1,112 research outputs found
Non-Hermitian Localization and Population Biology
The time evolution of spatial fluctuations in inhomogeneous d-dimensional
biological systems is analyzed. A single species continuous growth model, in
which the population disperses via diffusion and convection is considered.
Time-independent environmental heterogeneities, such as a random distribution
of nutrients or sunlight are modeled by quenched disorder in the growth rate.
Linearization of this model of population dynamics shows that the fastest
growing localized state dominates in a time proportional to a power of the
logarithm of the system size. Using an analogy with a Schrodinger equation
subject to a constant imaginary vector potential, we propose a delocalization
transition for the steady state of the nonlinear problem at a critical
convection threshold separating localized and extended states. In the limit of
high convection velocity, the linearized growth problem in dimensions
exhibits singular scaling behavior described by a (d-1)-dimensional
generalization of the noisy Burgers' equation, with universal singularities in
the density of states associated with disorder averaged eigenvalues near the
band edge in the complex plane. The Burgers mapping leads to unusual transverse
spreading of convecting delocalized populations.Comment: 22 pages, 11 figure
Fundamental limits to optical response in absorptive systems
At visible and infrared frequencies, metals show tantalizing promise for
strong subwavelength resonances, but material loss typically dampens the
response. We derive fundamental limits to the optical response of absorptive
systems, bounding the largest enhancements possible given intrinsic material
losses. Through basic conservation-of-energy principles, we derive
geometry-independent limits to per-volume absorption and scattering rates, and
to local-density-of-states enhancements that represent the power radiated or
expended by a dipole near a material body. We provide examples of structures
that approach our absorption and scattering limits at any frequency, by
contrast, we find that common "antenna" structures fall far short of our
radiative LDOS bounds, suggesting the possibility for significant further
improvement. Underlying the limits is a simple metric, for a material with susceptibility , that enables
broad technological evaluation of lossy materials across optical frequencies.Comment: 21 pages and 6 figures (excluding appendices, references
Source localization in random acoustic waveguides
Mode coupling due to scattering by weak random inhomogeneities in waveguides leads to loss of coherence of wave fields at long distances of propagation. This in turn leads to serious deterioration of coherent source localization methods, such as matched field. We study with analysis and numerical simulations how such deterioration occurs and introduce a novel incoherent approach for long range source localization in random waveguides. It is based on a special form of transport theory for the incoherent fluctuations of the wave field. We study theoretically the statistical stability of the method and illustrate its performance with numerical simulations. We also show how it can be used to estimate the correlation function of the random fluctuations of the wave speed
Quantum Spin Lenses in Atomic Arrays
We propose and discuss `quantum spin lenses', where quantum states of
delocalized spin excitations in an atomic medium are `focused' in space in a
coherent quantum process down to (essentially) single atoms. These can be
employed to create controlled interactions in a quantum light-matter interface,
where photonic qubits stored in an atomic ensemble are mapped to a quantum
register represented by single atoms. We propose Hamiltonians for quantum spin
lenses as inhomogeneous spin models on lattices, which can be realized with
Rydberg atoms in 1D, 2D and 3D, and with strings of trapped ions. We discuss
both linear and non-linear quantum spin lenses: in a non-linear lens, repulsive
spin-spin interactions lead to focusing dynamics conditional to the number of
spin excitations. This allows the mapping of quantum superpositions of
delocalized spin excitations to superpositions of spatial spin patterns, which
can be addressed by light fields and manipulated. Finally, we propose
multifocal quantum spin lenses as a way to generate and distribute entanglement
between distant atoms in an atomic lattice array.Comment: 13 pages, 9 figure
An inhomogeneous Josephson phase in thin-film and High-Tc superconductors
In many cases inhomogeneities are known to exist near the metal (or
superconductor)-insulator transition, as follows from well-known domain-wall
arguments. If the conducting regions are large enough (i.e. when the T=0
superconducting gap is much larger than the single-electron level spacing), and
if they have superconducting correlations, it becomes energetically favorable
for the system to go into a Josephson-coupled zero-resistance state before
(i.e. at higher resistance than) becoming a "real" metal. We show that this is
plausible by a simple comparison of the relevant coupling constants. For small
grains in the above sense, the electronic grain structure is washed out by
delocalization and thus becomes irrelevant. When the proposed "Josephson state"
is quenched by a magnetic field, an insulating, rather then a metallic, state
should appear. This has been shown to be consistent with the existing data on
oxide materials as well as ultra-thin films. We discuss the Uemura correlations
versus the Homes law, and derive the former for the large-grain Josephson array
(inhomogenous superconductor) model. The small-grain case behaves like a dirty
homogenous metal. It should obey the Homes law provided that the system is in
the dirty supeconductivity limit. A speculation why that is typically the case
for d-wave superconductors is presented.Comment: Conference proceeding for "Fluctuations in Superconductors" held in
Nazareth, Israel in June, 2007; 6 pages with 1 figure, to appear in Physica
Strong disorder RG approach of random systems
There is a large variety of quantum and classical systems in which the
quenched disorder plays a dominant r\^ole over quantum, thermal, or stochastic
fluctuations : these systems display strong spatial heterogeneities, and many
averaged observables are actually governed by rare regions. A unifying approach
to treat the dynamical and/or static singularities of these systems has emerged
recently, following the pioneering RG idea by Ma and Dasgupta and the detailed
analysis by Fisher who showed that the Ma-Dasgupta RG rules yield asymptotic
exact results if the broadness of the disorder grows indefinitely at large
scales. Here we report these new developments by starting with an introduction
of the main ingredients of the strong disorder RG method. We describe the basic
properties of infinite disorder fixed points, which are realized at critical
points, and of strong disorder fixed points, which control the singular
behaviors in the Griffiths-phases. We then review in detail applications of the
RG method to various disordered models, either (i) quantum models, such as
random spin chains, ladders and higher dimensional spin systems, or (ii)
classical models, such as diffusion in a random potential, equilibrium at low
temperature and coarsening dynamics of classical random spin chains, trap
models, delocalization transition of a random polymer from an interface, driven
lattice gases and reaction diffusion models in the presence of quenched
disorder. For several one-dimensional systems, the Ma-Dasgupta RG rules yields
very detailed analytical results, whereas for other, mainly higher dimensional
problems, the RG rules have to be implemented numerically. If available, the
strong disorder RG results are compared with another, exact or numerical
calculations.Comment: review article, 195 pages, 36 figures; final version to be published
in Physics Report
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