Coupled ripplon-plasmon modes in a multielectron bubble

In multielectron bubbles, the electrons form an effectively two-dimensional layer at the inner surface of the bubble in helium. The modes of oscillation of the bubble surface (the ripplons) are influenced by the charge redistribution of the electrons along the surface. The dispersion relation for these charge redistribution modes (‘longitudinal plasmons’) is derived and the coupling of these modes to the ripplons is analysed. We find that the ripplon-plasmon coupling in a multielectron bubble differs markedly from that of electrons on a flat helium surface. An equation is presented relating the spherical harmonic components of the charge redistribution to those of the shape deformation of the bubble.     

Induced bubble shape oscillations and their impact on the rise velocity

When a 2-4 mm diameter bubble rising with constant velocity hits a thin wire, bubble shape oscillations can be induced. As a consequence also the bubble rise velocity strongly oscillates. With the help of a force balance we show that these velocity oscillations are an added-mass effect. Received 9 April 2002 / Received in final form 11 July 2002 Published online 14 October 2002 RID="a" ID="a"e-mail: lohse@tn.utwente.nl     

I. Formation and rise of a bubble stream in a viscous liquid

The continuous emission of gas bubbles from a single ejection orifice immersed in a viscous fluid is considered. We first present a semi empirical model of spherical bubble growth under constant flow conditions to predict the bubble volume at the detachment stage. In a second part, we propose a physical model to describe the rise velocity of in-line interacting bubbles and we derive an expression for the net viscous force acting on the surrounding fluid. Experimental results for air/water-glycerol systems are presented for a wide range of fluid viscosity and compared with theoretical predictions. An imagery technique was used to determine the bubble size and rise velocity. The effects of fluid viscosity, gas flow rate, orifice diameter and liquid depth on the bubble stream dynamic were analyzed. We have further studied the effect of large scale recirculation flow and the influence of a neighbouring bubble stream on the bubble growth and rising velocity. Received: 23 July 1997 / Revised: 16 December 1997 / Accepted: 11 May 1998     

Hydrodynamic interactions in the structural fluctuation of a ternary amphiphilic system C12E5/water/ n-octane

Dynamical fluctuations of microemulsion and lamellar structures in a ternary amphiphilic system C₁₂E ₅/water/n-octane are studied by means of neutron spin echo spectrometry. The decay rate of the time correlation of the concentration was analyzed in terms of a theory (M. Nonomura, T. Ohta, J. Chem. Phys. 110, 7516 (1999)), in which both van Hove and hydrodynamic interactions are considered. The result shows that the time correlation function is expressed mostly by a single exponential determined exclusively by hydrodynamic interactions. Received 1 December 1999 and Received in final form 12 March 2001     

Andreev-Lifshitz supersolid revisited for a few electrons on a square lattice II

In this second paper, using N = 3 polarized electrons (spinless fermions) interacting via a U/r Coulomb repulsion on a two dimensional L×L square lattice with periodic boundary conditions and nearest neighbor hopping t, we show that a single unpaired fermion can co-exist with a correlated two particle Wigner molecule for intermediate values of the Coulomb energy to kinetic energy ratio r _s = UL/(2t ). This supports in an ultimate mesoscopic limit a possibility proposed by Andreev and Lifshitz for the thermodynamic limit: a quantum crystal may have delocalized defects without melting, the number of sites of the crystalline array being smaller than the total number of particles. When L = 6, the ground state exhibits four regimes as r_s increases: a Hartree-Fock regime, a first supersolid regime where a correlated pair co-exists with a third fully delocalized particle, a second supersolid regime where the third particle is partly delocalized, and eventually a correlated lattice regime. Received 22 October 2002 Published online 23 May 2003 RID="a" ID="a"e-mail: jpichard@cea.fr     

