surface controls the heat transport from the hot plate to the fluid, which suggests that a less conducting fluid near the bottom surface will reduce the Nusselt number and the bulk temperature.

We propose a scheme for perfect excitation of a single two-level atom by a single photon in free space. The photon state has to match the time reversed photon state originating from spontaneous decay of a two-level system. Here, we discuss its experimental preparation. The state is characterized by a particular asymmetric exponentially shaped temporal profile. Any deviations from this ideal state limit the maximum absorption. Although perfect excitation requires an infinite amount of time, we demonstrate that there is a class of initial one-photon quantum states which can achieve almost perfect absorption even for a finite interaction time. Our results pave the way for realizing perfect coupling between flying and stationary qubits in free space thus opening a possibility for building scalable quantum networks.

Nanocrystalline silicon (nc-Si) films were systematically prepared via three ways: a) laser anneal or b) thermal anneal of the amorphous silicon (α-Si) films deposited by pulsed-laser ablation (PLA) in base vacuum, c) direct PLA in high-purity Ar gas with pressure of 10 Pa. The anneal-laser fluence, thermal-anneal temperature and ablation-laser fluence thresholds corresponding to the beginning of nanoparticles formation were respectively determined by using scanning electron microscopy (SEM), Raman and X-ray diffraction (XRD) techniques. Incorporated with crystallization mechanism, energies compensated for the formation of one Si nanoparticle in the three ways were calculated approximately. The result shows that for different crystallization ways, the potential barriers during the formation of one ∼16 nm nanoparticle are on the order of 10^-9 mJ.

A weakly nonlinear model is proposed for the Kelvin-Helmholtz instability in two-dimensional incompressible fluids. The second- and third-harmonic generation effects of single-mode perturbation, as well as the nonlinear correction to the exponential growth of the fundamental modulation are analyzed. An important resonance in the mode-coupling process is found. The nonlinear saturation time depends on the initial perturbation amplitude and the density ratio of the two fluids, but the nonlinear saturation amplitude depends only on the initial perturbation amplitude. The weakly nonlinear result is supported by numerical simulation. The practical system of boundary layer containing thermal conductivity is analyzed. Their nonlinear saturation amplitude can be predicted by our weakly nonlinear model.

A theoretical model is developed to study the strain effect on the instability of island formation in submonolayer heteroepitaxy in both thermodynamic and growth kinetic regimes. By using the linear-stability analysis, the elastic energy change of a circular island is derived. Combined with a rate equation theory, the interplay between growth kinetics and strain effect on the shape instability is analyzed and illustrated with the constructed morphological phase diagrams. Critical island sizes beyond which islands grow unstable are also derived and can be used to estimate the energy parameters. Well-defined scaling properties are also obtained for the shape instability.

An equilibrium random surface model in 3d is defined which includes versions of both the Stranski-Krastanow and Volmer-Weber models of crystal surface morphology. In a limiting case, the model reduces to one studied previously in a different context for which exact results are available in part of the phase diagram, including the critical temperature, the associated specific heat singularity and the geometrical character of the transition. Through a connection to the 2d Ising model, there is a natural association with the Schramm-Loewner evolution that has also been observed experimentally in a nonequilibrium deposition setting.

Phase separation is investigated in CO₂ under linear harmonic vibrations. The study is performed under weightlessness in a sounding rocket. The fluid is at critical density near its critical point to get benefit from universal behavior. Without vibration, phase separation is characterized by an interconnected pattern of vapor and liquid domains and a near linear growth law. Under vibration, three time regions have been identified. i) When the liquid-vapor domains are smaller than a few viscous boundary layer thickness, growth is unaffected by vibration. ii) Then the Bernoulli pressure across the interfaces makes the domains grow exponentially perpendicularly to the vibration direction while growth parallel to the vibration direction is unaffected. iii) When the domains reach the sample size, the pattern looks as periodic stripes perpendicular to the vibration direction and keep on growing parallel to the vibration direction. A theoretical approach of these phenomena is proposed.

It is generally known that the orbital diamagnetism of a classical system of charged particles in thermal equilibrium is identically zero —the Bohr-van Leeuwen theorem. Physically, this null result derives from the exact cancellation of the orbital diamagnetic moment associated with the complete cyclotron orbits of the charged particles by the paramagnetic moment subtended by the incomplete orbits skipping the boundary in the opposite sense. Motivated by this crucial but subtle role of the boundary, we have simulated here the case of a finite but unbounded system, namely that of a charged particle moving on the surface of a sphere in the presence of an externally applied uniform magnetic field. Following a real space-time approach based on the classical Langevin equation, we have computed the orbital magnetic moment that now indeed turns out to be non-zero and has the diamagnetic sign. To the best of our knowledge, this is the first report of the possibility of finite classical diamagnetism in principle, and it is due to the avoided cancellation.

The pulse widths of light from sonoluminescing gas bubbles in various solutions having quite different densities were measured by a time-correlated single-photon counting (TC/SPC) method. The measured values of the pulse width were found to be in the range of 150 ps to several ns. No appreciable difference in the measured pulse width and the bubble behavior for the sonoluminescing air bubbles in various solutions was found. The measured results for the pulse width of sonoluminescence (SL) in various solutions suggest that light is emitted from the core region where the temperature is almost uniform. In addition, the theoretical estimation for the pulse widths with thermal bremsstrahlung as emission mechanism for SL provides reasonable results.

