36,556 research outputs found
Effective one-dimensional description of confined diffusion biased by a transverse gravitational force
Diffusion of point-like non interacting particles in a two-dimensional (2D)
channel of varying cross section is considered. The particles are biased by a
constant force in the transverse direction. We apply our recurrence mapping
procedure, which enables us to derive an effective one-dimensional (1D)
evolution equation, governing the 1D density of the particles in the channel.
In the limit of stationary flow, we arrive at an extended Fick-Jacobs equation,
corrected by an effective diffusion coefficient D(x), depending on the
longitudinal coordinate x. Our result is an approximate formula for D(x),
involving also influence of the transverse force. Our calculations are verified
on the stationary diffusion in a linear cone, which is exactly solvable.Comment: 10 pages, 7 figures, submitted in Phys. Rev.
Engineering Quantum States, Nonlinear Measurements, and Anomalous Diffusion by Imaging
We show that well-separated quantum superposition states, measurements of
strongly nonlinear observables, and quantum dynamics driven by anomalous
diffusion can all be achieved for single atoms or molecules by imaging
spontaneous photons that they emit via resonance florescence. To generate
anomalous diffusion we introduce continuous measurements driven by L\'evy
processes, and prove a number of results regarding their properties. In
particular we present strong evidence that the only stable L\'evy density that
can realize a strictly continuous measurement is the Gaussian.Comment: revtex4-1, 17 pages, 7 eps figure
Measurement of dimensional stability
A technique was developed for measuring, with a precision of one part 10 to the 9th power, changes in physical dimensions delta L/L. Measurements have commenced on five materials: Heraeus-Schott Homosil (vitreous silica), Corning 7940 (vitreous silica), Corning ULE 7971 (titanium silicate), Schott Zero-Dur, and Owens-Illinois Cer-Vit C-101. The study was extended to include Universal Cyclops Invar LR-35 and Simonds-Saw Superinvar
Floppy modes and the free energy: Rigidity and connectivity percolation on Bethe Lattices
We show that negative of the number of floppy modes behaves as a free energy
for both connectivity and rigidity percolation, and we illustrate this result
using Bethe lattices. The rigidity transition on Bethe lattices is found to be
first order at a bond concentration close to that predicted by Maxwell
constraint counting. We calculate the probability of a bond being on the
infinite cluster and also on the overconstrained part of the infinite cluster,
and show how a specific heat can be defined as the second derivative of the
free energy. We demonstrate that the Bethe lattice solution is equivalent to
that of the random bond model, where points are joined randomly (with equal
probability at all length scales) to have a given coordination, and then
subsequently bonds are randomly removed.Comment: RevTeX 11 pages + epsfig embedded figures. Submitted to Phys. Rev.
Combinatorial models of rigidity and renormalization
We first introduce the percolation problems associated with the graph
theoretical concepts of -sparsity, and make contact with the physical
concepts of ordinary and rigidity percolation. We then devise a renormalization
transformation for -percolation problems, and investigate its domain of
validity. In particular, we show that it allows an exact solution of
-percolation problems on hierarchical graphs, for . We
introduce and solve by renormalization such a model, which has the interesting
feature of showing both ordinary percolation and rigidity percolation phase
transitions, depending on the values of the parameters.Comment: 22 pages, 6 figure
Affective iconic words benefit from additional sound–meaning integration in the left amygdala
Recent studies have shown that a similarity between sound and meaning of a word (i.e., iconicity) can help more readily access the meaning of that word, but the neural mechanisms underlying this beneficial role of iconicity in semantic processing remain largely unknown. In an fMRI study, we focused on the affective domain and examined whether affective iconic words (e.g., high arousal in both sound and meaning) activate additional brain regions that integrate emotional information from different domains (i.e., sound and meaning). In line with our hypothesis, affective iconic words, compared to their non‐iconic counterparts, elicited additional BOLD responses in the left amygdala known for its role in multimodal representation of emotions. Functional connectivity analyses revealed that the observed amygdalar activity was modulated by an interaction of iconic condition and activations in two hubs representative for processing sound (left superior temporal gyrus) and meaning (left inferior frontal gyrus) of words. These results provide a neural explanation for the facilitative role of iconicity in language processing and indicate that language users are sensitive to the interaction between sound and meaning aspect of words, suggesting the existence of iconicity as a general property of human language
Locally Optimal Control of Quantum Systems with Strong Feedback
For quantum systems with high purity, we find all observables that, when
continuously monitored, maximize the instantaneous reduction in the von Neumann
entropy. This allows us to obtain all locally optimal feedback protocols with
strong feedback, and explicit expressions for the best such protocols for
systems of size N <= 4. We also show that for a qutrit the locally optimal
protocol is the optimal protocol for a given range of control times, and derive
an upper bound on all optimal protocols with strong feedback.Comment: 4 pages, Revtex4. v2: published version (some errors corrected
Infinite-cluster geometry in central-force networks
We show that the infinite percolating cluster (with density P_inf) of
central-force networks is composed of: a fractal stress-bearing backbone (Pb)
and; rigid but unstressed ``dangling ends'' which occupy a finite
volume-fraction of the lattice (Pd). Near the rigidity threshold pc, there is
then a first-order transition in P_inf = Pd + Pb, while Pb is second-order with
exponent Beta'. A new mean field theory shows Beta'(mf)=1/2, while simulations
of triangular lattices give Beta'_tr = 0.255 +/- 0.03.Comment: 6 pages, 4 figures, uses epsfig. Accepted for publication in Physical
Review Letter
A simple formula for pooling knowledge about a quantum system
When various observers obtain information in an independent fashion about a
classical system, there is a simple rule which allows them to pool their
knowledge, and this requires only the states-of-knowledge of the respective
observers. Here we derive an equivalent quantum formula. While its realm of
applicability is necessarily more limited, it does apply to a large class of
measurements, and we show explicitly for a single qubit that it satisfies the
intuitive notions of what it means to pool knowledge about a quantum system.
This analysis also provides a physical interpretation for the trace of the
product of two density matrices.Comment: 5 pages, Revtex
- …