Quasi Two-dimensional Geometry Research Articles

Nonrelativistic Conformal Invariance in Mesoscopic Two-Dimensional Fermi Gases.

Two-dimensional Fermi gases with universal short-range interactions are known to exhibit a quantum anomaly, where a classical scale and conformal invariance is broken by quantum effects at strong coupling. We argue that in a quasi two-dimensional geometry, a conformal window remains at weak interactions. Using degenerate perturbation theory, we verify the conformal symmetry by computing the energy spectrum of mesoscopic particle ensembles in a harmonic trap, which separates into conformal towers formed by so-called primary states and their center-of-mass and breathing-mode excitations, the latter having excitation energies at precisely twice the harmonic oscillator energy. In addition, using Metropolis importance sampling, we compute the hyperradial distribution function of the many-body wave functions, which are predicted by the conformal symmetry in closed analytical form. The weakly interacting Fermi gas constitutes a system where the nonrelativistic conformal symmetry can be revealed using elementary methods, and our results are testable in current experiments on mesoscopic Fermi gases.

Electric field shielding of ultracold molecules

Ultracold Chemistry Because reactive collisions limit the lifetime of ultracold molecular ensembles, controlling chemical reactivity at ultralow temperatures has been a long-standing goal. Using large electric fields that trigger resonant dipolar interactions between potassium-rubidium molecules trapped in a quasi–two-dimensional geometry, Matsuda et al. report suppression of the reactive loss rate in the vicinity of the dipolar-mediated resonances by up to an order of magnitude below the background value. The proposed shielding mechanism is general and is expected to be effective in three-dimensional geometry. It could also be used for creating long-lived quantum molecular gases of other polar molecules under strong electric fields. Science , this issue p. [1324][1] [1]: /lookup/doi/10.1126/science.abe7370

Annihilation of point defect pairs in freely suspended liquid-crystal films

We study the annihilation of topological defect pairs in the quasi-twodimensional (2D) geometry of freely suspended smectic films. This elementary process is at the basis of all models describing the statistics of complex defect patterns. We prepare pairs with opposite topological charges and retrieve the interaction mechanisms from their trajectories. The square-root dependence of the defect separation on the time until annihilation and the asymmetry in propagation velocities of the opponents predicted by theory are confirmed. The importance of defect orientations is demonstrated. Trajectories are in general curved, depending on the mutual orientations (phase mismatch) of the defects and on the orientation of the pair respective to the far, undisturbed director. The experiments provide the basis for an adaption of the theoretical models to the real complexity of the annihilation.

Effective two-dimensional model for granular matter with phase separation.

Granular systems confined in vertically vibrated shallow horizontal boxes (quasi-two-dimensional geometry) present a liquid-to-solid phase transition when the frequency of the periodic forcing is increased. An effective model, where grains move and collide in two-dimensions is presented, which reproduces the aforementioned phase transition. The key element is that besides the two-dimensional degrees of freedom, each grain has an additional variable ɛ that accounts for the kinetic energy stored in the vertical motion in the real quasi-two-dimensional motion. This energy grows monotonically during free flight, mimicking the energy gained by collisions with the vibrating walls and, at collisions, this energy is instantaneously transferred to the horizontal degrees of freedom. As a result, the average values of ɛ and the kinetic temperature are decreasing functions of the local density, giving rise to an effective pressure that can present van der Waals loops. A kinetic theory approach predicts the conditions that must satisfy the energy growth function to obtain the phase separation, which are verified with molecular dynamics simulations. Notably, the effective equation of state and the critical points computed considering the velocity-time-of-flight correlations differ only slightly from those obtained by simple kinetic theory calculations that neglect those correlations.