Andreev-Lifshitz supersolid revisited for a few electrons on a square lattice. I

In 1969, Andreev and Lifshitz have conjectured the existence of a supersolid phase taking place at zero temperature between the quantum liquid and the solid. In this and a succeeding paper, we re-visit this issue for a few polarized electrons (spinless fermions) interacting via a U/r Coulomb repulsion on a two dimensional L×L square lattice with periodic boundary conditions and nearest neighbor hopping t. This paper is restricted to the magic number of particles N = 4 for which a square Wigner molecule is formed when U increases and to the size L = 6 suitable for exact numerical diagonalizations. When the Coulomb energy to kinetic energy ratio r _s = UL/(2t ) reaches a value r _s ^F ≈ 10, there is a level crossing between ground states of different momenta. Above r _s ^F, the mesoscopic crystallization proceeds through an intermediate regime ( r _s ^F < r _s < r _s ^W ≈ 28) where unpaired fermions with a reduced Fermi energy co-exist with a strongly paired, nearly solid assembly. We suggest that this is the mesoscopic trace of the supersolid proposed by Andreev and Lifshitz. When a random substrate is included, the level crossing at r _s ^F is avoided and gives rise to a lower threshold r _s ^F(W) < r _s ^F where two usual approximations break down: the Wigner surmise for the distribution of the first energy excitation and the Hartree-Fock approximation for the ground state. Received 21 June 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: jpichard@cea.fr     

Magnetic field dependence of electronic structures in a single and double quantum dots by 3D-MHFKS calculation

The 3-dimensional Mesh-Hartree-Fock-Kohn-Sham (3D-MHFKS) calculation is applied to study the magnetic (B-) field dependence of the electronic structures of circular-shaped vertical quantum dot (Q-dot) with electron number (N) in double barrier structure (DBS) and also coupled double Q-dots in triple barrier structure (TBS). One of the advantageous points of the 3D-MHFKS calculation is that the strength of coupling between two dots are explicitly evaluated by introducing the realistic barrier in TBS as a straightforward extension of 3D-MHFKS calculation of the single Q-dot in DBS. The calculated chemical potentials represented in B-N phase diagram are consistently and systematically discussed by showing the B-field dependence of the occupied single particle energy levels from the view point how the electronic states transfer sequentially from Fock-Darwin (FD) to lowest Landau (LL) and from LL to the spin flip (SF) and from SF to spin-polarized maximum density droplet (MDD) domains as increasing B-field in the Q-dots.     

Floating Wigner molecules and possible phase transitions in quantum dots

A floating Wigner crystal differs from the standard one by a spatial averaging over positions of the Wigner-crystal lattice. It has the same internal structure as the fixed crystal, but contrary to it, takes into account rotational and/or translational symmetry of the underlying jellium background. We study properties of a floating Wigner molecule in few-electron spin-polarized quantum dots, and show that the floating solid has the lower energy than the standard Wigner crystal with fixed lattice points. We also argue that internal rotational symmetry of individual dots can be broken in arrays of quantum dots, due to degenerate ground states and inter-dot Coulomb coupling. Received 12 September 2001 / Received in final form 24 April 2002 Published online 9 July 2002     

From independent particle towards collective motion for two polarized electrons on a square lattice

The two dimensional crossover from independent particle towards collective motion is studied using 2 polarized electrons (spinless fermions) interacting via a U/r Coulomb repulsion in a L×L square lattice with periodic boundary conditions and nearest neighbor hopping t. Three regimes characterize the ground state when U/t increases. Firstly, when the fluctuation Δr of the spacing r between the two particles is larger than the lattice spacing a, there is a scaling length L ₀ = π²(t/U) such that the relative fluctuation Δr/〈r〉 is a universal function of the dimensionless ratio L/L ₀, up to finite size corrections of order L^-2. L < L ₀ and L > L ₀ are respectively the limits of the free particle Fermi motion and of the correlated motion of a Wigner molecule. Secondly, when U/t exceeds a threshold U ^*(L)/t, Δr becomes smaller than a, giving rise to a correlated lattice regime where the previous scaling breaks down and analytical expansions in powers of t/U become valid. A weak random potential reduces the scaling length and favors the correlated motion. Received 28 March 2002 Published online 19 November 2002     

