Magnetic Susceptibility of an integrable anisotropic spin ladder system

We investigate the thermodynamics of a spin ladder model which possesses a free parameter besides the rung and leg couplings. The model is exactly solved by the Bethe Ansatz and exhibits a phase transition between a gapped and a gapless spin excitation spectrum. The magnetic susceptibility is obtained numerically and its dependence on the anisotropy parameter is determined. A connection with the compounds KCuCl3, Cu2(C5H12N2)2Cl4 and (C5H12N)2CuBr4 in the strong coupling regime is made and our results for the magnetic susceptibility fit the experimental data remarkably well.Comment: 12 pages, 12 figures included, submitted to Phys. Rev.

Exactly solvable models and ultracold Fermi gases

Exactly solvable models of ultracold Fermi gases are reviewed via their thermodynamic Bethe Ansatz solution. Analytical and numerical results are obtained for the thermodynamics and ground state properties of two- and three-component one-dimensional attractive fermions with population imbalance. New results for the universal finite temperature corrections are given for the two-component model. For the three-component model, numerical solution of the dressed energy equations confirm that the analytical expressions for the critical fields and the resulting phase diagrams at zero temperature are highly accurate in the strong coupling regime. The results provide a precise description of the quantum phases and universal thermodynamics which are applicable to experiments with cold fermionic atoms confined to one-dimensional tubes.Comment: based on an invited talk at Statphys24, Cairns (Australia) 2010. 16 pages, 6 figure

Exact solution for random walks on the triangular lattice with absorbing boundaries

The problem of a random walk on a finite triangular lattice with a single interior source point and zig-zag absorbing boundaries is solved exactly. This problem has been previously considered intractable.Comment: 10 pages, Latex, IOP macro

A note on graded Yang-Baxter solutions as braid-monoid invariants

We construct two $Osp(n|2m)$ solutions of the graded Yang-Baxter equation by using the algebraic braid-monoid approach. The factorizable S-matrix interpretation of these solutions is also discussed.Comment: 7 pages, UFSCARF-TH-94-1

Evidence for the super Tonks-Girardeau gas

We provide evidence in support of a recent proposal by Astrakharchik at al. for the existence of a super Tonks-Girardeau gas-like state in the attractive interaction regime of quasi-one-dimensional Bose gases. We show that the super Tonks-Giradeau gas-like state corresponds to a highly-excited Bethe state in the integrable interacting Bose gas for which the bosons acquire hard-core behaviour. The gas-like state properties vary smoothly throughout a wide range from strong repulsion to strong attraction. There is an additional stable gas-like phase in this regime in which the bosons form two-body bound states behaving like hard-core bosons.Comment: 10 pages, 1 figure, 2 tables, additional text on the stability of the super T-G gas-like stat

Exact solution and surface critical behaviour of open cyclic SOS lattice models

We consider the $L$-state cyclic solid-on-solid lattice models under a class of open boundary conditions. The integrable boundary face weights are obtained by solving the reflection equations. Functional relations for the fused transfer matrices are presented for both periodic and open boundary conditions. The eigen-spectra of the unfused transfer matrix is obtained from the functional relations using the analytic Bethe ansatz. For a special case of crossing parameter $\lambda=\pi/L$, the finite-size corrections to the eigen-spectra of the critical models are obtained, from which the corresponding conformal dimensions follow. The calculation of the surface free energy away from criticality yields two surface specific heat exponents, $\alpha_s=2-L/2\ell$ and $\alpha_1=1-L/\ell$, where $\ell=1,2,\cdots,L-1$ coprime to $L$. These results are in agreement with the scaling relations $\alpha_s=\alpha_b+\nu$ and $\alpha_1=\alpha_b-1$.Comment: 13 pages, LaTeX, to appear in J. Phys.

The Generation of Magnetic Fields Through Driven Turbulence

We have tested the ability of driven turbulence to generate magnetic field structure from a weak uniform field using three dimensional numerical simulations of incompressible turbulence. We used a pseudo-spectral code with a numerical resolution of up to $144^3$ collocation points. We find that the magnetic fields are amplified through field line stretching at a rate proportional to the difference between the velocity and the magnetic field strength times a constant. Equipartition between the kinetic and magnetic energy densities occurs at a scale somewhat smaller than the kinetic energy peak. Above the equipartition scale the velocity structure is, as expected, nearly isotropic. The magnetic field structure at these scales is uncertain, but the field correlation function is very weak. At the equipartition scale the magnetic fields show only a moderate degree of anisotropy, so that the typical radius of curvature of field lines is comparable to the typical perpendicular scale for field reversal. In other words, there are few field reversals within eddies at the equipartition scale, and no fine-grained series of reversals at smaller scales. At scales below the equipartition scale, both velocity and magnetic structures are anisotropic; the eddies are stretched along the local magnetic field lines, and the magnetic energy dominates the kinetic energy on the same scale by a factor which increases at higher wavenumbers. We do not show a scale-free inertial range, but the power spectra are a function of resolution and/or the imposed viscosity and resistivity. Our results are consistent with the emergence of a scale-free inertial range at higher Reynolds numbers.Comment: 14 pages (8 NEW figures), ApJ, in press (July 20, 2000?

Spin-charge separation in two-component Bose-gases

We show that one of the key characteristics of interacting one-dimensional electronic quantum systems, the separation of spin and charge, can be observed in a two-component system of bosonic ultracold atoms even close to a competing phase separation regime. To this purpose we determine the real-time evolution of a single particle excitation and the single-particle spectral function using density-matrix renormalization group techniques. Due to efficient bosonic cooling and good tunability this setup exhibits very good conditions for observing this strong correlation effect. In anticipation of experimental realizations we calculate the velocities for spin and charge perturbations for a wide range of parameters

Pearling instability of nanoscale fluid flow confined to a chemical channel

We investigate the flow of a nano-scale incompressible ridge of low-volatility liquid along a "chemical channel": a long, straight, and completely wetting stripe embedded in a planar substrate, and sandwiched between two extended less wetting solid regions. Molecular dynamics simulations, a simple long-wavelength approximation, and a full stability analysis based on the Stokes equations are used, and give qualitatively consistent results. While thin liquid ridges are stable both statically and during flow, a (linear) pearling instability develops if the thickness of the ridge exceeds half of the width of the channel. In the flowing case periodic bulges propagate along the channel and subsequently merge due to nonlinear effects. However, the ridge does not break up even when the flow is unstable, and the qualitative behavior is unchanged even when the fluid can spill over onto a partially wetting exterior solid region.Comment: 17 pages, 12 figures, submitted to Physics of Fluids, fixed equation numbering after Eq. (17

The packing of two species of polygons on the square lattice

We decorate the square lattice with two species of polygons under the constraint that every lattice edge is covered by only one polygon and every vertex is visited by both types of polygons. We end up with a 24 vertex model which is known in the literature as the fully packed double loop model. In the particular case in which the fugacities of the polygons are the same, the model admits an exact solution. The solution is obtained using coordinate Bethe ansatz and provides a closed expression for the free energy. In particular we find the free energy of the four colorings model and the double Hamiltonian walk and recover the known entropy of the Ice model. When both fugacities are set equal to two the model undergoes an infinite order phase transition.Comment: 21 pages, 4 figure