Compaction of granular material inside confined geometries

In both nature and the laboratory, loosely packed granular materials are often compacted inside confined geometries. Here, we explore such behaviour in a quasi-two dimensional geometry, where parallel rigid walls provide the confinement. We use the discrete element method to investigate the stress distribution developed within the granular packing as a result of compaction due to the displacement of a rigid piston. We observe that the stress within the packing increases exponentially with the length of accumulated grains, and show an extension to current analytic models which fits the measured stress. The micromechanical behaviour is studied for a range of system parameters, and the limitations of existing analytic models are described. In particular, we show the smallest sized systems which can be treated using existing models. Additionally, the effects of increasing piston rate, and variations of the initial packing fraction, are described.

Large Magnetoresistance in Diluted Magnetic Semiconductors in Quasi-two Dimensional Geometry

The carrier-induced magnetic solitons in diluted magnetic semiconductors have been introduced by using the gauge-invariant effective Lagrangian. We have discussed the large magnetoresistance effects in diluted magnetic semiconductors in quasi-two dimensional geometry, by using the path-integral method and the supersymmetric sigma formula. We have considered the interaction effects of the localization in DMS. The lowest order contribution in the long-range interactions, which are mediated with massless gauge fields between the magnetic solitons, is given by Hartree and Fock processes for the self-energy.

Fingering versus stability in the limit of zero interfacial tension.

The invasion of one fluid into another of higher viscosity in a quasi-two dimensional geometry typically produces complex fingering patterns. Because interfacial tension suppresses short-wavelength fluctuations, its elimination by using pairs of miscible fluids would suggest an instability producing highly ramified singular structures. Previous studies focused on wavelength selection at the instability onset and overlooked the striking features appearing more globally. Here we investigate the non-linear growth that occurs after the instability has been fully established. We find a rich variety of patterns that are characterized by the viscosity ratio between the inner and the outer fluid, η(in)/η(out), as distinct from the most-unstable wavelength, which determines the onset of the instability. As η(in)/η(out) increases, a regime dominated by long highly-branched fractal fingers gives way to one dominated by blunt stable structures characteristic of proportionate growth. Simultaneously, a central region of complete outer-fluid displacement grows until it encompasses the entire pattern at η(in)/η(out)≈0.3.

Vortex dynamics of rotating dipolar Bose–Einstein condensates

We study the influence of dipole–dipole interaction on the formation of vortices in a rotating dipolar Bose–Einstein condensate (BEC) of 52Cr and 164Dy atoms in quasi two-dimensional geometry. By numerically solving the corresponding time-dependent mean-field Gross–Pitaevskii equation, we show that the dipolar interaction enhances the number of vortices, while a repulsive contact interaction increases the stability of the vortices. Furthermore, an ordered vortex lattice of a relatively large number of vortices is found in a strongly dipolar BEC.

Roton immiscibility in a two-component dipolar Bose gas

We characterize the immiscibility-miscibility transition (IMT) of a two-component Bose-Einstein condensate (BEC) with dipole-dipole interactions. In particular, we consider the quasi-two dimensional geometry, where a strong trapping potential admits only zero-point motion in the trap direction, while the atoms are more free to move in the transverse directions. We employ the Bogoliubov treatment of the two-component system to identify both the well-known long-wavelength IMT in addition to a roton-like IMT, where the transition occurs at finite-wave number and is reminiscent of the roton softening in the single component dipolar BEC. Additionally, we verify the existence of the roton IMT in the fully trapped, finite systems by direct numerical simulation of the two-component coupled non-local Gross-Pitaevskii equations.

