Disorder-induced superfluidity

We use quantum Monte Carlo simulations to study the phase diagram of hard-core bosons with short-ranged {\it attractive} interactions, in the presence of uniform diagonal disorder. It is shown that moderate disorder stabilizes a glassy superfluid phase in a range of values of the attractive interaction for which the system is a Mott insulator, in the absence of disorder. A transition to an insulating Bose glass phase occurs as the strength of the disorder or interactions increases.Comment: 5 pages, 6 figure

You Have the Data ...The Writ of Habeas Data and Other Data Protection Rights: Is the United States Falling Behind?

In Part I of this Note, I will discuss the writ of habeas data that has been developed primarily, but not exclusively, in Latin American countries. I will discuss the intricacies of the writ, how it evolved, and how it is applied today. Using Argentina as an example, I will discuss how the writ would be used by an Argentine citizen to protect her personal data. Part II summarizes the previously employed data protection scheme in the European Union, the Data Protection Directive (“the Directive”), and will also discuss the new EU data protection regulation, the General Data Protection Regulation (GDPR), which became effective in May of 2018. I will discuss how the old Data Protection Directive is different from the GDPR, and how the rights given to EU Member citizens differ under each. I will cover the right to access, the right to stop processing, and the right to erasure, which are all provided within the new regulation (although previously alluded to in the Directive). I will provide an example of an EU Member citizen’s use of the rights provided under the GDPR. The next two Parts of this Note will shift focus to U.S. legislation. Part III of this Note delves into the United States’ ad hoc approach to data protection, discussing several piecemeal regulations within the United States, and what type of rights those regulations provide to everyday citizens. The focus of this Part is primarily HIPAA, but other ad hoc regulations are discussed. Finally, Part IV will propose suggestions for the United States to learn from changing and growing international regulatory norms. In this Part, I will discuss the possible sources of authority for Congress to pass a comprehensive legislative scheme regarding personal data protection, as well as the authority to amend already existing legislation to expand personal rights for data protection. Lastly, I will discuss a possible expansion of the writ of habeas corpus by the judiciary to include personal data

Condensate fragmentation as a sensitive measure of the quantum many-body behavior of bosons with long-range interactions

The occupation of more than one single-particle state and hence the emergence of fragmentation is a many-body phenomenon universal to systems of spatially confined interacting bosons. In the present study, we investigate the effect of the range of the interparticle interactions on the fragmentation degree of one- and two-dimensional systems. We solve the full many-body Schr\"odinger equation of the system using the recursive implementation of the multiconfigurational time-dependent Hartree for bosons method, R-MCTDHB. The dependence of the degree of fragmentation on dimensionality, particle number, areal or line density and interaction strength is assessed. It is found that for contact interactions, the fragmentation is essentially density independent in two dimensions. However, fragmentation increasingly depends on density the more long-ranged the interactions become. The degree of fragmentation is increasing, keeping the particle number $N$ fixed, when the density is decreasing as expected in one spatial dimension. We demonstrate that this remains, nontrivially, true also for long-range interactions in two spatial dimensions. We, finally, find that within our fully self-consistent approach, the fragmentation degree, to a good approximation, decreases universally as $N^{-1/2}$ when only $N$ is varied.Comment: 8 pages of RevTex4-1, 5 figure

Measuring the equation of state of trapped ultracold bosonic systems in an optical lattice with in-situ density imaging

We analyze quantitatively how imaging techniques with single-site resolution allow to measure thermodynamical properties that cannot be inferred from time-of-light images for the trapped Bose-Hubbard model. If the normal state extends over a sufficiently large range, the chemical potential and the temperature can be extracted from a single shot, provided the sample is in thermodynamic equilibrium. When the normal state is too narrow, temperature is low but can still be extracted using the fluctuation-dissipation theorem over the entire trap range as long as the local density approximation remains valid, as was recently suggested by Qi Zhou and Tin-Lun Ho [arXiv:0908.3015]. However, for typical present-day experiments, the number of samples needed is of the order of 1000 in order to get the temperature at least $10 \%$ accurate, but it is possible to reduce the variance by 2 orders of magnitude if the density-density correlation length is short, which is the case for the Bose-Hubbard model. Our results provide further evidence that cold gases in an optical lattices can be viewed as quantum analog computers.Comment: 8 pages, 10 figure

Decay modes of two repulsively interacting bosons

We study the decay of two repulsively interacting bosons tunneling through a delta potential barrier by direct numerical solution of the time-dependent Schr\"odinger equation. The solutions are analyzed according to the regions of particle presence: both particles inside the trap (in-in), one particle in and one particle out (in-out), and both particles outside (out-out). It is shown that the in-in probability is dominated by exponential decay, and its decay rate is predicted very well from outgoing boundary conditions. Up to a certain range of interaction strength the decay of in-out probability is dominated by the single particle decay mode. The decay mechanisms are adequately described by simple models.Comment: 18 pages, 13 figure

Influence of the trap shape on the superfluid-Mott transition in ultracold atomic gases

The coexistence of superfluid and Mott insulator, due to the quadratic confinement potential in current optical lattice experiments, makes the accurate detection of the superfluid-Mott transition difficult. Studying alternative trapping potentials which are experimentally realizable and have a flatter center, we find that the transition can be better resolved, but at the cost of a more difficult tuning of the particle filling. When mapping out the phase diagram using local probes and the local density approximation we find that the smoother gradient of the parabolic trap is advantageous.Comment: 5 pages, 6 figure

Maximally inhomogeneous G\"{o}del-Farnsworth-Kerr generalizations

It is pointed out that physically meaningful aligned Petrov type D perfect fluid space-times with constant zero-order Riemann invariants are either the homogeneous solutions found by G\"{o}del (isotropic case) and Farnsworth and Kerr (anisotropic case), or new inhomogeneous generalizations of these with non-constant rotation. The construction of the line element and the local geometric properties for the latter are presented.Comment: 4 pages, conference proceeding of Spanish Relativity Meeting (ERE 2009, Bilbao

Electromagnetic and Gravitational Invariants

The curvature invariants have been subject of recent interest in the context of the experimental detection of the gravitomagnetic field, namely due to the debate concerning the notions of "extrinsic" and "intrinsic" gravitomagnetism. In this work we explore the physical meaning of the curvature invariants, dissecting their relationship with the gravitomagnetic effects

Rotating solenoidal perfect fluids of Petrov type D

We prove that aligned Petrov type D perfect fluids for which the vorticity vector is not orthogonal to the plane of repeated principal null directions and for which the magnetic part of the Weyl tensor with respect to the fluid velocity has vanishing divergence, are necessarily purely electric or locally rotationally symmetric. The LRS metrics are presented explicitly.Comment: 6 pages, no figure