Efficient variational approach to dynamics of a spatially extended bosonic Kondo model

We develop an efficient variational approach to studying dynamics of a localized quantum spin coupled to a bath of mobile spinful bosons. We use parity symmetry to decouple the impurity spin from the environment via a canonical transformation and reduce the problem to a model of the interacting bosonic bath. We describe coherent time evolution of the latter using bosonic Gaussian states as a variational ansatz. We provide full analytical expressions for equations describing variational time evolution that can be applied to study in- and out-of-equilibrium phenomena in a wide class of quantum impurity problems. In the accompanying paper [Y. Ashida {\it et al.}, Phys. Rev. Lett. 123, 183001 (2019)], we present a concrete application of this general formalism to the analysis of the Rydberg Central Spin Model, in which the spin-1/2 Rydberg impurity undergoes spin-changing collisions in a dense cloud of two-component ultracold bosons. To illustrate new features arising from orbital motion of the bath atoms, we compare our results to the Monte Carlo study of the model with spatially localized bosons in the bath, in which random positions of the atoms give rise to random couplings of the standard central spin model.Comment: 15 pages, 6 figures. See also Phys. Rev. Lett. 123, 183001 (2019) [arXiv:1905.08523

Quantum Rydberg Central Spin Model

We consider dynamics of a Rydberg impurity in a cloud of ultracold bosonic atoms in which the Rydberg electron can undergo spin-changing collisions with surrounding atoms. This system realizes a new type of the quantum impurity problem that compounds essential features of the Kondo model, the Bose polaron, and the central spin model. To capture the interplay of the Rydberg-electron spin dynamics and the orbital motion of atoms, we employ a new variational method that combines an impurity-decoupling transformation with a Gaussian ansatz for the bath particles. We find several unexpected features of this model that are not present in traditional impurity problems, including interaction-induced renormalization of the absorption spectrum that eludes simple explanations from molecular bound states, and long-lasting oscillations of the Rydberg-electron spin. We discuss generalizations of our analysis to other systems in atomic physics and quantum chemistry, where an electron excitation of high orbital quantum number interacts with a spinful quantum bath.Comment: 6 pages, 5 figures. See also Phys. Rev. A 100, 043618 (2019) [arXiv:1905.09615

The Hidden Nuclear Spectrum of the Luminous IRAS Source FSC10214++4724

Optical spectropolarimetry of the luminous IRAS source FSC10214$+$4724 (z$=2.286$) reveals that the strong (\twid17\%) linear polarization detected by Lawrence \etal\/ is shared by both the narrow UV emission lines and the underlying continuum. This observation and the brightness of the source rule out synchrotron emission and dichroic extinction by dust as the polarizing mechanism, leaving scattering as the only plausible cause of the polarized emission. The narrowness of the lines requires that the scatterers be dust grains or cool ($<1.6\times$10$^4$~K) electrons. We can recover the spectrum that is incident on the scattering medium provided we make some reasonable assumptions regarding the source geometry. The scattered UV spectrum has a power law index $\alpha$~ of $-1.2 \pm 0.6$ ($F_\nu\propto\nu^\alpha$), steeper than what would be expected from a young burst of star formation, but similar to many AGN.Comment: 10 pages, with figure, uuencoded postscript Institute for Advanced Study number AST 94/1

Renormalization group study of the four-body problem

We perform a renormalization group analysis of the non-relativistic four-boson problem by means of a simple model with pointlike three- and four-body interactions. We investigate in particular the unitarity point where the scattering length is infinite and all energies are at the atom threshold. We find that the four-body problem behaves truly universally, independent of any four-body parameter. Our findings confirm the recent conjectures of Platter et al. and von Stecher et al. that the four-body problem is universal, now also from a renormalization group perspective. We calculate the corresponding relations between the four- and three-body bound states, as well as the full bound state spectrum and comment on the influence of effective range corrections.Comment: 11 pages, 6 figures; v2: revised and published versio

