A Second-Order Distributed Trotter-Suzuki Solver with a Hybrid Kernel

The Trotter-Suzuki approximation leads to an efficient algorithm for solving the time-dependent Schr\"odinger equation. Using existing highly optimized CPU and GPU kernels, we developed a distributed version of the algorithm that runs efficiently on a cluster. Our implementation also improves single node performance, and is able to use multiple GPUs within a node. The scaling is close to linear using the CPU kernels, whereas the efficiency of GPU kernels improve with larger matrices. We also introduce a hybrid kernel that simultaneously uses multicore CPUs and GPUs in a distributed system. This kernel is shown to be efficient when the matrix size would not fit in the GPU memory. Larger quantum systems scale especially well with a high number nodes. The code is available under an open source license.Comment: 11 pages, 10 figure

Dynamics of the Bose-Hubbard model: transition from Mott insulator to superfluid

We study the dynamics of phase transitions in the one dimensional Bose-Hubbard model. To drive the system from Mott insulator to superfluid phase, we change the tunneling frequency at a finite rate. We investigate the build up of correlations during fast and slow transitions using variational wave functions, dynamical Bogoliubov theory, Kibble-Zurek mechanism, and numerical simulations. We show that time-dependent correlations satisfy characteristic scaling relations that can be measured in optical lattices filled with cold atoms.Comment: 7+ pages, the Bogolubov section is completely rewritte

Sensitivity to perturbations in a quantum chaotic billiard

The Loschmidt echo (LE) measures the ability of a system to return to the initial state after a forward quantum evolution followed by a backward perturbed one. It has been conjectured that the echo of a classically chaotic system decays exponentially, with a decay rate given by the minimum between the width $\Gamma$ of the local density of states and the Lyapunov exponent. As the perturbation strength is increased one obtains a cross-over between both regimes. These predictions are based on situations where the Fermi Golden Rule (FGR) is valid. By considering a paradigmatic fully chaotic system, the Bunimovich stadium billiard, with a perturbation in a regime for which the FGR manifestly does not work, we find a cross over from $\Gamma$ to Lyapunov decay. We find that, challenging the analytic interpretation, these conjetures are valid even beyond the expected range.Comment: Significantly revised version. To appear in Physical Review E Rapid Communication

Measuring Spatial Subdivisions in Urban Mobility with Mobile Phone Data

Urban population grows constantly. By 2050 two thirds of the world population will reside in urban areas. This growth is faster and more complex than the ability of cities to measure and plan for their sustainability. To understand what makes a city inclusive for all, we define a methodology to identify and characterize spatial subdivisions: areas with over- and under-representation of specific population groups, named hot and cold spots respectively. Using aggregated mobile phone data, we apply this methodology to the city of Barcelona to assess the mobility of three groups of people: women, elders, and tourists. We find that, within the three groups, cold spots have a lower diversity of amenities and services than hot spots. Also, cold spots of women and tourists tend to have lower population income. These insights apply to the floating population of Barcelona, thus augmenting the scope of how inclusiveness can be analyzed in the city.Comment: 10 pages, 10 figures. To be presented at the Data Science for Social Good workshop at The Web Conference 202

A city of cities: Measuring how 15-minutes urban accessibility shapes human mobility in Barcelona

As cities expand, human mobility has become a central focus of urban planning and policy making to make cities more inclusive and sustainable. Initiatives such as the "15-minutes city" have been put in place to shift the attention from monocentric city configurations to polycentric structures, increasing the availability and diversity of local urban amenities. Ultimately they expect to increase local walkability and increase mobility within residential areas. While we know how urban amenities influence human mobility at the city level, little is known about spatial variations in this relationship. Here, we use mobile phone, census, and volunteered geographical data to measure geographic variations in the relationship between origin-destination flows and local urban accessibility in Barcelona. Using a Negative Binomial Geographically Weighted Regression model, we show that, globally, people tend to visit neighborhoods with better access to education and retail. Locally, these and other features change in sign and magnitude through the different neighborhoods of the city in ways that are not explained by administrative boundaries, and that provide deeper insights regarding urban characteristics such as rental prices. In conclusion, our work suggests that the qualities of a 15-minutes city can be measured at scale, delivering actionable insights on the polycentric structure of cities, and how people use and access this structure.Comment: 32 pages, 7 figure

Many-spin quantum dynamics during cross polarization in 8CB

We analyze theoretically and experimentally the quantum dynamics of a three-spin-1/2 system during cross polarization (CP). Our analysis takes into account a Hamiltonian behavior for a carbon C-13 coupled to two protons H-1 while the coupling to a spin bath is treated in the fast fluctuation approximation. This model is applied to the methylene and biphenyl groups of the smectic and nematic phases of the liquid crystal 4-n-octyl-4(´)-cyanobiphenyl (8CB). Experimental data from standard CP, combined with our theoretical results, allow us to separate the homonuclear H-1-H-1 and heteronuclear H-1-C-13 residual dipolar couplings. These values are in good agreement with those obtained by using a combination of CP under Lee-Goldburg conditions and standard CP data. A well differentiated relaxation behavior among the two phases seems to indicate that while the extreme narrowing approximation is appropriate for the nematic phase, the description of the smectic phase requires consideration of the slow-motion limit.Fil: Chattah, Ana Karina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; ArgentinaFil: Alvarez, Gonzalo Agustin. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Unidad Ejecutora Instituto de Nanociencia y Nanotecnología. Unidad Ejecutora Instituto de Nanociencia y Nanotecnología - Nodo Bariloche | Comisión Nacional de Energía Atómica. Unidad Ejecutora Instituto de Nanociencia y Nanotecnología. Unidad Ejecutora Instituto de Nanociencia y Nanotecnología - Nodo Bariloche; ArgentinaFil: Levstein, Patricia Rebeca. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Cucchietti, Fernando M.. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Pastawski, Horacio Miguel. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; ArgentinaFil: Raya, Jésus. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Hirschinger, Jérôme. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentin

Direct observation of quantum criticality in Ising spin chains

We use NMR quantum simulators to study antiferromagnetic Ising spin chains undergoing quantum phase transitions. Taking advantage of the sensitivity of the systems near criticality, we detect the critical points of the transitions using a direct measurement of the Loschmidt echo. We test our simulators for spin chains of even and odd numbers of spins, and compare the experimental results to theoretical predictions

Universality of the Lyapunov regime for the Loschmidt echo

The Loschmidt echo (LE) is a magnitude that measures the sensitivity of quantum dynamics to perturbations in the Hamiltonian. For a certain regime of the parameters, the LE decays exponentially with a rate given by the Lyapunov exponent of the underlying classically chaotic system. We develop a semiclassical theory, supported by numerical results in a Lorentz gas model, which allows us to establish and characterize the universality of this Lyapunov regime. In particular, the universality is evidenced by the semiclassical limit of the Fermi wavelength going to zero, the behavior for times longer than Ehrenfest time, the insensitivity with respect to the form of the perturbation and the behavior of individual (non-averaged) initial conditions. Finally, by elaborating a semiclassical approximation to the Wigner function, we are able to distinguish between classical and quantum origin for the different terms of the LE. This approach renders an understanding for the persistence of the Lyapunov regime after the Ehrenfest time, as well as a reinterpretation of our results in terms of the quantum--classical transition.Comment: 33 pages, 17 figures, uses Revtex