11,852 research outputs found
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 ,
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. 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 (), intermediate () and high redshift (). 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
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