Theoretical and Software Considerations for General Dynamic Analysis Using Multilevel Substructured Models

An approach is presented for the dynamic analysis of complex structure sy~t'=!!!S using the finite element method and multilevel substructured models. The fixedinterface method is selected for substructure reduction because of its efficiency, accurac and adaptability to restart and reanalysis. This method is extended to reduction of substructures which are themselves composed of reduced substructures. Emphasis is placed on the implementation and performance of the method in a general purpose software system. Solution algorithms consistent with the chosen data structures are presented in detail. This study demonstrates that successful finite element software requires the use of software executives to supplement the algorithmic language. As modeling and analysis techniques become more complex, proportionally more implementation effort is spent on data and computer resource management. Executive systems are essential tools for these tasks. The complexity of the implementation of restart and reanalysis porcedures also illustrate the need for executive systems to support the non computational aspects of the software. The example problems show that significant computational efficiencies can be achieved through proper use of substructuring and reduction techniques without sacrificing solution accuracy. The unique restart and reanalysis capabilities developed in this study and the flexible procedures for multilevel substructured modeling allow analysts to achieve economical yet accurate analyses of complex structural systems

Experiences modelling and using object-oriented telecommunication service frameworks in SDL

This paper describes experiences in using SDL and its associated tools to create telecommunication services by producing and specialising object-oriented frameworks. The chosen approach recognises the need for the rapid creation of validated telecommunication services. It introduces two stages to service creation. Firstly a software expert produces a service framework, and secondly a telecommunications ‘business consultant' specialises the framework by means of graphical tools to rapidly produce services. Here the focus is given to the underlying technology required. In particular, the advantages and disadvantages of SDL and tools for this purpose are highlighted

Hydrologic and Hydraulic Modeling of the Tunnel and Reservoir Plan System in Northeastern Illinois

The Tunnel and Reservoir Plan (TARP) was adopted by the Metropolitan Sanitary District of Greater Chicago in 1972 to address combined sewer overflow (CSO) pollution and flooding problems in 970 km2 of the Chicago metropolitan area served by combined sewers. TARP consists of about 175 km of tunnels, three reservoirs, 256 drop shafts, and over 600 connecting structures, pumping stations, and other appurtenances for the capture and storage of CSOs and for conveying the stored CSOs to water reclamation plants for treatment. The TARP system is comprised of three independent systems: the Calumet system serving the south suburbs and a portion of the south side of Chicago, the Upper Des Plaines system serving the northwest suburbs, and the Mainstream/ Des Plaines system serving the remainder of Chicago and the north, west and southwest suburbs. The Metropolitan Water Reclamation District of Greater Chicago (MWRDGC) desires to develop new, updated and enhanced computer models to allow for simulation of the TARP systems. The new models will be used to optimize operation of the system as actually constructed, to determine constraints in the system, identify physical changes that may be needed to improve performance, and allow what-if analyses to be performed for potential storm scenarios and facility revisions. The modeling includes development of a Physical Inventory system, Hydraulic Modeling of the TARP systems, and Hydrologic Modeling of the TARP service areas. The Physical Inventory provides a digital description of the physical geometry of the TARP system and the related hydraulic performance of system components. Hydrologic Modeling uses data for each dropshafts service area to determine hydrographs describing the inflows to the TARP systems. A ma jor component of the Hydrologic Modeling is to develop tools and methods that allow robust simulation of the extreme heterogeneity of highly urbanized systems and that provide guidance for data compilation needed to improve the accuracy of such simulations. Hydraulic Modeling uses the information from the Physical Inventory and the Hydrologic Modeling to simulate hydraulic response of the TARP system to different inputs. The Hydraulic Modeling tools developed are capable of simulating the range of possible flows in the system, from gravity flows over a dry bed to mixed gravity/surcharged flows to shocks and hydraulic transients