On the many-body Van der Waals binding energy of a dense fluid

We consider a dense system of neutral atoms. When the atoms are represented by isotropic oscillators (Drude-Lorentz model) interacting with nonretarded dipole-dipole forces, the binding energy of the system is given exactly by a well-known expression which is written as a sum of two-bond, three-bond, etc., Van der Waals interactions. For a Bravais lattice this expression for the binding energy can be computed numerically to arbitrary accuracy. This has been done for the f.c.c. lattices of the noble-gas solids by Lucas. For a fluid an exact evaluation would require the knowledge of higher-order molecular distribution functions. Various approximations are discussed for this case, the simplest of which is the so-called long-wavelength approximation due to Doniach. When this approximation is checked by comparison with the exact result for a lattice, it turns out that the two-bond contribution leads to a value which is more than twice too large. Some more refined approximations are considered which treat the two-bond contribution exactly. It is pointed out that the model is consistent only if the distance of closest approach between the atoms is not too small.     

约化胞与电子衍射谱的标定

对应于14种布喇菲点阵有44种约化胞,不但约化矢的选法是唯一的,而且可以根据约化矢标量积矩阵(a·a b·b c·c b·c c·a a·b)的不同形式,确定布喇菲点阵类型。在晶体点阵已知的情况下,从点阵参数计算出倒易点阵中的平面约化胞,并与试验得到的电子衍射谱对比以标定衍射斑点的指数。在晶体点阵未知的情况下,从已知转角的两个电子衍射谱中选三个接近中心的衍射斑点,相当于三个低指数倒易矢量。由它们构成倒易点阵的一个初基胞,变换成正点阵的初基胞后,经过约化得出约化胞和相应的布喇菲单胞的类型和参数,同时标定衍射斑点的指数。这些标定计算已编成电子计算机程序,可以用来直接确定晶体点阵类型和进行物相分析。     

The energy distribution of an ion in a radiofrequency trap interacting with a nonuniform neutral buffer gas

An ion in a radiofrequency (rf) trap sympathetically cooled by a simultaneously trapped neutral buffer gas exhibits deviations from thermal statistics caused by collision-induced coupling of the rf field to the ion motion. For a uniform density distribution of the buffer gas, the energy distribution of the ion can be described by Tsallis statistics. Moreover, runaway heating of the ion occurs if the buffer gas particles are sufficiently heavy relative to the ion. In typical experiments, however, ultracold buffer gases are confined in traps resulting in localised, non-uniform density distributions. Using a superstatistical approach, we develop an analytical model for an ion interacting with a localised buffer gas. We demonstrate theoretically that limiting collisions to the centre of the ion trap enables cooling at far greater mass ratios than achievable using a uniform buffer gas, but that an upper limit to the usable mass ratio exists even in this case. Furthermore, we analytically derive the functional form of the energy distribution for an ion interacting with a buffer gas held in a harmonic potential. The analytical distribution obtained is found to be in excellent agreement with the results of numerical simulations.     

Observation of sub-Bragg diffraction of waves in crystals

We investigate the diffraction conditions and associated formation of stop gaps for waves in crystals with different Bravais lattices. We identify a prominent stop gap in high-symmetry directions that occurs at a frequency below the ubiquitous first-order Bragg condition. This sub-Bragg-diffraction condition is demonstrated by reflectance spectroscopy on two-dimensional photonic crystals with a centered rectangular lattice, revealing prominent diffraction peaks for both the sub-Bragg and first-order Bragg conditions. These results have implications for wave propagation in 2 of the 5 two-dimensional Bravais lattices and 7 out of 14 three-dimensional Bravais lattices, such as centered rectangular, triangular, hexagonal, and body-centered cubic.     

