Classical particle scattering for power-law two-body potentials

We present a rigorous study of the classical scattering for anytwo-body inter-particle potential of the form $v(r)=g/r^\gamma$, with\gamma\textgreater{}0, for repulsive (g\textgreater{}0) and attractive (g\textless{}0)interactions. We give a derivation of the complete power series of thedeflection angle in terms of the impact factor for the weak scatteringregime (large impact factors) as well as the asymptotic expressionsfor the hard scattering regime (small impact factors). We see a verydifferent qualitative and quantitative behavior depending whether theinteraction is repulsive or attractive. In the latter case, thefamilies of trajectories depend also strongly on the value of$\gamma$. We also study carefully the modifications of the resultswhen a regularization is introduced in the potential at small scales.We check and illustrate all the results with the exact integration ofthe equations of motion.Comment: 23 pages, 17 figure

Cold uniform spherical collapse revisited

We report results of a study of the Newtonian dynamics of N self-gravitating particles which start in a quasi-uniform spherical configuration, without initial velocities. These initial conditions would lead to a density singularity at the origin at a finite time when N \rightarrow \infty, but this singularity is regulated at any finite N (by the associated density fluctuations). While previous studies have focussed on the behaviour as a function of N of the minimal size reached during the contracting phase, we examine in particular the size and energy of the virialized halo which results. We find the unexpected result that the structure decreases in size as N increases, scaling in proportion to N^{-1/3}, a behaviour which is associated with an ejection of kinetic energy during violent relaxation which grows in proportion to N^{1/3}. This latter scaling may be qualitatively understood, and if it represents the asymptotic behaviour in N implies that this ejected energy is unbounded above. We discuss also tests we have performed which indicate that this ejection is a mean-field phenomenon (i.e. a result of collisionless dynamics).Comment: 10 pages, 9 figures; proceedings of "Invisible Universe" conference, Paris, July 200

Fidelity and superconductivity in two-dimensional t-J models

We compute the ground-state fidelity and various correlations to gauge the competition between different orders in two-dimensional t-J-type models. Using exact numerical diagonalization techniques, these quantities are examined for (i) the plain t-J and t-t'-J models, (ii) for the t-J model perturbed by infinite-range d-wave or extended-s-wave superconductivity inducing terms, and (iii) the t-J model, plain and with a d-wave perturbation, in the presence of non-magnetic quenched disorder. Various properties at low hole doping are contrasted with those at low electron filling. In the clean case, our results are consistent with previous work that concluded that the plain t-J model supports d-wave superconductivity. As a consequence of the strong correlations present in the low hole doping regime, we find that the magnitude of the d-wave condensate occupation is small even in the presence of large d-wave superconductivity inducing terms. In the dirty case, we show the robustness of the ground state in the strongly correlated regime against disorder.Comment: 11 pages, 12 figures, as publishe

Entropy of isolated quantum systems after a quench

A diagonal entropy, which depends only on the diagonal elements of the system's density matrix in the energy representation, has been recently introduced as the proper definition of thermodynamic entropy in out-of-equilibrium quantum systems. We study this quantity after an interaction quench in lattice hard-core bosons and spinless fermions, and after a local chemical potential quench in a system of hard-core bosons in a superlattice potential. The former systems have a chaotic regime, where the diagonal entropy becomes equivalent to the equilibrium microcanonical entropy, coinciding with the onset of thermalization. The latter system is integrable. We show that its diagonal entropy is additive and different from the entropy of a generalized Gibbs ensemble, which has been introduced to account for the effects of conserved quantities at integrability.Comment: 6 pages, 4 figures, as published (updated supplemental material

Generalized Thermalization in an Integrable Lattice System

After a quench, observables in an integrable system may not relax to the standard thermal values, but can relax to the ones predicted by the generalized Gibbs ensemble (GGE) [M. Rigol et al., Phys. Rev. Lett. 98, 050405 (2007)]. The GGE has been shown to accurately describe observables in various one-dimensional integrable systems, but the origin of its success is not fully understood. Here we introduce a microcanonical version of the GGE and provide a justification of the GGE based on a generalized interpretation of the eigenstate thermalization hypothesis, which was previously introduced to explain thermalization of nonintegrable systems. We study relaxation after a quench of one-dimensional hard-core bosons in an optical lattice. Exact numerical calculations for up to 10 particles on 50 lattice sites (~10^10 eigenstates) validate our approach.Comment: 8 pages, 9 figures, as publishe

On the recovery of ISW fluctuations using large-scale structure tracers and CMB temperature and polarization anisotropies

In this work we present a method to extract the signal induced by the integrated Sachs-Wolfe (ISW) effect in the cosmic microwave background (CMB). It makes use of the Linear Covariance-Based filter introduced by Barreiro et al., and combines CMB data with any number of large-scale structure (LSS) surveys and lensing information. It also exploits CMB polarization to reduce cosmic variance. The performance of the method has been thoroughly tested with simulations taking into account the impact of non-ideal conditions such as incomplete sky coverage or the presence of noise. In particular, three galaxy surveys are simulated, whose redshift distributions peak at low ($z \simeq 0.3$), intermediate ($z \simeq 0.6$) and high redshift ($z \simeq 0.9$). The contribution of each of the considered data sets as well as the effect of a mask and noise in the reconstructed ISW map is studied in detail. When combining all the considered data sets (CMB temperature and polarization, the three galaxy surveys and the lensing map), the proposed filter successfully reconstructs a map of the weak ISW signal, finding a perfect correlation with the input signal for the ideal case and around 80 per cent, on average, in the presence of noise and incomplete sky coverage. We find that including CMB polarization improves the correlation between input and reconstruction although only at a small level. Nonetheless, given the weakness of the ISW signal, even modest improvements can be of importance. In particular, in realistic situations, in which less information is available from the LSS tracers, the effect of including polarisation is larger. For instance, for the case in which the ISW signal is recovered from CMB plus only one survey, and taking into account the presence of noise and incomplete sky coverage, the improvement in the correlation coefficient can be as large as 10 per cent.Comment: 17 pages, 15 figures, accepted for publication in MNRA