Simulation of two-dimensional vortex dynamics

The two-dimensional XY model is simulated with a time-dependent Ginzburg-Landau type dynamics. The data are, in the limit of small driving force, well described by the Minnhagen phenomenology for vortex dynamics of a two-dimensional superfluid. This phenomenology is different and distinguishable from the conventional AHNS phenomenology. The Minnhagen phenomenology has been observed in recent experiments on Josephson-junction arrays and high-T_c BSCCO films. The present simulations suggest that this reflects an intrinsic property of the vortex dynamics for a two-dimensional superfluid.     

Shear induced anisotropy in two-dimensional liquids

The behavior of a dense two-dimensional soft disc liquid under shear is studied via nonequilibrium molecular dynamics. The structure factor for the liquid at a given shear rate is evaluated directly by plotting the particle positions, taken at random from the NEMD simulation at that shear, onto photographic film and using light scattering to obtain a diffraction pattern. The pair correlation function of this system is also extracted directly by histogramming the particle positions with respect to a given central particle as a function of separation and angle. The pair correlation function is compared to that approximated by a Fourier series expansion to rank ten. Results are reported as a function of shear rate from a shear rate of 0.1 (when the fluid is essentially Newtonian) to 10 (when the fluid can display a string phase). The appearance of the string phase is discussed and shown to be a consequence of the definition of temperature in the simulation algorithm. A modification of the algorithm is proposed. Comparisons between this work and previous work with three-dimensional liquids are given. The two-dimensional structure factor is compared with that obtained from a real colloidal suspension via light scattering.     

“Phonons” in two-dimensional vortex lattices

The macroscopic dynamics of regular lattices formed by 2D vortices of various physical origin is considered. The effective equations describing this dynamics are derived and their properties are analyzed. The general feature of the evolution of such systems and their peculiarities distinguishing qualitatively vortex ensembles from ordinary crystals are considered.     

Equilibrium theory of two-dimensional simple liquids

Using the Wigner-Kirkwood expansion and bare Lennard-Jones (LJ) (12-6) potential, an effectiveLJ potential is derived, which includes the quantum effects through the expressions of the effective diameter∂(T, λ) and well-depth (T, λ). We use theWCA perturbation theory to calculate the free energy and pressure for theLJ and effectiveLJ potentials. Simple analytic expressions are given for the reference system and the first order correction calculated. The results are quite good at high density. The quantum effects on the free energy and pressure are also discussed.     

Fundamental and vortex solitons in a two-dimensional optical lattice

Fundamental and vortex solitons in a two-dimensional optically induced waveguide array are reported. In the strong localization regime the fundamental soliton is largely confined to one lattice site, whereas the vortex state comprises four fundamental modes superimposed in a square configuration with a phase structure that is topologically equivalent to the conventional vortex. However, in the weak localization regime, both the fundamental and the vortex solitons spread over many lattice sites. We further show that fundamental and the vortex solitons are stable against small perturbations in the strong localization regime.     

Topological aspect of vortex lines in two-dimensional Gross—Pitaevskii theory

Using the -mapping topological theory, we study the topological structure of vortex lines in a two-dimensional generalized Gross-Pitaevskii theory in (3+1)-dimensional space-time. We obtain the reduced dynamic equation in the framework of the two-dimensional Gross-Pitaevskii theory, from which a conserved dynamic quantity is derived on the stable vortex lines. Such equations can also be used to discuss Bose-Einstein condensates in heterogeneous and highly nonlinear systems. We obtain an exact dynamic equation with a topological term, which is ignored in traditional hydrodynamic equations. The explicit expression of vorticity as a function of the order parameter is derived, where the δ function indicates that the vortices can only be generated from the zero points of Φ and are quantized in terms of the Hopf indices and Brouwer degrees. The -mapping topological current theory also provides a reasonable way to study the bifurcation theory of vortex lines in the two-dimensional Gross-Pitaevskii theory.