Quasi-one-dimensional foam drainage

Foam drainage is considered in a froth flotation cell. Air flow through the foam is described by a simple two-dimensional deceleration flow, modelling the foam spilling over a weir. Foam microstructure is given in terms of the number of channels (Plateau borders) per unit area, which scales as the inverse square of bubble size. The Plateau border number density decreases with height in the foam, and also decreases horizontally as the weir is approached. Foam drainage equations, applicable in the dry foam limit, are described. These can be used to determine the average cross-sectional area of a Plateau border, denoted A, as a function of position in the foam. Quasi-one-dimensional solutions are available in which A only varies vertically, in spite of the two-dimensional nature of the air flow and Plateau border number density fields. For such situations the liquid drainage relative to the air flow is purely vertical. The parametric behaviour of the system is investigated with respect to a number of dimensionless parameters: K (the strength of capillary suction relative to gravity), α (the deceleration of the air flow), and n and h (respectively, the horizontal and vertical variations of the Plateau border number density). The parameter K is small, implying the existence of boundary layer solutions: capillary suction is negligible except in thin layers near the bottom boundary. The boundary layer thickness (when converted back to dimensional variables) is independent of the height of the foam. The deceleration parameter α affects the Plateau border area on the top boundary: weaker decelerations give larger Plateau border areas at the surface. For weak decelerations, there is rapid convergence of the boundary layer solutions at the bottom onto ones with negligible capillary suction higher up. For strong decelerations, two branches of solutions for A are possible in the K = 0 limit: one is smooth, and the other has a distinct kink. The full system, with small but non-zero capillary suction, lies relatively close to the kinked solution branch, but convergence from the lower boundary layer onto this branch is distinctly slow. Variations in the Plateau border number density (non-zero n and h) increase individual Plateau border areas relative to the case of uniformly sized bubbles. For strong decelerations and negligible capillarity, solutions closely follow the kinked solution branch if bubble sizes are only slightly non-uniform. As the extent of non-uniformity increases, the Plateau border area reaches a maximum corresponding to no net upward velocity of foam liquid. In the case of vertical variation of number density, liquid content profiles and Plateau border area profiles cease to be simply proportional to one another. Plateau border areas match at the top of the foam independent of h, implying a considerable difference in liquid content for foams which exhibit different number density profiles. Received 3 July 2001     

Far-infrared response of quantum-dot molecules

We report an analysis of the dipole response of a symmetric quantum-dot molecule as a function of the dot-dot separation and intensity of a perpendicular magnetic field. The potential barrier is assumed proportional to the interdot distance using a two-center oscillator potential. The results are obtained within the symmetry-unrestricted TDLSDA. It is shown that the FIR details, specially the fragmentation of the low-energy brach, are quite sensitive to the interdot separation and that in both the small and large separation limits the results converge towards the analytic Kohn's magnetoplasmon energies. The validity of the LSDA is checked by comparison with the Hartree-Fock dipole spectrum in one case. Received 29 November 2000     

On the theory of light scattering in molecular liquids

The theory of light scattering for a system of linear molecules with anisotropic polarizabilities is considered. As a starting point for our theory, we express the result of a scattering experiment in VV and VH symmetry as dynamic correlation functions of tensorial densities ρ _lm(q) with l = 0 and l = 2. l, m denote indices of spherical harmonics. To account for all observed hydrodynamic singularities, a generalization of the theory of Schilling and Scheidsteger [1] for these correlation functions is presented, which is capable to describe the light scattering experiments from the liquid regime to the glassy state. As a microscopic theory it fulfills all sum rules contrary to previous phenomenological theories. We emphasize the importance of the helicity index m for the microscopic theory by showing, that only the existence of m = 1 components lead to the well known Rytov dip in liquids and to the appearance of transversal sound waves in VH symmetry in the deeply supercooled liquid and the glass. Exact expressions for the phenomenological frequency dependent rotation translation coupling coefficients of previous theories are derived. Received 3 July 2000 and Received in final form 7 November 2000     

