Universality and Scaling Behaviour of Injected Power in Elastic Turbulence in Worm-like Micellar Gel

We study the statistical properties of spatially averaged global injected power fluctuations for Taylor-Couette flow of a worm-like micellar gel formed by surfactant CTAT. At sufficiently high Weissenberg numbers (Wi) the shear rate and hence the injected power p(t) at a constant applied stress shows large irregular fluctuations in time. The nature of the probability distribution function (pdf) of p(t) and the power-law decay of its power spectrum are very similar to that observed in recent studies of elastic turbulence for polymer solutions. Remarkably, these non-Gaussian pdfs can be well described by an universal large deviation functional form given by the Generalized Gumbel (GG) distribution observed in the context of spatially averaged global measures in diverse classes of highly correlated systems. We show by in-situ rheology and polarized light scattering experiments that in the elastic turbulent regime the flow is spatially smooth but random in time, in agreement with a recent hypothesis for elastic turbulence.Comment: 8 pages, 3 figure

Ground state of an S=1/2S=1/2 distorted diamond chain - model of Cu3Cl6(H2O)2⋅2H8C4SO2\rm Cu_3 Cl_6 (H_2 O)_2 \cdot 2H_8 C_4 SO_2

We study the ground state of the model Hamiltonian of the trimerized $S=1/2$ quantum Heisenberg chain $\rm Cu_3 Cl_6 (H_2 O)_2 \cdot 2H_8 C_4 SO_2$ in which the non-magnetic ground state is observed recently. This model consists of stacked trimers and has three kinds of coupling constants between spins; the intra-trimer coupling constant $J_1$ and the inter-trimer coupling constants $J_2$ and $J_3$. All of these constants are assumed to be antiferromagnetic. By use of the analytical method and physical considerations, we show that there are three phases on the $\tilde J_2 - \tilde J_3$ plane ($\tilde J_2 \equiv J_2/J_1$, $\tilde J_3 \equiv J_3/J_1$), the dimer phase, the spin fluid phase and the ferrimagnetic phase. The dimer phase is caused by the frustration effect. In the dimer phase, there exists the excitation gap between the two-fold degenerate ground state and the first excited state, which explains the non-magnetic ground state observed in $\rm Cu_3 Cl_6 (H_2 O)_2 \cdot 2H_8 C_4 SO_2$. We also obtain the phase diagram on the $\tilde J_2 - \tilde J_3$ plane from the numerical diagonalization data for finite systems by use of the Lanczos algorithm.Comment: LaTeX2e, 15 pages, 21 eps figures, typos corrected, slightly detailed explanation adde

Universality in the entanglement structure of ferromagnets

Systems of exchange-coupled spins are commonly used to model ferromagnets. The quantum correlations in such magnets are studied using tools from quantum information theory. Isotropic ferromagnets are shown to possess a universal low-temperature density matrix which precludes entanglement between spins, and the mechanism of entanglement cancellation is investigated, revealing a core of states resistant to pairwise entanglement cancellation. Numerical studies of one-, two-, and three-dimensional lattices as well as irregular geometries showed no entanglement in ferromagnets at any temperature or magnetic field strength.Comment: 4 pages, 2 figure

Spin Gap of Two-Dimensional Antiferromagnet Representing CaV4_4O9_9

We examined a two-dimensional Heisenberg model with two kinds of exchange energies, $J_e$ and $J_c$. This model describes localized spins at vanadium ions in a layer of CaV$_4$O$_9$, for which a spin gap is found by a recent experiment. Comparing the high temperature expansion of the magnetic susceptibility to experimental data, we determined the exchange energies as $J_e \simeq$ 610 K and $J_c \simeq$ 150 K. By the numerical diagonalization we estimated the spin gap as $\Delta \sim 0.2J_e \simeq$ 120 K, which consists with the experimental value 107 K. Frustration by finite $J_c$ enhances the spin gap.Comment: 12 pages of LaTex, 4 figures availavule upon reques

A chiral spin liquid wave function and the Lieb-Schulz-Mattis theorem

We study a chiral spin liquid wave function defined as a Gutwziller projected BCS state with a complex pairing function. After projection, spontaneous dimerization is found for any odd but finite number of chains, thus satisfying the Lieb-Schultz-Mattis theorem, whereas for even number of chains there is no dimerization. The two-dimensional thermodynamic limit is consistently reached for large number of chains since the dimer order parameter vanishes in this limit. This property clearly supports the possibility of a spin liquid ground state in two dimensions with a gap to all {\em physical} excitations and with no broken translation symmetry.Comment: 4 pages, 4 picture

Magnetic Order Beyond RKKY in the Classical Kondo Lattice

We study the Kondo lattice model of band electrons coupled to classical spins, in three dimensions, using a combination of variational calculation and Monte Carlo. We use the weak coupling `RKKY' window and the strong coupling regime as benchmarks, but focus on the physically relevant intermediate coupling regime. Even for modest electron-spin coupling the phase boundaries move away from the RKKY results, the non interacting Fermi surface no longer dictates magnetic order, and weak coupling `spiral' phases give way to collinear order. We use these results to revisit the classic problem of 4f magnetism and demonstrate how both electronic structure and coupling effects beyond RKKY control the magnetism in these materials.Comment: 6 pages, 4 figs. Improved figures, expanded captions. To appear in Europhys. Let

A non-Hermitian critical point and the correlation length of strongly correlated quantum systems

We study a non-Hermitian generalization of quantum systems in which an imaginary vector potential is added to the momentum operator. In the tight-binding approximation, we make the hopping energy asymmetric in the Hermitian Hamiltonian. In a previous article, we conjectured that the non-Hermitian critical point where the energy gap vanishes is equal to the inverse correlation length of the Hermitian system and we confirmed the conjecture for two exactly solvable systems. In this article, we present more evidence for the conjecture. We also argue the basis of our conjecture by noting the dispersion relation of the elementary excitation.Comment: 25 pages, 18 figure

Schwarzschild horizon dynamics and SU(2) Chern-Simons theory

We discuss the effect of different choices in partial gauge fixing of bulk local Lorentz invariance, on the description of the horizon degrees of freedom of a Schwarzschild black hole as an SU(2) Chern-Simons theory with specific sources. A classically equivalent description in terms of an ISO(2) Chern-Simons theory is also discussed. Further, we demonstrate that both these descriptions can be partially gauge fixed to a horizon theory with U(1) local gauge invariance, with the solder form sources being subject to extra constraints in directions orthogonal to an internal vector field left invariant by U(1) transformations. Seemingly disparate approaches on characterization of the horizon theory for the Schwarzschild black hole (as well as spherical Isolated Horizons in general) are thus shown to be equivalent physically.Comment: 22 pages Latex, no figures, version accepted for publication in Physical Review

Exact solution of a model of time-dependent evolutionary dynamics in a rugged fitness landscape

A simplified form of the time dependent evolutionary dynamics of a quasispecies model with a rugged fitness landscape is solved via a mapping onto a random flux model whose asymptotic behavior can be described in terms of a random walk. The statistics of the number of changes of the dominant genotype from a finite set of genotypes are exactly obtained confirming existing conjectures based on numerics.Comment: 5 pages RevTex 2 figures .ep