Electron on a cylinder with topological defects in a homogeneous magnetic field

In this work we study the effects of the geometry and topology of a cylinder on the energy levels of an electron moving in a homogeneous magnetic field. We consider the existence of topological defects as a screw dislocation and a disclination. When we take the region of movement as the full cylindrical surface, we find that, by increasing the strength of the screw dislocation, the dispersion on the electronic energy levels is affected and monotonically increasing. For an electron moving in an almost flat region we show that the dispersion on the Landau levels decrease monotonically as we increase the strength of the screw dislocation. The lowest Landau level can reach a zero value, leaving the energy of the system solely given by the geometry of the cylinder, which does not depend on the magnetic field. In both situations, as we change the deficit angle of the disclination, we observe that the energy levels are shifted and the magnitude of such shift depends on the magnetic field. The Landau levels for a flat sample are recovered in the limit of an infinite cylinder radius.     

A novel approach to topological defects in a vector order parameter system

Based on Duan's topological current theory, we propose a novel approach to study the topological properties of topological defects in a two-dimensional complex vector order parameter system. This method shows explicitly the fine topological structure of defects. The branch processes of defects in the vector order parameter system have also been investigated with this method.     

Topological aspects in a two-component Bose condensed system in neutron star

By making use of Duan--Ge's decomposition theory of gauge potential and the topological current theory proposed by Prof. Duan Yi-Shi, we study a two-component superfluid Bose condensed system, which is supposed to be realized in the interior of neutron stars in the form of the coexistence of a neutron superfluid and a protonic superconductor. We propose that this system possesses vortex lines. The topological charges of the vortex lines are characterized by the Hopf indices and the Brower degrees of φ-mapping.     

The two-dimensional Coulomb gas on a sphere: Exact results

At the special value of the reduced inverse temperature=2, the equilibrium statistical mechanics of a two-dimensional Coulomb gas confined to the surface of a sphere is an exactly solvable problem, just as it was for the Coulomb gas in a plane. The thermodynamic quantities and all the correlation functions can be calculated. Use is made of an isomorphism between the classical Coulomb gas and the free Fermi field theory associated with the Dirac operator on the sphere.Laboratory associated with the Centre National de la Recherche Scientifique.     

Dynamics of a hard sphere granular impurity

An impurity particle coupling to its host fluid via inelastic hard sphere collisions is considered. It is shown that the exact equation for its distribution function can be mapped onto that for an impurity with elastic collisions and an effective mass. The application of this result to the Enskog-Lorentz kinetic equation leads to several conclusions: (1) every solution in the elastic case is equivalent to a class of solutions in the granular case; (2) for an equilibrium host fluid the granular impurity approaches equilibrium at a different temperature, with a dominant diffusive mode at long times; (3) for a granular host fluid in its scaling state, the granular impurity approaches the corresponding scaling solution.     

Nucleation on a sphere: the roles of curvature,confinement and ensemble

ABSTRACT

By combining Monte Carlo simulations and analytical models, we demonstrate and explain how the gas-to-liquid phase transition of colloidal systems confined to a spherical surface depends on the curvature and size of the surface, and on the choice of thermodynamic ensemble. We find that the geometry of the surface affects the shape of the free energy profile and the size of the critical nucleus by altering the perimeter–area ratio of isotropic clusters. Confinement to a smaller spherical surface results in both a lower nucleation barrier and a smaller critical nucleus size. Furthermore, the liquid domain does not grow indefinitely on a sphere. Saturation of the liquid density in the grand canonical ensemble and the depletion of the gas phase in the canonical ensemble lead to a minimum in the free energy profile, with a sharp increase in free energy for additional growth beyond this minimum.     

Classical Behavior After a Phase Transition: II. The Formation of Classical Defects

Classical defects (monopoles, vortices, etc.) are a characteristic consequence of many phase transitions of quantum fields. Most likely these include transitions in the early universe and such defects would be expected to be present in the universe today. We continue our analysis of the onset of classical behavior after a second-order phase transition in quantum field theory and show how defects appear after such transitions.     

Classical Behavior After a Phase Transition: I. Classical Order Parameters

We analyze the onset of classical field configurations after a phase transition. Firstly, we motivate the problem by means of a toy model in quantum mechanics. Subsequently, we consider a scalar field theory in which the system-field interacts with its environment, represented both by further scalar fields and by its own short-wavelength modes. We show that for very rapid quenches, the order parameter can be treated classically by the time taken for it to achieve its ground state values (spinodal time).     

Topological Vortices in a Spin-Triplet Superconductor

Based on the complex three-component order parameter model of a spin-triplet superconductor, by using the C-mapping theory, we derive a new equation describing the distribution of the magnetic field for vortices, which can be reduced to the modified London equation in the case of ｜ψ^2｜^2 ~- ｜ψ^3｜^2 = 0 and Wl^1= 1. A magnetic flux quantization condition for vortices in a spin-triplet superconductor is also derived, which is topological-invariant. Fhrthermore, the branch processes during the evolution of the vortices in a spin-triplet superconductor are discussed. We also point out that the sum of the magnetic flux quantization that those vortices carried is 2nФo （Фo is the unit magnetic flux）, that is to say, the sum of winding number is even, which needs to be proved by experiment.     

Viscosity of Lennard-Jones fluid: Integral equation method

One of the most useful models to study the real systems is the Lennard-Jones (LJ) potential which has an attractive and repulsive part. In this work we use this potential model and examine the viscosity of one-component LJ fluids and LJ binary fluid mixtures. For this purpose, we apply the integral equation method and solve numerically the Ornstein-Zernike (OZ) integral equation by using the mean spherical approximation (MSA). Thus, we obtain the pair correlation functions to calculate the viscosity of these fluids. Finally, we compare our results with computer simulation results and the available experimental data and illustrate the ability of the LJ model to predict the results.     