Melting behavior of large disordered sodium clusters

The melting-like transition in disordered sodium clusters Na₉₂ and Na₁₄₂ is studied by performing density functional constant-energy molecular dynamics simulations. The orbital-free version of the density functional formalism is used. In Na₁₄₂ the atoms are distributed in two distinct shells (surface and inner shells) and this cluster melts in two steps: the first one, at ≈130 K, is characterized by the development of a high intrashell atomic mobility, and the second, homogeneous melting at ≈270 K, involves diffusive motion of all the atoms across the whole cluster volume. On the contrary, the melting of Na₉₂ proceeds smoothly over a very broad temperature interval, without any abrupt change in the thermal or structural indicators. The occurrence of two steps in the melting transition is suggested to be related to the existence of a grouping of the atoms in radial shells, even if those shells present a large degree of internal disorder. It then appears that a cluster can be considered fully amorphous (totally disordered) only when there are no radial regions of low atomic density separating shells. The isomer of Na₉₂ studied here fulfills this criterion and its thermal behavior can be considered as representative of that expected for fully amorphous clusters. Disordered Na₁₄₂, on the other hand, that has a discernible structure of an inner and a surface shell, should be considered as not fully disordered. The thermal behavior of these two clusters is also compared to that of icosahedral (totally ordered) sodium clusters of the same sizes. Received 5 February 2001 and Received in final form 21 May 2001     

Magnetic reconstructions at the surface of the B2 FeV alloy

We present an ab initio study of the magnetic surface reconstructions of the B2 FeV alloy using a self-consistent tight-binding linearized muffin tin orbital method developed in the atomic spheres approximation. For (001) and (111), the surface reconstruction stabilizes configurations unstable in the bulk alloy. When Fe is at the (001) surface, a c(2×2) in-plane antiferromagnetic order is found to be the ground state with magnetic moments of -2.32 and 2.27. A p(1×1) ↓ ferromagnetic order is displayed in case of V toplayer with a magnetic moment of -1.83. At the (111) surface, we obtain for Fe toplayer two solutions p(1×1)↑ and p(2×1). The configuration p(1×1)↑ is found to be the ground state with a magnetic moment per atom of 2.34. For V toplayer, only the p(1×1) ↓ solution is obtained with a moment of -0.84. In all cases, the Fe-V coupling is always antiparallel like in the bulk. Our results are discussed and compared to experiments. Received 11 August 2000 and Received in final form 8 June 2001     

Vertical melting of a stack of membranes

A stack of tensionless membranes with nonlinear curvature energy and vertical harmonic interaction is studied. At low temperatures, the system forms a lamellar phase. At a critical temperature, the stack disorders vertically in a melting-like transition. Received 26 April 2000 and Received in final form 16 August 2000     

Synchronization of underdamped Josephson-junction arrays

Our recent experiments show that arrays of underdamped Josephson junctions radiate coherently only above a threshold number of junctions switched onto the radiating state. For each junction, the radiating state is a resonant step in the current-voltage characteristics due to the interaction between the junctions in the array and an electromagnetic cavity. Here we show that a model of a one-dimensional array of Josephson junctions coupled to a resonator can produce many features of the coherent be havior above threshold, including coherent radiation of power and the shape of the array current-voltage characteristic. The model also makes quantitative predictions about the degree of coherence of the junctions in the array. However, in this model there is no threshold; the experimental below-threshold region behavior could not be reproduced.Received: 11 April 2003, Published online: 23 July 2003PACS: 74.50.+r Tunneling phenomena; point contacts, weak links, Josephson effects - 85.25.-j Superconducting devices     

Fast intramolecular dynamics of triphenyl phosphite investigated by <Emphasis Type="Bold">2</Emphasis>H NMR

