Eulerian Walkers as a model of Self-Organised Criticality

We propose a new model of self-organized criticality. A particle is dropped at random on a lattice and moves along directions specified by arrows at each site. As it moves, it changes the direction of the arrows according to fixed rules. On closed graphs these walks generate Euler circuits. On open graphs, the particle eventually leaves the system, and a new particle is then added. The operators corresponding to particle addition generate an abelian group, same as the group for the Abelian Sandpile model on the graph. We determine the critical steady state and some critical exponents exactly, using this equivalence.Comment: 4 pages, RevTex, 4 figure

Quasiadiabatic dynamics of ultracold bosonic atoms in a one-dimensional optical superlattice

We study the quasiadiabatic dynamics of a one-dimensional system of ultracold bosonic atoms loaded in an optical superlattice. Focusing on a slow linear variation in time of the superlattice potential, the system is driven from a conventional Mott insulator phase to a superlattice-induced Mott insulator, crossing in between a gapless critical superfluid region. Due to the presence of a gapless region, a number of defects depending on the velocity of the quench appear. Our findings suggest a power-law dependence similar to the Kibble-Zurek mechanism for intermediate values of the quench rate. For the temporal ranges of the quench dynamics that we considered, the scaling of defects depends nontrivially on the width of the superfluid region.Comment: 6 Pages, 4 Figure

The Oslo model, hyperuniformity, and the quenched Edwards-Wilkinson model

We present simulations of the 1-dimensional Oslo rice pile model in which the critical height at each site is randomly reset after each toppling. We use the fact that the stationary state of this sandpile model is hyperuniform to reach system of sizes $> 10^7$. Most previous simulations were seriously flawed by important finite size corrections. We find that all critical exponents have values consistent with simple rationals: $\nu=4/3$ for the correlation length exponent, $D =9/4$ for the fractal dimension of avalanche clusters, and $z=10/7$ for the dynamical exponent. In addition we relate the hyperuniformity exponent to the correlation length exponent $\nu$. Finally we discuss the relationship with the quenched Edwards-Wilkinson (qEW) model, where we find in particular that the local roughness exponent is $\alpha_{\rm loc} = 1$.Comment: 20 pages, 26 figure

Fast trimers in one-dimensional extended Fermi-Hubbard model

We consider a one-dimensional two component extended Fermi-Hubbard model with nearest neighbor interactions and mass imbalance between the two species. We study the stability of trimers, various observables for detecting them, and expansion dynamics. We generalize the definition of the trimer gap to include the formation of different types of clusters originating from nearest neighbor interactions. Expansion dynamics reveal rapidly propagating trimers, with speeds exceeding doublon propagation in strongly interacting regime. We present a simple model for understanding this unique feature of the movement of the trimers, and we discuss the potential for experimental realization.Comment: 10 pages, 10 figure

Zero-temperature Hysteresis in Random-field Ising Model on a Bethe Lattice

We consider the single-spin-flip dynamics of the random-field Ising model on a Bethe lattice at zero temperature in the presence of a uniform external field. We determine the average magnetization as the external field is varied from minus infinity to plus infinity by setting up the self-consistent field equations, which we show are exact in this case. We find that for a 3-coordinated Bethe lattice, there is no jump discontinuity in magnetization for arbitrarily small gaussian disorder, but the discontinuity is present for larger coordination numbers. We have checked our results by Monte Carlo simulations employing a technique for simulating classical interacting systems on the Bethe lattice which avoids surface effects altogether.Comment: latex file with 5 eps figures. This version is substantially revised with new material. Submitted to J. Phys.

Effect of phonon-phonon interactions on localization

We study the heat current J in a classical one-dimensional disordered chain with on-site pinning and with ends connected to stochastic thermal reservoirs at different temperatures. In the absence of anharmonicity all modes are localized and there is a gap in the spectrum. Consequently J decays exponentially with system size N. Using simulations we find that even a small amount of anharmonicity leads to a J~1/N dependence, implying diffusive transport of energy.Comment: 4 pages, 2 figures, Published versio

Magnetic properties of EuPtSi3_3 single crystals

Single crystals of EuPtSi$_3$, which crystallize in the BaNiSn$_3$-type crystal structure, have been grown by high temperature solution growth method using molten Sn as the solvent. EuPtSi$_3$ which lacks the inversion symmetry and has only one Eu site in the unit cell is found to be an antiferromagnet with two successive magnetic transitions at $T_{\rm N1}$ = 17 K and $T_{\rm N2}$ = 16 K, as inferred from magnetic susceptibility, heat capacity and $^{151}$Eu M\"ossbauer measurements. The isothermal magnetization data for $H \parallel$ [001] reveal a metamagnetic transition at a critical field $H_{\rm c}$ = 1 T. The magnetization saturates to a moment value of 6.43 $\mu_{\rm B}$/Eu above 5.9 T (9.2 T) for $H \parallel$ [001] ([100]), indicating that these fields are spin-flip fields for the divalent Eu moments along the two axes. The origin of this anisotropic behaviour is discussed. A magnetic (H, T) phase diagram has been constructed from the temperature dependence of isothermal magnetization data. The reduced jump in the heat capacity at $T_{\rm N1}$ indicates a transition to an incommensurate, amplitude modulated antiferromagnetic structure. The shape of the hyperfine field split M\"ossbauer spectrum at $T_{\rm N1}$ provides additional support for the proposed nature of this magnetic transition.Comment: 6 pages, 6 figures. Submitted to Phys. Rev.