Direct Statistical Simulation of Jets and Vortices in 2D Flows

In this paper we perform Direct Statistical Simulations of a model of two-dimensional flow that exhibits a transition from jets to vortices. The model employs two-scale Kolmogorov forcing, with energy injected directly into the zonal mean of the flow. We compare these results with those from Direct Numerical Simulations. For square domains the solution takes the form of jets, but as the aspect ratio is increased a transition to isolated coherent vortices is found. We find that a truncation at second order in the equal-time but nonlocal cumulants that employs zonal averaging (zonal CE2) is capable of capturing the form of the jets for a range of Reynolds numbers as well as the transition to the vortex state, but, unsurprisingly, is unable to reproduce the correlations found for the fully nonlinear (non-zonally symmetric) vortex state. This result continues the program of promising advances in statistical theories of turbulence championed by Kraichnan

Exact Equal Time Statistics of Orszag-McLaughlin Dynamics By The Hopf Characteristic Functional Approach

By employing Hopf's functional method, we find the exact characteristic functional for a simple nonlinear dynamical system introduced by Orszag. Steady-state equal-time statistics thus obtained are compared to direct numerical simulation. The solution is both non-trivial and strongly non-Gaussian.Comment: 6 pages and 2 figure

Critical behavior of Ginzburg-Landau model coupled to massless Dirac fermions

We point out interesting effects of additional massless Dirac fermions with N_F colors upon the critical behavior of the Ginzburg-Landau model. For increasing N_F, the model is driven into the type II regime of superconductivity. The critical exponents are given as a function of N_F.Comment: RevTex4, 4 pages, 1 figure; author information and latest update to this paper at http://www.physik.fu-berlin.de/~kleinert/institution.html; version 2: new references and comments on chiral symmetry breaking adde

Large-N solutions of the Heisenberg and Hubbard-Heisenberg models on the anisotropic triangular lattice: application to Cs2_2CuCl4_4 and to the layered organic superconductors κ\kappa-(BEDT-TTF)2_2X

We solve the Sp(N) Heisenberg and SU(N) Hubbard-Heisenberg models on the anisotropic triangular lattice in the large-N limit. These two models may describe respectively the magnetic and electronic properties of the family of layered organic materials $\kappa$-(BEDT-TTF)$_2$X. The Heisenberg model is also relevant to the frustrated antiferromagnet, Cs$_2$CuCl$_4$. We find rich phase diagrams for each model. The Sp(N) antiferromagnet is shown to have five different phases as a function of the size of the spin and the degree of anisotropy of the triangular lattice. The effects of fluctuations at finite-N are also discussed. For parameters relevant to Cs$_2$CuCl$_4$ the ground state either exhibits incommensurate spin order, or is in a quantum disordered phase with deconfined spin-1/2 excitations and topological order. The SU(N) Hubbard-Heisenberg model exhibits an insulating dimer phase, an insulating box phase, a semi-metallic staggered flux phase (SFP), and a metallic uniform phase. The uniform and SFP phases exhibit a pseudogap. A metal-insulator transition occurs at intermediate values of the interaction strength.Comment: Typos corrected, one reference added. 20 pages, 17 figures, RevTeX 3.

Staggered Flux Phase in a Model of Strongly Correlated Electrons

We present numerical evidence for the existence of a staggered flux (SF) phase in the half-filled two-leg t-U-V-J ladder, with true long-range order in the counter-circulating currents. The density-matrix renormalization-group (DMRG) / finite-size scaling approach, generalized to describe complex-valued Hamiltonians and wavefunctions, is employed. The SF phase exhibits robust currents at intermediate values of the interaction strength.Comment: Version to appear in Phys. Rev. Let

Nonlinear Modes of Liquid Drops as Solitary Waves

The nolinear hydrodynamic equations of the surface of a liquid drop are shown to be directly connected to Korteweg de Vries (KdV, MKdV) systems, giving traveling solutions that are cnoidal waves. They generate multiscale patterns ranging from small harmonic oscillations (linearized model), to nonlinear oscillations, up through solitary waves. These non-axis-symmetric localized shapes are also described by a KdV Hamiltonian system. Recently such ``rotons'' were observed experimentally when the shape oscillations of a droplet became nonlinear. The results apply to drop-like systems from cluster formation to stellar models, including hyperdeformed nuclei and fission.Comment: 11 pages RevTex, 1 figure p

The Heisenberg antiferromagnet on an anisotropic triangular lattice: linear spin-wave theory

We consider the effect of quantum spin fluctuations on the ground state properties of the Heisenberg antiferromagnet on an anisotropic triangular lattice using linear spin-wave theory. This model should describe the magnetic properties of the insulating phase of the kappa-(BEDT-TTF)_2 X family of superconducting molecular crystals. The ground state energy, the staggered magnetization, magnon excitation spectra and spin-wave velocities are computed as a function of the ratio between the second and first neighbours, J2/J1. We find that near J2/J1 = 0.5, i.e., in the region where the classical spin configuration changes from a Neel ordered phase to a spiral phase, the staggered magnetization vanishes, suggesting the possibility of a quantum disordered state. In this region, the quantum correction to the magnetization is large but finite. This is in contrast to the frustrated Heisenberg model on a square lattice, for which the quantum correction diverges logarithmically at the transition from the Neel to the collinear phase. For large J2/J1, the model becomes a set of chains with frustrated interchain coupling. For J2 > 4 J1, the quantum correction to the magnetization, within LSW, becomes comparable to the classical magnetization, suggesting the possibility of a quantum disordered state. We show that, in this regime, quantum fluctuations are much larger than for a set of weakly coupled chains with non-frustated interchain coupling.Comment: 10 pages, RevTeX + epsf, 5 figures Replaced with published version. Comparison to series expansions energies include