The first analysis of rapid intramolecular motions of triphenyl phosphite by ²H NMR is presented. The fragile slowing down of the primary relaxation is followed by a solid-echo method. The occurrence of a fast reorientation of the phenyl side groups is demonstrated in the supercooled liquid state, identified as a two-fold flip on the basis of simple lineshape simulations. Coexistence of both static and motionally averaged components in “two phase” spectra indicate a broad distribution of correlation times for this relaxation. This dynamical behavior is shown to persist in the glacial phase. Received 28 May 2002 / Received in final form 1st October 2002 Published online 31 December 2002     

Growth and shapes of a cubic lyotropic liquid crystal

Monocrystals of the cubic lyotropic liquid crystal phase V₁ are studied in droplets of the mixture C ₁₂ EO ₆/water surrounded by water vapor of controlled pressure p. Shapes of monocrystals are found to depend on the conditions of growth from the lamellar phase and on the nature of the substrate. After the growth, when the lamellar phase is exhausted and crystals are in equilibrium with water vapors, their shapes are shown to depend on the pressure p. Thermodynamic aspects of these phenomena are discussed. Received 22 November 2000     

Surface state on first-order ferroelectrics

In the presence of a surface the Landau-Devonshire equations of ferroelectricity must be extended to include a boundary condition. For a ferroelectric with a second-order transition in the case when the polarization p(z) increases at the surface, it is well known that a surface state occurs in a range of temperature above the bulk critical temperature t_CB . Here we explore the corresponding effect for a first-order ferroelectric. We show that a surface state can occur, but only if the surface effect is sufficiently strong. Analytic expressions are derived and illustrated for p(z), the surface value p_S =p(0) and the free energy. The transition from the paraelectric state (p=0) to the surface state is first order, and for completeness we establish the dependence of the three critical temperatures (supercooling, thermodynamic and superheating) on a boundary-condition parameter y. In a final section, we derive and illustrate expressions for p(z)in the temperature range t<t_CB .     

The properties of free polymer surfaces and their influence on the glass transition temperature of thin polystyrene films

We present a detailed study of free polymer surfaces and their effects on the measured glass transition temperature (T_g) of thin polystyrene (PS) films. Direct measurements of the near-surface properties of PS films are made by monitoring the embedding of 10 and 20 nm diameter gold spheres into the surface of spin-cast PS films. At a temperature T = 378K( > T_g), the embedding of the spheres is driven by geometrical considerations arising from the wetting of the gold spheres by the PS. At temperatures below T_g ( 363K < T < 370K), both sets of spheres embed 3-4 nm into the PS films and stop. These studies suggest that a liquid-like surface layer exists in glassy PS films and also provide an estimate for the lower bound of the thickness of this layer of 3-4 nm. This qualitative idea is supported by a series of calculations based upon a previously developed theoretical model for the indentation of nanoscale spheres into linear viscoelastic materials. Comparing data with simulations shows that this surface layer has properties similar to those of a bulk sample of PS having a temperature of 374 K. Ellipsometric measurements of the T_g are also performed on thin spin-cast PS films with thicknesses in the range 8nm < h < 290nm. Measurements are performed on thin PS films that have been capped by thermally evaporating 5 nm thick metal (Au and Al) capping layers on top of the polymer. The measured T_g values (as well as polymer metal interface structure) in such samples depend on the metal used as the capping layer, and cast doubt on the general validity of using evaporative deposition to cover the free surface. We also prepared films that were capped by a new non-evaporative procedure. These films were shown to have a T_g that is the same as that of bulk PS (370±1 K) for all film thicknesses measured (> 7 nm). The subsequent removal of the metal layer from these films was shown to restore a thickness-dependent T_g in these samples that was essentially the same as that observed for uncapped PS films. An estimate of the thickness of the liquid-like surface layer was also extracted from the ellipsometry measurements and was found to be 5±1 nm. The combined ellipsometry and embedding studies provide strong evidence for the existence of a liquid-like surface layer in thin glassy PS films. They show that the presence of the free surface is an important parameter in determining the existence of T_g reductions in thin PS films.