Interplay between structure and density anomaly for an isotropic core-softened ramp-like potential

Using molecular dynamics simulations and integral equations wee investigate the structure, the thermodynamics, and the dynamics of a system of particles interacting through a continuous core-softened ramp-like interparticle potential. We found density, dynamic and structural anomalies similar to that found in water. Analysis of the radial distribution function for several temperatures at fixed densities shows a pattern that may be related to the origin of density anomaly.     

Evolution of the vortex state in the BCS-BEC crossover of a quasi two-dimensional superfluid Fermi gas

We use the path-integral formalism to investigate the vortex properties of a quasi-two dimensional(2D) Fermi superfluid system trapped in an optical lattice potential.Within the framework of mean-field theory,the cooper pair density,the atom number density,and the vortex core size are calculated from weakly interacting BCS regime to strongly coupled while weakly interacting BEC regime.Numerical results show that the atoms gradually penetrate into the vortex core as the system evolves from BEC to BCS regime.Meanwhile,the presence of the optical lattice allows us to analyze the vortex properties in the crossover from three-dimensional(3D) to 2D case.Furthermore,using a simple re-normalization procedure,we find that the two-body bound state exists only when the interaction is stronger than a critical one denoted by G_c which is obtained as a function of the lattice potential's parameter.Finally,we investigate the vortex core size and find that it grows with increasing interaction strength.In particular,by analyzing the behavior of the vortex core size in both BCS and BEC regimes,we find that the vortex core size behaves quite differently for positive and negative chemical potentials.     

Superfluidity and Anderson localisation for a weakly interacting Bose gas in a quasiperiodic potential

Using exact diagonalisation and Density Matrix Renormalisation group (DMRG) approach we analyse the transition to a localised state of a weakly interacting quasi-1D Bose gas subjected to a quasiperiodic potential. The analysis is performed by calculating the superfluid fraction, density profile, momentum distribution and visibility for different periodicities of the second lattice and in the presence (or not) of a weak repulsive interaction. It is shown that the transition is sharper towards the maximally incommensurate ratio between the two lattice periodicities, and shifted to higher values of the second lattice strength by weak repulsive interactions. We also relate our results to recent experiments.     

Lattice dynamics of an anharmonic crystal: evidence for interactions between atomic vibrations at high temperatures

In studying the lattice dynamics of a strongly anharmonic crystal, we solve a set of nonlinear Langevin equations for interacting oscillators while a multiwell potential is calculated in the displacive limit from the first principles. The model applied to the peculiar vibrations of beta-Zr along [111] allows us to analyze all contributions to the spectral density and their influence on each other. We predict the effect of induced anharmonicity for quick vibrations due to their interaction with intrinsically anharmonic slow vibrations. This effect results in the broadband distribution in energy of inelastic neutron scattering known as the symmetry-forbidden phonon-branch splitting.     

Dynamics of Bose-Einstein condensates in a one-dimensional optical lattice with double-well potential

We study dynamical behaviors of the weakly interacting Bose-Einstein condensate in the one-dimensional optical lattice with an overall double-well potential by solving the time-dependent Gross-Pitaevskii equation. It is observed that the double-well potential dominates the dynamics of such a system even if the lattice depth is several times larger than the height of the double-well potential. This result suggests that the condensate flows without resistance in the periodic lattice just like the case of a single particle moving in periodic potentials. Nevertheless, the effective mass of atoms is increased, which can be experimentally verified since it is connected to the Josephson oscillation frequency. Moreover, the periodic lattice enhances the nonlinearity of the double-well condensate, making the condensate more “self-trapped” in the π-mode self-trapping regime.     

Ground State at High Density

Weak limits as the density tends to infinity of classical ground states of integrable pair potentials are shown to minimize the mean-field energy functional. By studying the latter we derive global properties of high-density ground state configurations in bounded domains and in infinite space. Our main result is a theorem stating that for interactions having a strictly positive Fourier transform the distribution of particles tends to be uniform as the density increases, while high-density ground states show some pattern if the Fourier transform is partially negative. The latter confirms the conclusion of earlier studies by Vlasov (in J. Phys. (USSR) IX:25–40, 1945), Kirzhnits and Nepomnyashchii (in Sov. Phys. JETP 32:1191–1197, 1971), and Likos et al. (in J. Chem. Phys. 126:224502, 2007). Other results include the proof that there is no Bravais lattice among high-density ground states of interactions whose Fourier transform has a negative part and the potential diverges or has a cusp at zero. We also show that in the ground state configurations of the penetrable sphere model particles are superimposed on the sites of a close-packed lattice.     

