Bethe Ansatz study of one-dimensional Bose and Fermi gases with periodic and hard wall boundary conditions

We extend the exact periodic Bethe Ansatz solution for one-dimensional bosons and fermions with delta-interaction and arbitrary internal degrees of freedom to the case of hard wall boundary conditions. We give an analysis of the ground state properties of fermionic systems with two internal degrees of freedom, including expansions of the ground state energy in the weak and strong coupling limits in the repulsive and attractive regimes.Comment: 27 pages, 6 figures, key reference added, typos correcte

Non-Markovian dynamics in a spin star system: The failure of thermalization

In most cases, a small system weakly interacting with a thermal bath will finally reach the thermal state with the temperature of the bath. We show that this intuitive picture is not always true by a spin star model where non-Markov effect predominates in the whole dynamical process. The spin star system consists a central spin homogeneously interacting with an ensemble of identical noninteracting spins. We find that the correlation time of the bath is infinite, which implies that the bath has a perfect memory, and that the dynamical evolution of the central spin must be non- Markovian. A direct consequence is that the final state of the central spin is not the thermal state equilibrium with the bath, but a steady state which depends on its initial state.Comment: 8 page

On the definition of temperature in dense granular media

In this Letter we report the measurement of a pseudo-temperature for compacting granular media on the basis of the Fluctuation-Dissipation relations in the aging dynamics of a model system. From the violation of the Fluctuation-Dissipation Theorem an effective temperature emerges (a dynamical temperature T_{dyn}) whose ratio with the equilibrium temperature T_d^{eq} depends on the particle density. We compare the results for the Fluctuation-Dissipation Ratio (FDR) T_{dyn}/T_d^{eq} at several densities with the outcomes of Edwards' approach at the corresponding densities. It turns out that the FDR and the so-called Edwards' ratio coincide at several densities (very different ages of the system), opening in this way the door to experimental checks as well as theoretical constructions.Comment: RevTex4 4 pages, 4 eps figure

Excitation lines and the breakdown of Stokes-Einstein relations in supercooled liquids

By applying the concept of dynamical facilitation and analyzing the excitation lines that result from this facilitation, we investigate the origin of decoupling of transport coefficients in supercooled liquids. We illustrate our approach with two classes of models. One depicts diffusion in a strong glass former, and the other in a fragile glass former. At low temperatures, both models exhibit violation of the Stokes-Einstein relation, $D\sim\tau^{-1}$, where $D$ is the self diffusion constant and $\tau$ is the structural relaxation time. In the strong case, the violation is sensitive to dimensionality $d$, going as $D\sim\tau^{-2/3}$ for $d=1$, and as $D\sim \tau^{-0.95}$ for $d=3$. In the fragile case, however, we argue that dimensionality dependence is weak, and show that for $d=1$, $D \sim \tau^{-0.73}$. This scaling for the fragile case compares favorably with the results of a recent experimental study for a three-dimensional fragile glass former.Comment: 7 pages, 7 figures, submitted to Phys. Rev.

String correlation functions of the spin-1/2 Heisenberg XXZ chain

We calculate certain string correlation functions, originally introduced as order parameters in integer spin chains, for the spin-1/2 XXZ Heisenberg chain at zero temperature and in the thermodynamic limit. For small distances, we obtain exact results from Bethe Ansatz and exact diagonalization, whereas in the large-distance limit, field-theoretical arguments yield an asymptotic algebraic decay. We also make contact with two-point spin-correlation functions in the asymptotic limit.Comment: 23 pages, 4 figures. An incomplete discussion on the limit to the spin-spin correlation function is corrected on page 1

Numerical Estimation of the Asymptotic Behaviour of Solid Partitions of an Integer

The number of solid partitions of a positive integer is an unsolved problem in combinatorial number theory. In this paper, solid partitions are studied numerically by the method of exact enumeration for integers up to 50 and by Monte Carlo simulations using Wang-Landau sampling method for integers up to 8000. It is shown that, for large n, ln[p(n)]/n^(3/4) = 1.79 \pm 0.01, where p(n) is the number of solid partitions of the integer n. This result strongly suggests that the MacMahon conjecture for solid partitions, though not exact, could still give the correct leading asymptotic behaviour.Comment: 6 pages, 4 figures, revtex

Dynamical Behaviour of Low Autocorrelation Models

We have investigated the nature of the dynamical behaviour in low autocorrelation binary sequences. These models do have a glass transition $T_G$ of a purely dynamical nature. Above the glass transition the dynamics is not fully ergodic and relaxation times diverge like a power law $\tau\sim (T-T_G)^{-\gamma}$ with $\gamma$ close to $2$. Approaching the glass transition the relaxation slows down in agreement with the first order nature of the dynamical transition. Below the glass transition the system exhibits aging phenomena like in disordered spin glasses. We propose the aging phenomena as a precise method to determine the glass transition and its first order nature.Comment: 19 pages + 14 figures, LateX, figures uuencoded at the end of the fil

Ground-state properties of the attractive one-dimensional Bose-Hubbard model

We study the ground state of the attractive one-dimensional Bose-Hubbard model, and in particular the nature of the crossover between the weak interaction and strong interaction regimes for finite system sizes. Indicator properties like the gap between the ground and first excited energy levels, and the incremental ground-state wavefunction overlaps are used to locate different regimes. Using mean-field theory we predict that there are two distinct crossovers connected to spontaneous symmetry breaking of the ground state. The first crossover arises in an analysis valid for large L with finite N, where L is the number of lattice sites and N is the total particle number. An alternative approach valid for large N with finite L yields a second crossover. For small system sizes we numerically investigate the model and observe that there are signatures of both crossovers. We compare with exact results from Bethe ansatz methods in several limiting cases to explore the validity for these numerical and mean-field schemes. The results indicate that for finite attractive systems there are generically three ground-state phases of the model.Comment: 17 pages, 12 figures, Phys.Rev.B(accepted), minor changes and updated reference

Kovacs effect and fluctuation-dissipation relations in 1D kinetically constrained models

Strong and fragile glass relaxation behaviours are obtained simply changing the constraints of the kinetically constrained Ising chain from symmetric to purely asymmetric. We study the out-of-equilibrium dynamics of those two models focusing on the Kovacs effect and the fluctuation--dissipation relations. The Kovacs or memory effect, commonly observed in structural glasses, is present for both constraints but enhanced with the asymmetric ones. Most surprisingly, the related fluctuation-dissipation (FD) relations satisfy the FD theorem in both cases. This result strongly differs from the simple quenching procedure where the asymmetric model presents strong deviations from the FD theorem.Comment: 13 pages and 7 figures. To be published in J. Phys.