6,645 research outputs found

    Distribution of sizes of erased loops for loop-erased random walks

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    We study the distribution of sizes of erased loops for loop-erased random walks on regular and fractal lattices. We show that for arbitrary graphs the probability P(l)P(l) of generating a loop of perimeter ll is expressible in terms of the probability Pst(l)P_{st}(l) of forming a loop of perimeter ll when a bond is added to a random spanning tree on the same graph by the simple relation P(l)=Pst(l)/lP(l)=P_{st}(l)/l. On dd-dimensional hypercubical lattices, P(l)P(l) varies as lσl^{-\sigma} for large ll, where σ=1+2/z\sigma=1+2/z for 1<d<41<d<4, where z is the fractal dimension of the loop-erased walks on the graph. On recursively constructed fractals with d~<2\tilde{d} < 2 this relation is modified to σ=1+2dˉ/(d~z)\sigma=1+2\bar{d}/{(\tilde{d}z)}, where dˉ\bar{d} is the hausdorff and d~\tilde{d} is the spectral dimension of the fractal.Comment: 4 pages, RevTex, 3 figure

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

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    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

    Two simple models of classical heat pumps

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    Motivated by recent studies on models of particle and heat quantum pumps, we study similar simple classical models and examine the possibility of heat pumping. Unlike many of the usual ratchet models of molecular engines, the models we study do not have particle transport. We consider a two-spin system and a coupled oscillator system which exchange heat with multiple heat reservoirs and which are acted upon by periodic forces. The simplicity of our models allows accurate numerical and exact solutions and unambiguous interpretation of results. We demonstrate that while both our models seem to be built on similar principles, one is able to function as a heat pump (or engine) while the other is not.Comment: 4 pages, 4 figure

    Fast trimers in one-dimensional extended Fermi-Hubbard model

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    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

    Enhanced conduction band density of states in intermetallic EuTSi3_3 (T=Rh, Ir)

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    We report on the physical properties of single crystalline EuRhSi3_3 and polycrystalline EuIrSi3_3, inferred from magnetisation, electrical transport, heat capacity and 151^{151}Eu M\"ossbauer spectroscopy. These previously known compounds crystallise in the tetragonal BaNiSn3_3-type structure. The single crystal magnetisation in EuRhSi3_3 has a strongly anisotropic behaviour at 2 K with a spin-flop field of 13 T, and we present a model of these magnetic properties which allows the exchange constants to be determined. In both compounds, specific heat shows the presence of a cascade of two close transitions near 50 K, and the 151^{151}Eu M\"ossbauer spectra demonstrate that the intermediate phase has an incommensurate amplitude modulated structure. We find anomalously large values, with respect to other members of the series, for the RKKY N\'eel temperature, for the spin-flop field (13 T), for the spin-wave gap (\simeq 20-25 K) inferred from both resistivity and specific heat data, for the spin-disorder resistivity in EuRhSi3_3 (35\simeq 35 μ\muOhm.cm) and for the saturated hyperfine field (52 T). We show that all these quantities depend on the electronic density of states at the Fermi level, implying that the latter must be strongly enhanced in these two materials. EuIrSi3_3 exhibits a giant magnetoresistance ratio, with values exceeding 600 % at 2 K in a field of 14 T.Comment: 6 pages, 8 figure

    Spin glasses in the limit of an infinite number of spin components

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    We consider the spin glass model in which the number of spin components, m, is infinite. In the formulation of the problem appropriate for numerical calculations proposed by several authors, we show that the order parameter defined by the long-distance limit of the correlation functions is actually zero and there is only "quasi long range order" below the transition temperature. We also show that the spin glass transition temperature is zero in three dimensions.Comment: 9 pages, 13 figure

    Quenched Averages for self-avoiding walks and polygons on deterministic fractals

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    We study rooted self avoiding polygons and self avoiding walks on deterministic fractal lattices of finite ramification index. Different sites on such lattices are not equivalent, and the number of rooted open walks W_n(S), and rooted self-avoiding polygons P_n(S) of n steps depend on the root S. We use exact recursion equations on the fractal to determine the generating functions for P_n(S), and W_n(S) for an arbitrary point S on the lattice. These are used to compute the averages ,,, , and <logWn(S)><log W_n(S)> over different positions of S. We find that the connectivity constant μ\mu, and the radius of gyration exponent ν\nu are the same for the annealed and quenched averages. However,  nlogμ+(αq2)logn ~ n log \mu + (\alpha_q -2) log n, and  nlogμ+(γq1)logn ~ n log \mu + (\gamma_q -1)log n, where the exponents αq\alpha_q and γq\gamma_q take values different from the annealed case. These are expressed as the Lyapunov exponents of random product of finite-dimensional matrices. For the 3-simplex lattice, our numerical estimation gives αq0.72837±0.00001 \alpha_q \simeq 0.72837 \pm 0.00001; and γq1.37501±0.00003\gamma_q \simeq 1.37501 \pm 0.00003, to be compared with the annealed values αa=0.73421\alpha_a = 0.73421 and γa=1.37522\gamma_a = 1.37522.Comment: 17 pages, 10 figures, submitted to Journal of Statistical Physic

    Magnetic behaviour of PrPd2B2C

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    We have synthesized a new quaternary borocarbide PrPd2_{2}B2_{2}C and measured its magnetization, electrical resistivity and specific heat. The compound crystallizes in the LuNi2_{2}B2_{2}C-type tetragonal structure (space group {\it I4/mmm}). Above 100 K the magnetic susceptibility follows Curie-Weiss behavior with effective moment μeff\mu_{eff} = 3.60 μB\mu_{B}, which is very close to the value expected for Pr3+^{3+} ions. We do not find evidence for magnetic or superconducting transition down to 0.5 K. Specific heat exhibits a broad Schottky type anomaly with a peak at 24 K, very likely related to crystal electric field (CEF) excitation. The magnetic properties suggest the presence of a singlet CEF ground state leading to a Van-Vleck paramagnetic ground state.Comment: 2 pages, 2 figure

    Comment on ``Can Disorder Induce a Finite Thermal Conductivity in 1D Lattices?''

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    In a recent paper [Phys. Rev. Lett. 86, 63 (2001)], Li et al have reported that the nonequilibrium heat conducting steady state of a disordered harmonic chain is not unique. In this comment we point out that for a large class of stochastic heat baths the uniqueness of the steady state can be proved, and therefore the findings of Li et al could be either due to their use of deterministic heat baths or insufficient equilibration times in the simulations. We give a simple example where the uniquness of the steady state can be explicitly demonstrated.Comment: 1 page, 1 figure, accepted for publication in Phys. Rev. Let
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