On the coexistence of superconductivity and charge density waves

We study a simple tight-binding (Hubbard) model for electrons interacting via a short range attractive potential. We show that on a cubic lattice, for a half-filled band the ground state may feature both superconductivity and a charge density wave. We examine the response of such a ground state to an external magnetic field and describe the effect of the charge density wave on the Meissner effect.     

Solution of the four-nucleon Schrödinger equation

We present a solution of the Schrödinger equation for the case of four nucleons interacting via the Malfliet-Tjon potential. The Schrodinger equation is integrated by means of the Green function Monte Carlo method. The adaption of this method to treat finite systems is given. For the four-nucleon case, the ground-state eigenvalue is found to be ?31.3 ± 0.2 MeV and the rms point mass radius 1.36 ± 0.01 fm. The point mass distribution is given and does not exhibit a central depression. The method is also applied to the problem of four helium atoms interacting via the Lennard-Jones potential.     

Long-Range Order in Nonequilibrium Systems of Interacting Brownian Linear Oscillators

Long-range order (lro) is established with the help of a generalized Peierls argument for non-equilibrium lattice systems of one-dimensional (linear) interacting oscillators whose equation of motion (for a finite number of them) is the Smolouchowski equation for the density of a probability distribution. Interaction is mediated through the pair nearest-neighbor quadratic translation invariant potential. The initial density is Gibbsian with a potential energy satisfying the Ruelle superstability and regularity conditions.     

Interacting fermions on a random lattice

We extend previous work on the properties of the Dirac lagrangian on two-dimensional random lattices to the case where interaction terms are included. Although for free fermions the chiral symmetry of the doubles is spontaneously broken by their interaction with the lattice and they decouple from long-distance physics, our results in this paper show that all is undone by quantum corrections in an interacting field theory and that the end result is very similar to what is found with Wilson fermions. Two field-theoretical models with interacting fermions are studied by perturbation expansion in the field theory coupling constant. These are a model with one fermion and one boson species interacting via a scalar Yukawa coupling and the massive Thirring model. It is shown that on the random lattice ultraviolet finite diagrams and finite parts of ultraviolet divergent diagrams have the correct continuum limit. Ultraviolet divergent parts can be removed by the same renormalisation procedure as in the continuum, but do not exhibit the same dependence on the lagrangian mass. In the case of the massive Thirring model this causes a fermion mass correction of order the cut-off scale, which breaks the chiral symmetry of the remaining light fermion; there is consequently a fine-tuning problem. In the context of the same model we discuss the effect of the Goldstone boson associated with the spontaneous breakdown of the chiral symmetry of the doubles on two-dimensional models with vector couplings.     

The distribution of the valence electron density in predominantly ionic crystals with different Bravais sublattices

Based on the theory of the local-density functional, self-consistent valence electron densities are calculated for CaO with a rock-salt lattice, CaF₂ with a fluorite lattice, K₂O with an antifluorite lattice, and for their constituent sublattices. It is shown that in the crystals with different Bravais sublattices, the anionic sublattice is a framework with covalent bonds containing a metal sublattice inside of them. The coupling between the sublattices is characterized by the density difference, which is deflned as the difference between the total electron density and the densities of the individual sublattices. The density difference is found to be an order of magnitude smaller than the crystal and sublattice densities, which is evidence of weak hybridization of the sublattices and of the predominately ionic character of the bonding between them.     