Near limit behavior of the detonation velocity

The behavior of the detonation velocity near the limits is investigated. Circular tubes of diameters 65, 44 and 13mm are used. To simulate a quasi two-dimensional rectangular geometry thin annular channels are also used. The annular channels are formed by a 1.5m long insert of a smaller diameter tube into the larger outer diameter detonation tube. Premixed mixtures of C2H2+2.5O2+70%Ar, CH4+2O2 and C2H2+5N2O+50%Ar are used in the present study. The high argon dilution stoichiometric C2H2+2.5O2 mixture has a regular cell size and piecewise laminar reaction zone and thus referred to as “stable”. The other two mixtures give highly irregular cell pattern and a turbulent reaction zone and are hence, referred to as “unstable” mixtures. Pressure transducers and optical fibers spaced 10cm apart along the tube are used for pressure and velocity measurements. Cell size of the three mixtures studied is also determined using smoked foils in both the circular tubes and annular channels. The ratio d/λ (representing the number of cells across the tube diameter) is found to be an appropriate sensitivity parameter to characterize the mixture. The present results indicate that well within the limit, the detonation velocity is generally a few percent below the theoretical Chapman–Jouguet (CJ) value. As the limit is approached, the velocity decreases rapidly to a minimum value before the detonation fails. The narrow range of values of d/λ of the mixture where the velocity drops rapidly is found to correspond to the range of values for the onset of single headed spinning detonations. Thus we may conclude that the onset of single headed spin can be used as a criterion for defining the limits. Spinning detonations are also observed near the limits in annular channels.

Anisotropic Superfluidity in a Dipolar Bose Gas

We study the superfluid character of a dipolar Bose-Einstein condensate (DBEC) in a quasi-two dimensional geometry. We consider the dipole polarization to have some nonzero projection into the plane of the condensate so that the effective interaction is anisotropic in this plane, yielding an anisotropic dispersion relation. By performing direct numerical simulations of a probe moving through the DBEC, we observe the sudden onset of drag or creation of vortex-antivortex pairs at critical velocities that depend strongly on the direction of the probe's motion. This anisotropy emerges because of the anisotropic manifestation of a rotonlike mode in the system.

Pattern Formation at the Nematic Smectic-B Interface

Free growth properties of the smectic B liquid crystalline phase into the supercooled nematic have been investigated in quasi-twodimensional geometry. Different orientation combinations of the two phases have been achieved experimentally and the interfacial patterns have been studied and analysed as a function of undercooling. The angular dependence of the surface tension has been deduced from the shape of the interface in thermal equilibrium. The experimentally determined surface tension anisotropy has been incorporated into computer simulations based on the phase-field model. The simulations have reproduced qualitatively the rich variety of morphologies observed in the experiments for a given set of undercoolings in three geometries. Anisotropic heat diffusion on the nematic side, relevant to our experimental system has also been introduced. Both in the experiments and in the simulations we find that the growth is faster in the lower heat diffusion direction.

Influence of laser irradiation on the morphology of fractal electrodeposition

This work presents the effect of cw argon ion laser irradiation on far from equilibrium fractal growths from CuSO 4 aqueous solutions in a quasi two-dimensional geometry. We find that the polarization orientation of the laser electric field influences the growth process. A laser electric field parallel to the field generated by the applied voltage causes an increase in the rate of the growth process. A slight inhibition of the process is observed when the two fields have crossed polarization. An interpretation based on the hypothesis of the polarization of the molecules and of the fractal growth caused by the laser electric field is given. A numerical simulation based on a perturbed diffusion model is shown to give results in agreement with the experimental data.

Nematic-Smectic B Interface. Equilibrium and Growth Properties

Abstract The equilibrium morphology of the nematic (N) - smectic B (SmB) interface, and its growth properties have been studied in quasi-twodimensional geometry. After thermal equilibration at the N - SmB phase transition temperature TNS two different equilibrium shapes of the SmB phase were found, depending on its orientation. The surface tension anisotropy has been determined from the shape anisotropy of the smectic body. An interesting “inverse process” has been detected in melting of the rapidly grown smectic phase. The stable nematic phase nucleated substancially below TNS . Most of these nematic germs had uniform oval shape, totally different from that of the equilibrium smectic seed. The morphology of the growing smectic B phase in a supercooled nematic also has been studied. Different morphologies were observed, depending on the substance, undercooling ΔT = TNS - T, and alignment of the growing SmB germ. In order to compare the growth dynamics, the area of the patterns was measured and the square ...