Ultra-Light Dark Matter in Ultra-Faint Dwarf Galaxies

Cold Dark Matter (CDM) models struggle to match the observations at galactic scales. The tension can be reduced either by dramatic baryonic feedback effects or by modifying the particle physics of CDM. Here, we consider an ultra-light scalar field DM particle manifesting a wave nature below a DM particle mass-dependent Jeans scale. For DM mass $m\sim10^{-22}{\rm eV}$, this scenario delays galaxy formation and avoids cusps in the center of the dark matter haloes. We use new measurements of half-light mass in ultra-faint dwarf galaxies Draco II and Triangulum II to estimate the mass of the DM particle in this model. We find that if the stellar populations are within the core of the density profile then the data are in agreement with a wave dark matter model having a DM particle with $m\sim 3.7-5.6\times 10^{-22}{\rm eV}$. The presence of this extremely light particle will contribute to the formation of a central solitonic core replacing the cusp of a Navarro-Frenk-White profile and bringing predictions closer to observations of cored central density in dwarf galaxies.Comment: matching version accepted by MNRA

Bethe Ansatz approach to quench dynamics in the Richardson model

By instantaneously changing a global parameter in an extended quantum system, an initially equilibrated state will afterwards undergo a complex non-equilibrium unitary evolution whose description is extremely challenging. A non-perturbative method giving a controlled error in the long time limit remained highly desirable to understand general features of the quench induced quantum dynamics. In this paper we show how integrability (via the algebraic Bethe ansatz) gives one numerical access, in a nearly exact manner, to the dynamics resulting from a global interaction quench of an ensemble of fermions with pairing interactions (Richardson's model). This possibility is deeply linked to the specific structure of this particular integrable model which gives simple expressions for the scalar product of eigenstates of two different Hamiltonians. We show how, despite the fact that a sudden quench can create excitations at any frequency, a drastic truncation of the Hilbert space can be carried out therefore allowing access to large systems. The small truncation error which results does not change with time and consequently the method grants access to a controlled description of the long time behavior which is a hard to reach limit with other numerical approaches.Comment: Proceedings of the CRM (Montreal) workshop on Integrable Quantum Systems and Solvable Statistical Mechanics Model

Dynamic crossover in the global persistence at criticality

We investigate the global persistence properties of critical systems relaxing from an initial state with non-vanishing value of the order parameter (e.g., the magnetization in the Ising model). The persistence probability of the global order parameter displays two consecutive regimes in which it decays algebraically in time with two distinct universal exponents. The associated crossover is controlled by the initial value m_0 of the order parameter and the typical time at which it occurs diverges as m_0 vanishes. Monte-Carlo simulations of the two-dimensional Ising model with Glauber dynamics display clearly this crossover. The measured exponent of the ultimate algebraic decay is in rather good agreement with our theoretical predictions for the Ising universality class.Comment: 5 pages, 2 figure

Dynamical correlation functions of the mesoscopic pairing model

We study the dynamical correlation functions of the Richardson pairing model (also known as the reduced or discrete-state BCS model) in the canonical ensemble. We use the Algebraic Bethe Ansatz formalism, which gives exact expressions for the form factors of the most important observables. By summing these form factors over a relevant set of states, we obtain very precise estimates of the correlation functions, as confirmed by global sum-rules (saturation above 99% in all cases considered). Unlike the case of many other Bethe Ansatz solvable theories, simple two-particle states are sufficient to achieve such saturations, even in the thermodynamic limit. We provide explicit results at half-filling, and discuss their finite-size scaling behavior

Nonequilibrium critical dynamics of the two-dimensional Ising model quenched from a correlated initial state

The universality class, even the order of the transition, of the two-dimensional Ising model depends on the range and the symmetry of the interactions (Onsager model, Baxter-Wu model, Turban model, etc.), but the critical temperature is generally the same due to self-duality. Here we consider a sudden change in the form of the interaction and study the nonequilibrium critical dynamical properties of the nearest-neighbor model. The relaxation of the magnetization and the decay of the autocorrelation function are found to display a power law behavior with characteristic exponents that depend on the universality class of the initial state.Comment: 6 pages, 5 figures, submitted to Phys. Rev.

Dynamical density-density correlations in the one-dimensional Bose gas

The zero-temperature dynamical structure factor of the one-dimensional Bose gas with delta-function interaction (Lieb-Liniger model) is computed using a hybrid theoretical/numerical method based on the exact Bethe Ansatz solution, which allows to interpolate continuously between the weakly-coupled Thomas-Fermi and strongly-coupled Tonks-Girardeau regimes. The results should be experimentally accessible with Bragg spectroscopy.Comment: 4 pages, 3 figures, published versio

Entanglement Entropy of Two Spheres

We study the entanglement entropy S_{AB} of a massless free scalar field on two spheres A and B whose radii are R_1 and R_2, respectively, and the distance between the centers of them is r. The state of the massless free scalar field is the vacuum state. We obtain the result that the mutual information S_{A;B}:=S_A+S_B-S_{AB} is independent of the ultraviolet cutoff and proportional to the product of the areas of the two spheres when r>>R_1,R_2, where S_A and S_B are the entanglement entropy on the inside region of A and B, respectively. We discuss possible connections of this result with the physics of black holes.Comment: 17 pages, 9 figures; v4, added references, revised argument in section V, a typo in eq.(25) corrected, published versio

Experimental study of vapor-cell magneto-optical traps for efficient trapping of radioactive atoms

We have studied magneto-optical traps (MOTs) for efficient on-line trapping of radioactive atoms. After discussing a model of the trapping process in a vapor cell and its efficiency, we present the results of detailed experimental studies on Rb MOTs. Three spherical cells of different sizes were used. These cells can be easily replaced, while keeping the rest of the apparatus unchanged: atomic sources, vacuum conditions, magnetic field gradients, sizes and power of the laser beams, detection system. By direct comparison, we find that the trapping efficiency only weakly depends on the MOT cell size. It is also found that the trapping efficiency of the MOT with the smallest cell, whose diameter is equal to the diameter of the trapping beams, is about 40% smaller than the efficiency of larger cells. Furthermore, we also demonstrate the importance of two factors: a long coated tube at the entrance of the MOT cell, used instead of a diaphragm; and the passivation with an alkali vapor of the coating on the cell walls, in order to minimize the losses of trappable atoms. These results guided us in the construction of an efficient large-diameter cell, which has been successfully employed for on-line trapping of Fr isotopes at INFN's national laboratories in Legnaro, Italy.Comment: 9 pages, 7 figures, submitted to Eur. Phys. J.

Time evolution of 1D gapless models from a domain-wall initial state: SLE continued?

We study the time evolution of quantum one-dimensional gapless systems evolving from initial states with a domain-wall. We generalize the path-integral imaginary time approach that together with boundary conformal field theory allows to derive the time and space dependence of general correlation functions. The latter are explicitly obtained for the Ising universality class, and the typical behavior of one- and two-point functions is derived for the general case. Possible connections with the stochastic Loewner evolution are discussed and explicit results for one-point time dependent averages are obtained for generic \kappa for boundary conditions corresponding to SLE. We use this set of results to predict the time evolution of the entanglement entropy and obtain the universal constant shift due to the presence of a domain wall in the initial state.Comment: 27 pages, 10 figure

Zero dimensional area law in a gapless fermion system

The entanglement entropy of a gapless fermion subsystem coupled to a gapless bulk by a "weak link" is considered. It is demonstrated numerically that each independent weak link contributes an entropy proportional to lnL, where L is linear dimension of the subsystem.Comment: 6 pages, 11 figures; added 3d computatio