Glassy behavior in a binary atomic mixture

We experimentally study one-dimensional, lattice-modulated Bose gases in the presence of an uncorrelated disorder potential formed by localized impurity atoms, and compare to the case of correlated quasidisorder formed by an incommensurate lattice. While the effects of the two disorder realizations are comparable deeply in the strongly interacting regime, both showing signatures of Bose-glass formation, we find a dramatic difference near the superfluid-to-insulator transition. In this transition region, we observe that random, uncorrelated disorder leads to a shift of the critical lattice depth for the breakdown of transport as opposed to the case of correlated quasidisorder, where no such shift is seen. Our findings, which are consistent with recent predictions for interacting bosons in one dimension, illustrate the important role of correlations in disordered atomic systems.     

Effective potential between two gluons from the scalar glueball

Starting from the 0⁺⁺ glueball mass and wave function computed from lattice QCD, we compute the local potential between two constituent gluons. Since the properties of constituent gluons are still a matter of research, we allow for them to be either massless, or massive with a mass around 0.7GeV. Both pictures are actually used in the literature. When the gluons are massless, the corresponding local potential is shown to be compatible with a Cornell form, that is a linear confinement plus a short-range Coulomb part, with standard values for the flux tube energy density and for the strong coupling constant. When the gluons are massive, the confining potential is a saturating one, commonly used to simulate string-breaking effects. These results fill a gap between lattice QCD and phenomenological models: The picture of the scalar glueball as a bound state of two constituent gluons interacting via a phenomenological potential is shown to emerge from pure gauge lattice QCD computations. Moreover, we show that the allowed potential shape is constrained by the mass of the constituent gluons.     

Magneto-elastic phase transition in a linear chain within the double and super-exchange model

In this work a magneto-elastic phase transition in a linear chain was obtained due the interplay between magnetism and lattice distortion in a double and super-exchange model. We consider a linear chain consisting of classical localized spins interacting with itinerant electrons. Due to the double exchange interaction, localized spins align ferromagnetically. This ferromagnetic tendency is expected to be frustrated by the anti-ferromagnetic super-exchange interaction between neighbor localized spins. Additionally, the lattice parameter is allowed to have small changes, which contributes harmonically to the energy of the system. The phase diagram is obtained as a function of the electron density and the super-exchange interaction using a Monte Carlo minimization. At low super-exchange interaction energy phase transition between electron-full ferromagnetic distorted and electron-empty anti-ferromagnetic undistorted phases occurs. In this case all electrons and lattice distortions were found within the ferromagnetic domain. For high super-exchange interaction energy, phase transition between two site distorted periodic arrangement of independent magnetic polarons ordered anti-ferromagnetically and the electron-empty anti-ferromagnetic undistorted phase was found. For this high interaction energy, Wigner crystallization, lattice distortion and charge distribution inside two-site polarons were obtained.     

用多光束干涉模拟晶格图案

利用多束激光干涉，可形成三维晶格结构，计算结果指出，用四束光或六束光可形成大部分的布拉格（Ｂｒａｇｇ）点阵。同时用Ｈｅ－Ｎｅ激光器获得了体心正方和面心立方的相干图案，晶格常数和计算结果相符，该研究对构成可见和红外区域的光子晶有一定意义。     

Dielectric-barrier discharges in two-dimensional lattice potentials

We use a pin-grid electrode to introduce a corrugated electrical potential into a planar dielectric-barrier discharge (DBD) system, so that the amplitude of the applied electric field has the profile of a two-dimensional square lattice. The lattice potential provides a template for the spatial distribution of plasma filaments in the system and has pronounced effects on the patterns that can form. The positions at which filaments become localized within the lattice unit cell vary with the width of the discharge gap. The patterns that appear when filaments either overfill or underfill the lattice are reminiscent of those observed in other physical systems involving 2D lattices. We suggest that the connection between lattice-driven DBDs and other areas of physics may benefit from the further development of models that treat plasma filaments as interacting particles.