We show that entanglement monotones reveal the pronounced enhancement of entanglement at a quantum phase transition, when they are sensitive to long-range high-order correlations. Such monotones are found to develop a sharp interferometric peak at the critical point, and to exhibit universal scaling. We demonstrate that similar features are shared by noise correlation spectra, and verify that these experimentally accessible quantities encode entanglement information and probe separability. We give a prescription, for mesoscopic scale systems of how to extract the pronounced enhancement of entanglement at a quantum phase transition from limited accessible experimental data.

In this paper, we study a non-equilibrium Fermi-edge problem where the system under investigation is a single electron reservoir put under an AC electric field. We show that the electron Green's function and other correlation functions in the problem can be solved and expressed exactly in terms of a well-defined integral. The qualitative behaviors of the solution is studied and compared with the situation where the impurity is coupled to more than one reservoir at different chemical potentials.

We have studied the Nernst coefficient, ν(T), of epitaxial thin films of the superconductor Y_1-xCa_xBa₂Cu₃O_y with x=0.05 and x=0.1. The x=0.1 sample has been measured at three different values of y, in the over- (OV), optimally- (OP), and under-doped (UD) states. As the doping level is reduced, ν(T) starts to fall linearly with T at the temperature (T^*) where we expect to see the influence of the pseudogap. The onset temperature of the superconducting fluctuation contribution to ν(T) was found to vary slowly with the hole concentration (p) between p=0.118 and 0.197. For the OP and UD samples, ν(T>T^*) is unusually large, being comparable with |S tan θ| where S is the Seebeck coefficient and θ the Hall angle.

Once again the world of condensed matter has been surprised by the discovery of yet another class of high-temperature superconductors. The first reactions would of course be that these iron-pnictide– and iron-chalcogenide–based materials must in some way be related to the copper-oxide–based superconductors for which a large number of theories exist although a general consensus regarding the correct theory has not yet been reached. Here, we point out that the basic physical paradigm of the new iron-based superconductors is entirely different from the cuprates. Their fundamental properties, structural and electronic, are dominated by the exceptionally large pnictide electronic polarizabilities.

We report on the electric-field tuning of a magnetic phase transition temperature (T_L) in multiferroic Ni₃V₂O₈ thin films. The simultaneous magnetic and ferroelectric transition in Ni₃V₂O₈ exhibits a clear dielectric anomaly; we monitored T_L under applied electric and magnetic fields using dielectric measurements. The transition temperature increases by 0.2 K±0.05 K when the sample is biased approximately 25 MV/m compared to zero bias. This electric-field control of the magnetic transition can be qualitatively understood using a mean-field model incorporating a tri-linear coupling between the magnetic order parameters and spontaneous polarization. The shape of the electric field-temperature phase boundary is consistent with the proper order parameter for the multiferroic phase in Ni₃V₂O₈ being a linear combination of the magnetic and ferroelectric correlation functions.

Synchronization of heterogeneous systems that consist of oscillatory and passive elements are studied in cardiac myocytes/fibroblasts co-cultures. It is found that beating clusters of cardiac myocytes surrounded by fibroblasts will be formed. The beatings of the cardiac myocyte clusters are not correlated at early times, but get synchronized as the cultures mature. This synchronization can be understood by a Kuramoto model with a time-increasing coupling strength. Our findings show that the growth of the coupling strength between clusters is linear, while the overall wave dynamics of the system is controlled by the passive fibroblast in the system which presumably is growing exponentially.

The behavior of supercooled polymer melt composed of short chains with 10 beads between rapidly oscillating plates is simulated by using a hybrid simulation of molecular dynamics and computational fluid dynamics. The flow profiles of polymer melt near an oscillating plate are quite different from those of Newtonian fluid. The viscous boundary layer of the melt is much thinner than that of the Newtonian fluid due to the shear thinning of the melt. Three different rheological regimes, i.e., the viscous fluid, viscoelastic liquid, and viscoelastic solid regimes, form over the oscillating plate according to the local Deborah numbers. The melt behaves as a viscous fluid when ωτ^R ≲ 1, and the crossover between the liquid-like and solid-like regime takes place around ωτ^α ≃ 1 (where ω is the angular frequency of the plate, and τ^R and τ^α are the Rouse and α relaxation times, respectively).

The conventional wisdom is that social networks exhibit an assortative mixing pattern, whereas biological and technological networks show a disassortative mixing pattern. However, the recent research on the online social networks modifies the widespread belief, and many online social networks show a disassortative or neutral mixing feature. Especially, we found that an online social network, Wealink, underwent a transition from degree assortativity characteristic of real social networks to degree disassortativity characteristic of many online social networks, and the transition can be reasonably elucidated by a simple network model that we propose. The relations among network assortativity, clustering, and modularity are also discussed in the paper.

We investigate the main features of a measure of fidelity between states in a general family of probabilistic theories admitting classical probability theory and standard quantum theory as particular instances. We apply the aforementioned measure to investigate information-theoretical features of these theories related to the conservation of information during the evolution of closed physical systems. In particular, we derive a generalization of a fundamental result in quantum theory relevant for the measurement problem: Zurek's recent extension of the no-cloning theorem.

We perform numerical lattice simulations of an excitable medium. We show that the interaction of a spiral wave with a periodic train of planar fronts leads to annihilation of the spiral wave even when i) the period of the fronts is longer than the period of the spiral and ii) the annihilating fronts are released at a significant distance from the spiral. The observed annihilation is not due to spiral drift, and occurs well inside the lattice.