21 research outputs found
Quantum harmonic oscillator systems with disorder
We study many-body properties of quantum harmonic oscillator lattices with
disorder. A sufficient condition for dynamical localization, expressed as a
zero-velocity Lieb-Robinson bound, is formulated in terms of the decay of the
eigenfunction correlators for an effective one-particle Hamiltonian. We show
how state-of-the-art techniques for proving Anderson localization can be used
to prove that these properties hold in a number of standard models. We also
derive bounds on the static and dynamic correlation functions at both zero and
positive temperature in terms of one-particle eigenfunction correlators. In
particular, we show that static correlations decay exponentially fast if the
corresponding effective one-particle Hamiltonian exhibits localization at low
energies, regardless of whether there is a gap in the spectrum above the ground
state or not. Our results apply to finite as well as to infinite oscillator
systems. The eigenfunction correlators that appear are more general than those
previously studied in the literature. In particular, we must allow for
functions of the Hamiltonian that have a singularity at the bottom of the
spectrum. We prove exponential bounds for such correlators for some of the
standard models
Spectra of soft ring graphs
We discuss of a ring-shaped soft quantum wire modeled by interaction
supported by the ring of a generally nonconstant coupling strength. We derive
condition which determines the discrete spectrum of such systems, and analyze
the dependence of eigenvalues and eigenfunctions on the coupling and ring
geometry. In particular, we illustrate that a random component in the coupling
leads to a localization. The discrete spectrum is investigated also in the
situation when the ring is placed into a homogeneous magnetic field or threaded
by an Aharonov-Bohm flux and the system exhibits persistent currents.Comment: LaTeX 2e, 17 pages, with 10 ps figure
Defining pathways to healthy sustainable urban development
Goals and pathways to achieve sustainable urban development have multiple interlinkages with human health and wellbeing. However, these interlinkages have not been examined in depth in recent discussions on urban sustainability and global urban science. This paper fills that gap by elaborating in detail the multiple links between urban sustainability and human health and by mapping research gaps at the interface of health and urban sustainability sciences. As researchers from a broad range of disciplines, we aimed to: 1) define the process of urbanization, highlighting distinctions from related concepts to support improved conceptual rigour in health research; 2) review the evidence linking health with urbanization, urbanicity, and cities and identify cross-cutting issues; and 3) highlight new research approaches needed to study complex urban systems and their links with health. This novel, comprehensive knowledge synthesis addresses issue of interest across multiple disciplines. Our review of concepts of urban development should be of particular value to researchers and practitioners in the health sciences, while our review of the links between urban environments and health should be of particular interest to those outside of public health. We identify specific actions to promote health through sustainable urban development that leaves no one behind, including: integrated planning; evidence-informed policy-making; and monitoring the implementation of policies. We also highlight the critical role of effective governance and equity-driven planning in progress towards sustainable, healthy, and just urban development
Generalized eigenfunctions and spectral theory for strongly local Dirichlet forms
We present an introduction to the framework of strongly local Dirichlet forms
and discuss connections between the existence of certain generalized
eigenfunctions and spectral properties within this framework. The range of
applications is illustrated by a list of examples