Soliton Stability in a Generalized Sine-Gordon Potential

We study stability of a generalized sine-Gordon model with two coupled scalar fields in two dimensions. Topological soliton solutions are found from the first-order equations that solve the equations of motion. The perturbation equations can be cast in terms of a Schrödinger-like operators for fluctuations and their spectra are calculated.     

LJ流体非牛顿现象的分子动力学模拟

使用非平衡分子动力学模拟方法研究了单原子LJ流体的非牛顿流变行为,并在系统中分别施加稳态Couette流场和振荡剪切流场.在Couette流场的模拟中,流体出现剪切变稀和法向应力差效应,不同剪切率下的径向分布函数反映了流体分子由于剪切所导致的微观结构变化,通过分析势能函数发现当剪切率增大时,分子间排斥作用增强,吸引作用减弱.在振荡剪切流场的模拟中,发现剪切应力和剪切率之间的相位差随频率增加而增加,随频率增加复数粘度的实部先增大再减小,虚部单调增加,导致虚部粘度相对实部粘度比例增大,弹性模量和粘性模量之比也随频率增加而增加.这三点现象表明LJ流体出现粘弹性行为,且在高频率下,弹性所占比重增大.     

A new mechanism of formation of topological defects

In this talk we discuss a new mechanism of formation of topological defects due to enhanced magnitude oscillations of a complex scalar order-parameter (OP) field during bubble collisions in a first order phase transition.     

Topological hierarchy matters — topological matters with superlattices of defects

Topological insulators/superconductors are new states of quantum matter with metallic edge/surface states.In this paper,we review the defects effect in these topological states and study new types of topological matters — topological hierarchy matters.We find that both topological defects(quantized vortices) and non topological defects(vacancies) can induce topological mid-gap states in the topological hierarchy matters after considering the superlattice of defects.These topological mid-gap states have nontrivial topological properties,including the nonzero Chern number and the gapless edge states.Effective tight-binding models are obtained to describe the topological mid-gap states in the topological hierarchy matters.     

Effect of curvature on interfacial segregation: Electronic contribution to the point defect/interface binding energy

The electronic contribution to the driving force for segregation to a curved interface between a cylindrical fiber of insulator embedded in a metal matrix is calculated. The solute/curved-interface binding energy is shown to vary as the inverse of the radius of curvature of the interface in the limit of a small radius. This result implies that the propensity for segregation of curved interfaces is larger than that of planar interfaces.     

The pressure of a hard sphere fluid on a curved surface

Utilizing the integral equation approach to the hard sphere fluid system developed in the preceding paper, the hard sphere-hard wall interaction is studied. For the case of a flat wall, perturbation solutions of the integral equation valid to second and third order in the packing fraction,y, are derived. For a surface of arbitrary curvature, an equation of state valid to second order in the packing fraction is also derived. When applied to very small cavities, it is found that the pressure at high densities is significantly higher than it would be for a flat wall.     

Isobaric-isothermal molecular dynamics study on the glass transition of a Lennard-Jones system

By means of constant-pressure, constant-temperature molecular dynamics simulations, we study the glass transition of a system composed of 864 Lennard-Jones particles with periodic boundary conditions. We calculate the thermodynamic properties, the structure properties, the diffusion constant and the microscopic structural parameters of our system, all of which show, at the nearly same temperature, the behaviours characteristic of the glass transition. The effect of the quench rate is such that the lower the quench rate, the lower the glass transition temperature and the more stable the obtained glass. Our simulations indicate that, for argon, the critical quench rate which separates the glass-forming quench rates and the crystal-forming quench rates is in the range between 4×10¹⁰ K/sec and 40×10¹¹ K/sec.     

Relativistic fluid sphere on pseudo-spheroidal space-time

A new exact closed form solution of Einstein's field equations is reported describing the space-time in the interior of a fluid sphere in equilibrium. The physical 3-space,t=constant of its space-time has the geometry of a 3-pseudo spheroid. The suitability of this solution for describing the model of a relativistic superdense star is discussed and the stability of the model under radial pulsations is examined.     

Structural features of a Lennard-Jones system at melting and crystallization

The structural features of the crystallization and melting of a system of particles whose pair interaction is described by the Lennard-Jones potential have been considered. The bond order parameter method is used to quantitatively describe the orientational short-range order. The rotational invariants of the second (q _l ) and third (w _l ) orders are calculated for each particle of the system. These calculations require only information on the snapshot of atom positions, which is quite easily obtained in experiments, and provide the distribution functions of particles in q _l and w _l (where l is the rank of an invariant; the results for l = 4, 6 are presented), which are important characteristics of the phase state of the system. It has been shown that the cumulant of the distribution of particles in w ₆ is very sensitive to the destruction/formation of the short-range orientational order in the Lennard-Jones system and, correspondingly, can be used as a criterion of the melting and crystallization of this system.     

Singular point of a system of Lennard-Jones particles at negative pressures

The method of molecular dynamics is used in a system of 2048 Lennard-Jones particles to determine the spinodal of a stretched liquid and crystal and the lines of their phase equilibrium at negative pressures. It is shown that a metastable extension of the melting line does not reach the zero isotherm, and ends on the spinodal of a stretched liquid. The point of termination of metastable liquid-crystal phase equilibrium is the singular point at a thermodynamic surface of states.